{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Interleaved strings\n", "\n", "Given two strings a and b and a target c, could c be formed form some interleaving/merge of a and b?\n", "\n", "For example,\n", "Given:\n", "s1 = \"aabcc\",\n", "s2 = \"dbbca\",\n", "\n", "When s3 = \"aadbbcbcac\", return true.\n", "When s3 = \"aadbbbaccc\", return false." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import random\n", "import string" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "s1 = \"aabcc\"\n", "s2 = \"dbbca\"\n", "\n", "s3t = \"aadbbcbcac\"\n", "s3f = \"aadbbbaccc\"" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(0, ''), (1, 'a'), (2, 'aa'), (3, 'aab'), (4, 'aabc'), (5, 'aabcc')]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[(i, s1[:i]) for i in range(len(s1)+1)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`dp_table[i, j]` is True if first `i` + `j` characters of `s3` can be formed from interleaving of first `i` characters of `s1` and first `j` characters of `s2`." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[True, False, False, False, False, False],\n", " [False, False, False, False, False, False],\n", " [False, False, False, False, False, False],\n", " [False, False, False, False, False, False],\n", " [False, False, False, False, False, False],\n", " [False, False, False, False, False, False]]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dp_table = [[False] * (len(s1) + 1) for _ in range(len(s2) + 1)]\n", "dp_table[0][0] = True\n", "dp_table" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "{(0, 0): False,\n", " (0, 1): False,\n", " (0, 2): False,\n", " (0, 3): False,\n", " (0, 4): False,\n", " (0, 5): False,\n", " (1, 0): False,\n", " (1, 1): False,\n", " (1, 2): False,\n", " (1, 3): False,\n", " (1, 4): False,\n", " (1, 5): False,\n", " (2, 0): False,\n", " (2, 1): False,\n", " (2, 2): False,\n", " (2, 3): False,\n", " (2, 4): False,\n", " (2, 5): False,\n", " (3, 0): False,\n", " (3, 1): False,\n", " (3, 2): False,\n", " (3, 3): False,\n", " (3, 4): False,\n", " (3, 5): False,\n", " (4, 0): False,\n", " (4, 1): False,\n", " (4, 2): False,\n", " (4, 3): False,\n", " (4, 4): False,\n", " (4, 5): False,\n", " (5, 0): False,\n", " (5, 1): False,\n", " (5, 2): False,\n", " (5, 3): False,\n", " (5, 4): False,\n", " (5, 5): False}" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dp_table = {(i, j): False\n", " for i in range(len(s1)+1)\n", " for j in range(len(s2)+1)}\n", "dp_table" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def show_table(table):\n", " return '\\n'.join(\n", " ' '.join(str(table[i, j])[0] for j in sorted(set([k[1] for k in table])))\n", " for i in sorted(set([k[0] for k in table]))) " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def show_table(table):\n", " return '\\n'.join(\n", " ' '.join('T' if table[i, j] else '.' for j in sorted(set([k[1] for k in table])))\n", " for i in sorted(set([k[0] for k in table]))) " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ". . . . . .\n", ". . . . . .\n", ". . . . . .\n", ". . . . . .\n", ". . . . . .\n", ". . . . . .\n" ] } ], "source": [ "print(show_table(dp_table))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "aabcc dbbca aadbbcbcac\n", "aa 0 0 ! ! ! True\n", "s2 0 1 ! d a False\n", "s2 0 2 ! b a False\n", "s2 0 3 ! b d False\n", "s2 0 4 ! c b False\n", "s2 0 5 ! a b False\n", "s1 1 0 a ! a True\n", "xx 1 1 a d a False\n", "xx 1 2 a b d False\n", "xx 1 3 a b b False\n", "xx 1 4 a c b False\n", "xx 1 5 a a c False\n", "s1 2 0 a ! a True\n", "s2 2 1 a d d True\n", "s2 2 2 a b b True\n", "s2 2 3 a b b True\n", "s2 2 4 a c c True\n", "xx 2 5 a a b False\n", "s1 3 0 b ! d False\n", "s1 3 1 b d b True\n", "s2 3 2 b b b True\n", "s1 3 2 b b b True\n", "xx 3 3 b b c False\n", "s1 3 4 b c b True\n", "xx 3 5 b a c False\n", "s1 4 0 c ! b False\n", "xx 4 1 c d b False\n", "s1 4 2 c b c True\n", "s2 4 3 c b b True\n", "s2 4 4 c c c True\n", "s1 4 4 c c c True\n", "s2 4 5 c a a True\n", "s1 5 0 c ! b False\n", "xx 5 1 c d c False\n", "xx 5 2 c b b False\n", "s1 5 3 c b c True\n", "xx 5 4 c c a False\n", "s1 5 5 c a c True\n", "T . . . . .\n", "T . . . . .\n", "T T T T T .\n", ". T T . T .\n", ". . T T T T\n", ". . . T . T\n" ] }, { "data": { "text/plain": [ "{(1, 0): (0, 0, 'a', 's1'),\n", " (2, 0): (1, 0, 'a', 's1'),\n", " (2, 1): (2, 0, 'd', 's2'),\n", " (2, 2): (2, 1, 'b', 's2'),\n", " (2, 3): (2, 2, 'b', 's2'),\n", " (2, 4): (2, 3, 'c', 's2'),\n", " (3, 1): (2, 1, 'b', 's1'),\n", " (3, 2): (2, 2, 'b', 's1'),\n", " (3, 4): (2, 4, 'b', 's1'),\n", " (4, 2): (3, 2, 'c', 's1'),\n", " (4, 3): (4, 2, 'b', 's2'),\n", " (4, 4): (3, 4, 'c', 's1'),\n", " (4, 5): (4, 4, 'a', 's2'),\n", " (5, 3): (4, 3, 'c', 's1'),\n", " (5, 5): (4, 5, 'c', 's1')}" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s3 = s3t\n", "\n", "print(s1, s2, s3)\n", "\n", "dp_table = {(i, j): False\n", " for i in range(len(s1)+1)\n", " for j in range(len(s2)+1)}\n", "\n", "backpointers = {}\n", "\n", "for i in range(len(s1)+1):\n", " for j in range(len(s2)+1):\n", " if i == 0 and j == 0:\n", " dp_table[i, j] = True\n", " print('aa', i, j, '!', '!', '!', dp_table[i, j])\n", " elif i == 0:\n", " # extend by character from s2\n", " if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n", " dp_table[i, j] = True\n", " backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n", " print('s2', i, j, '!', s2[j-1], s3[i+j-1], dp_table[i, j])\n", " elif j == 0:\n", " # extend by character from s1\n", " if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n", " dp_table[i, j] = True\n", " backpointers[i, j] = (i-1, j, s1[i-1], 's1')\n", " print('s1', i, j, s1[i-1], '!', s3[i+j-1], dp_table[i, j])\n", " else:\n", " # extend by character from s2\n", " if dp_table[i, j-1] and s2[j-1] == s3[i+j-1]:\n", " dp_table[i, j] = True\n", " backpointers[i, j] = (i, j-1, s2[j-1], 's2')\n", " print('s2', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j]) \n", " # extend by character from s1\n", " if dp_table[i-1, j] and s1[i-1] == s3[i+j-1]:\n", " dp_table[i, j] = True\n", " backpointers[i, j] = (i-1, j, s1[i-1], 's1') \n", " print('s1', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n", " if not dp_table[i, j]:\n", " print('xx', i, j, s1[i-1], s2[j-1], s3[i+j-1], dp_table[i, j])\n", "\n", "print(show_table(dp_table))\n", "backpointers" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def is_interleave(seq1, seq2, seq3, return_backpointers=False, return_table=False, debug=False):\n", " \"\"\"Return true if seq3 is some interleaved merge of seq1 and seq2.\n", " If return_backpointers, also return the set of backpointers to\n", " reconstruct the interleaving\"\"\"\n", " \n", " # dp_table[i, j] is True if first i+j characters of seq is made up of \n", " # an interleaving of the first i characters of seq1 and the \n", " # first j characters of seq2\n", " \n", " if len(seq1) + len(seq2) != len(seq3):\n", " if return_backpointers or return_table:\n", " retval = [False]\n", " if return_backpointers:\n", " retval += [{}]\n", " if return_table:\n", " retval += [{}]\n", " return tuple(retval)\n", " else:\n", " return False\n", " \n", " dp_table = {(i, j): False\n", " for i in range(len(seq1)+1)\n", " for j in range(len(seq2)+1)}\n", "\n", " backpointers = {}\n", "\n", " for i in range(len(seq1)+1):\n", " for j in range(len(seq2)+1):\n", " if i == 0 and j == 0:\n", " dp_table[i, j] = True\n", " if debug: print('xxxx', i, j, '!', '!', '!', dp_table[i, j])\n", " elif i == 0:\n", " # extend by character from seq2\n", " if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n", " dp_table[i, j] = True\n", " backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n", " if debug: print('seq2', i, j, '!', seq2[j-1], seq3[i+j-1], dp_table[i, j])\n", " elif j == 0:\n", " # extend by character from seq1\n", " if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n", " dp_table[i, j] = True\n", " backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1')\n", " if debug: print('seq1', i, j, seq1[i-1], '!', seq3[i+j-1], dp_table[i, j])\n", " else:\n", " # extend by character from seq2\n", " if dp_table[i, j-1] and seq2[j-1] == seq3[i+j-1]:\n", " dp_table[i, j] = True\n", " backpointers[i, j] = (i, j-1, seq2[j-1], 'seq2')\n", " if debug: print('seq2', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j]) \n", " # extend by character from seq1\n", " if dp_table[i-1, j] and seq1[i-1] == seq3[i+j-1]:\n", " dp_table[i, j] = True\n", " backpointers[i, j] = (i-1, j, seq1[i-1], 'seq1') \n", " if debug: print('seq1', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n", " if not dp_table[i, j]:\n", " if debug: print('xxxx', i, j, seq1[i-1], seq2[j-1], seq3[i+j-1], dp_table[i, j])\n", "\n", " if return_backpointers or return_table:\n", " retval = [dp_table[len(seq1), len(seq2)]]\n", " if return_backpointers:\n", " retval += [backpointers]\n", " if return_table:\n", " retval += [dp_table]\n", " return tuple(retval)\n", " else:\n", " return dp_table[len(seq1), len(seq2)]" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_interleave(s1, s2, s3t)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(True,\n", " {(1, 0): (0, 0, 'a', 'seq1'),\n", " (2, 0): (1, 0, 'a', 'seq1'),\n", " (2, 1): (2, 0, 'd', 'seq2'),\n", " (2, 2): (2, 1, 'b', 'seq2'),\n", " (2, 3): (2, 2, 'b', 'seq2'),\n", " (2, 4): (2, 3, 'c', 'seq2'),\n", " (3, 1): (2, 1, 'b', 'seq1'),\n", " (3, 2): (2, 2, 'b', 'seq1'),\n", " (3, 4): (2, 4, 'b', 'seq1'),\n", " (4, 2): (3, 2, 'c', 'seq1'),\n", " (4, 3): (4, 2, 'b', 'seq2'),\n", " (4, 4): (3, 4, 'c', 'seq1'),\n", " (4, 5): (4, 4, 'a', 'seq2'),\n", " (5, 3): (4, 3, 'c', 'seq1'),\n", " (5, 5): (4, 5, 'c', 'seq1')})" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_interleave(s1, s2, s3t, return_backpointers=True)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "(True,\n", " {(1, 0): (0, 0, 'a', 'seq1'),\n", " (2, 0): (1, 0, 'a', 'seq1'),\n", " (2, 1): (2, 0, 'd', 'seq2'),\n", " (2, 2): (2, 1, 'b', 'seq2'),\n", " (2, 3): (2, 2, 'b', 'seq2'),\n", " (2, 4): (2, 3, 'c', 'seq2'),\n", " (3, 1): (2, 1, 'b', 'seq1'),\n", " (3, 2): (2, 2, 'b', 'seq1'),\n", " (3, 4): (2, 4, 'b', 'seq1'),\n", " (4, 2): (3, 2, 'c', 'seq1'),\n", " (4, 3): (4, 2, 'b', 'seq2'),\n", " (4, 4): (3, 4, 'c', 'seq1'),\n", " (4, 5): (4, 4, 'a', 'seq2'),\n", " (5, 3): (4, 3, 'c', 'seq1'),\n", " (5, 5): (4, 5, 'c', 'seq1')},\n", " {(0, 0): True,\n", " (0, 1): False,\n", " (0, 2): False,\n", " (0, 3): False,\n", " (0, 4): False,\n", " (0, 5): False,\n", " (1, 0): True,\n", " (1, 1): False,\n", " (1, 2): False,\n", " (1, 3): False,\n", " (1, 4): False,\n", " (1, 5): False,\n", " (2, 0): True,\n", " (2, 1): True,\n", " (2, 2): True,\n", " (2, 3): True,\n", " (2, 4): True,\n", " (2, 5): False,\n", " (3, 0): False,\n", " (3, 1): True,\n", " (3, 2): True,\n", " (3, 3): False,\n", " (3, 4): True,\n", " (3, 5): False,\n", " (4, 0): False,\n", " (4, 1): False,\n", " (4, 2): True,\n", " (4, 3): True,\n", " (4, 4): True,\n", " (4, 5): True,\n", " (5, 0): False,\n", " (5, 1): False,\n", " (5, 2): False,\n", " (5, 3): True,\n", " (5, 4): False,\n", " (5, 5): True})" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_interleave(s1, s2, s3t, return_backpointers=True, return_table=True)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_interleave(s1, s2, s3f)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "xxxx 0 0 ! ! ! True\n", "seq2 0 1 ! b a False\n", "seq2 0 2 ! b a False\n", "seq2 0 3 ! b a False\n", "seq1 1 0 a ! a True\n", "xxxx 1 1 a b a False\n", "xxxx 1 2 a b a False\n", "xxxx 1 3 a b b False\n", "seq1 2 0 a ! a True\n", "xxxx 2 1 a b a False\n", "xxxx 2 2 a b b False\n", "xxxx 2 3 a b a False\n", "seq1 3 0 a ! a True\n", "seq2 3 1 a b b True\n", "xxxx 3 2 a b a False\n", "xxxx 3 3 a b b False\n", "seq1 4 0 a ! b False\n", "seq1 4 1 a b a True\n", "seq2 4 2 a b b True\n", "seq2 4 3 a b b True\n" ] }, { "data": { "text/plain": [ "(True,\n", " {(1, 0): (0, 0, 'a', 'seq1'),\n", " (2, 0): (1, 0, 'a', 'seq1'),\n", " (3, 0): (2, 0, 'a', 'seq1'),\n", " (3, 1): (3, 0, 'b', 'seq2'),\n", " (4, 1): (3, 1, 'a', 'seq1'),\n", " (4, 2): (4, 1, 'b', 'seq2'),\n", " (4, 3): (4, 2, 'b', 'seq2')})" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_interleave('aaaa', 'bbb', 'aaababb', return_backpointers=True, debug=True)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def show_backtrace(bps):\n", " i = max([0] + [k[0] for k in bps])\n", " j = max([0] + [k[1] for k in bps])\n", " chars = ''\n", " if (i, j) in bps:\n", " while i != 0 or j != 0:\n", " if bps[i, j][3] == 'seq1':\n", " chars += bps[i, j][2].upper()\n", " else:\n", " chars += bps[i, j][2]\n", " i, j = bps[i, j][0], bps[i, j][1] \n", " return ''.join(list(reversed(chars)))\n", " else:\n", " return ''" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def make_string(length, alphabet=None):\n", " if not alphabet:\n", " alphabet = 'abcdefgh'\n", " return ''.join(random.choice(alphabet) for _ in range(length)) " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'ddbcceaffddbbddddehffcdffbffdfdfdddcehhgaddfddbgda'" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "make_string(50)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def interleave(s1, s2, wander_limit=10, debug=False):\n", " i1 = i2 = wander = 0\n", " interleaved = []\n", " while i1 <= len(s1) and i2 <= len(s2):\n", " if i1 == len(s1):\n", " if debug: print(i1, i2, wander, 'remaining s2', s2[i2:])\n", " interleaved += s2[i2:]\n", " i2 = len(s2) + 1\n", " elif i2 == len(s2):\n", " if debug: print(i1, i2, wander, 'remaining s1', s1[i1:])\n", " interleaved += s1[i1:]\n", " i1 = len(s1) + 1\n", " else:\n", " if wander == wander_limit:\n", " step = -1\n", " elif wander == -wander_limit:\n", " step = +1\n", " else:\n", " step = random.choice([+1, -1])\n", " if step == +1:\n", " if debug: print(i1, i2, wander, 'adding', s1[i1])\n", " interleaved += s1[i1]\n", " i1 += 1\n", " wander += 1\n", " else:\n", " if debug: print(i1, i2, wander, 'adding', s2[i2])\n", " interleaved += s2[i2]\n", " i2 += 1\n", " wander -= 1\n", " return ''.join(interleaved)\n", " " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 0 0 adding f\n", "1 0 1 adding f\n", "2 0 2 adding d\n", "3 0 3 adding v\n", "3 1 2 adding d\n", "4 1 3 adding g\n", "5 1 4 adding g\n", "6 1 5 adding v\n", "6 2 4 adding d\n", "7 2 5 adding z\n", "7 3 4 adding h\n", "8 3 5 adding w\n", "8 4 4 adding z\n", "8 5 3 adding y\n", "8 6 2 adding b\n", "9 6 3 adding u\n", "9 7 2 adding d\n", "10 7 3 adding w\n", "10 8 2 adding u\n", "10 9 1 adding w\n", "10 10 0 adding u\n", "10 11 -1 adding g\n", "11 11 0 adding c\n", "12 11 1 adding x\n", "12 12 0 adding z\n", "12 13 -1 adding b\n", "13 13 0 adding a\n", "14 13 1 adding v\n", "14 14 0 adding a\n", "15 14 1 adding x\n", "15 15 0 adding f\n", "16 15 1 adding f\n", "17 15 2 adding v\n", "17 16 1 adding c\n", "18 16 2 adding a\n", "19 16 3 adding h\n", "20 16 4 remaining s2 vzxy\n" ] }, { "data": { "text/plain": [ "('ffddggdhbdgcbaaffcah',\n", " 'vvzwzyuwuwuxzvxvvzxy',\n", " 'ffdvdggvdzhwzybudwuwugcxzbavaxffvcahvzxy',\n", " 40)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s1 = make_string(20)\n", "s2 = make_string(20, alphabet='uvwxyz')\n", "il = interleave(s1, s2, wander_limit=5, debug=True)\n", "s1, s2, il, len(il)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "xxxx 0 0 ! ! ! True\n", "seq2 0 1 ! f f True\n", "seq2 0 2 ! f f True\n", "seq2 0 3 ! d d True\n", "seq2 0 4 ! d v False\n", "seq2 0 5 ! g d False\n", "seq2 0 6 ! g g False\n", "seq2 0 7 ! d g False\n", "seq2 0 8 ! h v False\n", "seq2 0 9 ! b d False\n", "seq2 0 10 ! d z False\n", "seq2 0 11 ! g h False\n", "seq2 0 12 ! c w False\n", "seq2 0 13 ! b z False\n", "seq2 0 14 ! a y False\n", "seq2 0 15 ! a b False\n", "seq2 0 16 ! f u False\n", "seq2 0 17 ! f d False\n", "seq2 0 18 ! c w False\n", "seq2 0 19 ! a u False\n", "seq2 0 20 ! h w False\n", "seq1 1 0 v ! f False\n", "xxxx 1 1 v f f False\n", "xxxx 1 2 v f d False\n", "seq1 1 3 v d v True\n", "seq2 1 4 v d d True\n", "seq2 1 5 v g g True\n", "seq2 1 6 v g g True\n", "xxxx 1 7 v d v False\n", "xxxx 1 8 v h d False\n", "xxxx 1 9 v b z False\n", "xxxx 1 10 v d h False\n", "xxxx 1 11 v g w False\n", "xxxx 1 12 v c z False\n", "xxxx 1 13 v b y False\n", "xxxx 1 14 v a b False\n", "xxxx 1 15 v a u False\n", "xxxx 1 16 v f d False\n", "xxxx 1 17 v f w False\n", "xxxx 1 18 v c u False\n", "xxxx 1 19 v a w False\n", "xxxx 1 20 v h u False\n", "seq1 2 0 v ! f False\n", "xxxx 2 1 v f d False\n", "xxxx 2 2 v f v False\n", "xxxx 2 3 v d d False\n", "xxxx 2 4 v d g False\n", "xxxx 2 5 v g g False\n", "seq1 2 6 v g v True\n", "seq2 2 7 v d d True\n", "xxxx 2 8 v h z False\n", "xxxx 2 9 v b h False\n", "xxxx 2 10 v d w False\n", "xxxx 2 11 v g z False\n", "xxxx 2 12 v c y False\n", "xxxx 2 13 v b b False\n", "xxxx 2 14 v a u False\n", "xxxx 2 15 v a d False\n", "xxxx 2 16 v f w False\n", "xxxx 2 17 v f u False\n", "xxxx 2 18 v c w False\n", "xxxx 2 19 v a u False\n", "xxxx 2 20 v h g False\n", "seq1 3 0 z ! d False\n", "xxxx 3 1 z f v False\n", "xxxx 3 2 z f d False\n", "xxxx 3 3 z d g False\n", "xxxx 3 4 z d g False\n", "xxxx 3 5 z g v False\n", "xxxx 3 6 z g d False\n", "seq1 3 7 z d z True\n", "seq2 3 8 z h h True\n", "xxxx 3 9 z b w False\n", "xxxx 3 10 z d z False\n", "xxxx 3 11 z g y False\n", "xxxx 3 12 z c b False\n", "xxxx 3 13 z b u False\n", "xxxx 3 14 z a d False\n", "xxxx 3 15 z a w False\n", "xxxx 3 16 z f u False\n", "xxxx 3 17 z f w False\n", "xxxx 3 18 z c u False\n", "xxxx 3 19 z a g False\n", "xxxx 3 20 z h c False\n", "seq1 4 0 w ! v False\n", "xxxx 4 1 w f d False\n", "xxxx 4 2 w f g False\n", "xxxx 4 3 w d g False\n", "xxxx 4 4 w d v False\n", "xxxx 4 5 w g d False\n", "xxxx 4 6 w g z False\n", "xxxx 4 7 w d h False\n", "seq1 4 8 w h w True\n", "xxxx 4 9 w b z False\n", "xxxx 4 10 w d y False\n", "xxxx 4 11 w g b False\n", "xxxx 4 12 w c u False\n", "xxxx 4 13 w b d False\n", "xxxx 4 14 w a w False\n", "xxxx 4 15 w a u False\n", "xxxx 4 16 w f w False\n", "xxxx 4 17 w f u False\n", "xxxx 4 18 w c g False\n", "xxxx 4 19 w a c False\n", "xxxx 4 20 w h x False\n", "seq1 5 0 z ! d False\n", "xxxx 5 1 z f g False\n", "xxxx 5 2 z f g False\n", "xxxx 5 3 z d v False\n", "xxxx 5 4 z d d False\n", "xxxx 5 5 z g z False\n", "xxxx 5 6 z g h False\n", "xxxx 5 7 z d w False\n", "seq1 5 8 z h z True\n", "xxxx 5 9 z b y False\n", "xxxx 5 10 z d b False\n", "xxxx 5 11 z g u False\n", "xxxx 5 12 z c d False\n", "xxxx 5 13 z b w False\n", "xxxx 5 14 z a u False\n", "xxxx 5 15 z a w False\n", "xxxx 5 16 z f u False\n", "xxxx 5 17 z f g False\n", "xxxx 5 18 z c c False\n", "xxxx 5 19 z a x False\n", "xxxx 5 20 z h z False\n", "seq1 6 0 y ! g False\n", "xxxx 6 1 y f g False\n", "xxxx 6 2 y f v False\n", "xxxx 6 3 y d d False\n", "xxxx 6 4 y d z False\n", "xxxx 6 5 y g h False\n", "xxxx 6 6 y g w False\n", "xxxx 6 7 y d z False\n", "seq1 6 8 y h y True\n", "seq2 6 9 y b b True\n", "xxxx 6 10 y d u False\n", "xxxx 6 11 y g d False\n", "xxxx 6 12 y c w False\n", "xxxx 6 13 y b u False\n", "xxxx 6 14 y a w False\n", "xxxx 6 15 y a u False\n", "xxxx 6 16 y f g False\n", "xxxx 6 17 y f c False\n", "xxxx 6 18 y c x False\n", "xxxx 6 19 y a z False\n", "xxxx 6 20 y h b False\n", "seq1 7 0 u ! g False\n", "xxxx 7 1 u f v False\n", "xxxx 7 2 u f d False\n", "xxxx 7 3 u d z False\n", "xxxx 7 4 u d h False\n", "xxxx 7 5 u g w False\n", "xxxx 7 6 u g z False\n", "xxxx 7 7 u d y False\n", "xxxx 7 8 u h b False\n", "seq1 7 9 u b u True\n", "seq2 7 10 u d d True\n", "xxxx 7 11 u g w False\n", "xxxx 7 12 u c u False\n", "xxxx 7 13 u b w False\n", "xxxx 7 14 u a u False\n", "xxxx 7 15 u a g False\n", "xxxx 7 16 u f c False\n", "xxxx 7 17 u f x False\n", "xxxx 7 18 u c z False\n", "xxxx 7 19 u a b False\n", "xxxx 7 20 u h a False\n", "seq1 8 0 w ! v False\n", "xxxx 8 1 w f d False\n", "xxxx 8 2 w f z False\n", "xxxx 8 3 w d h False\n", "xxxx 8 4 w d w False\n", "xxxx 8 5 w g z False\n", "xxxx 8 6 w g y False\n", "xxxx 8 7 w d b False\n", "xxxx 8 8 w h u False\n", "xxxx 8 9 w b d False\n", "seq1 8 10 w d w True\n", "xxxx 8 11 w g u False\n", "xxxx 8 12 w c w False\n", "xxxx 8 13 w b u False\n", "xxxx 8 14 w a g False\n", "xxxx 8 15 w a c False\n", "xxxx 8 16 w f x False\n", "xxxx 8 17 w f z False\n", "xxxx 8 18 w c b False\n", "xxxx 8 19 w a a False\n", "xxxx 8 20 w h v False\n", "seq1 9 0 u ! d False\n", "xxxx 9 1 u f z False\n", "xxxx 9 2 u f h False\n", "xxxx 9 3 u d w False\n", "xxxx 9 4 u d z False\n", "xxxx 9 5 u g y False\n", "xxxx 9 6 u g b False\n", "xxxx 9 7 u d u False\n", "xxxx 9 8 u h d False\n", "xxxx 9 9 u b w False\n", "seq1 9 10 u d u True\n", "xxxx 9 11 u g w False\n", "xxxx 9 12 u c u False\n", "xxxx 9 13 u b g False\n", "xxxx 9 14 u a c False\n", "xxxx 9 15 u a x False\n", "xxxx 9 16 u f z False\n", "xxxx 9 17 u f b False\n", "xxxx 9 18 u c a False\n", "xxxx 9 19 u a v False\n", "xxxx 9 20 u h a False\n", "seq1 10 0 w ! z False\n", "xxxx 10 1 w f h False\n", "xxxx 10 2 w f w False\n", "xxxx 10 3 w d z False\n", "xxxx 10 4 w d y False\n", "xxxx 10 5 w g b False\n", "xxxx 10 6 w g u False\n", "xxxx 10 7 w d d False\n", "xxxx 10 8 w h w False\n", "xxxx 10 9 w b u False\n", "seq1 10 10 w d w True\n", "xxxx 10 11 w g u False\n", "xxxx 10 12 w c g False\n", "xxxx 10 13 w b c False\n", "xxxx 10 14 w a x False\n", "xxxx 10 15 w a z False\n", "xxxx 10 16 w f b False\n", "xxxx 10 17 w f a False\n", "xxxx 10 18 w c v False\n", "xxxx 10 19 w a a False\n", "xxxx 10 20 w h x False\n", "seq1 11 0 u ! h False\n", "xxxx 11 1 u f w False\n", "xxxx 11 2 u f z False\n", "xxxx 11 3 u d y False\n", "xxxx 11 4 u d b False\n", "xxxx 11 5 u g u False\n", "xxxx 11 6 u g d False\n", "xxxx 11 7 u d w False\n", "xxxx 11 8 u h u False\n", "xxxx 11 9 u b w False\n", "seq1 11 10 u d u True\n", "seq2 11 11 u g g True\n", "seq2 11 12 u c c True\n", "xxxx 11 13 u b x False\n", "xxxx 11 14 u a z False\n", "xxxx 11 15 u a b False\n", "xxxx 11 16 u f a False\n", "xxxx 11 17 u f v False\n", "xxxx 11 18 u c a False\n", "xxxx 11 19 u a x False\n", "xxxx 11 20 u h f False\n", "seq1 12 0 x ! w False\n", "xxxx 12 1 x f z False\n", "xxxx 12 2 x f y False\n", "xxxx 12 3 x d b False\n", "xxxx 12 4 x d u False\n", "xxxx 12 5 x g d False\n", "xxxx 12 6 x g w False\n", "xxxx 12 7 x d u False\n", "xxxx 12 8 x h w False\n", "xxxx 12 9 x b u False\n", "xxxx 12 10 x d g False\n", "xxxx 12 11 x g c False\n", "seq1 12 12 x c x True\n", "xxxx 12 13 x b z False\n", "xxxx 12 14 x a b False\n", "xxxx 12 15 x a a False\n", "xxxx 12 16 x f v False\n", "xxxx 12 17 x f a False\n", "xxxx 12 18 x c x False\n", "xxxx 12 19 x a f False\n", "xxxx 12 20 x h f False\n", "seq1 13 0 z ! z False\n", "xxxx 13 1 z f y False\n", "xxxx 13 2 z f b False\n", "xxxx 13 3 z d u False\n", "xxxx 13 4 z d d False\n", "xxxx 13 5 z g w False\n", "xxxx 13 6 z g u False\n", "xxxx 13 7 z d w False\n", "xxxx 13 8 z h u False\n", "xxxx 13 9 z b g False\n", "xxxx 13 10 z d c False\n", "xxxx 13 11 z g x False\n", "seq1 13 12 z c z True\n", "seq2 13 13 z b b True\n", "seq2 13 14 z a a True\n", "xxxx 13 15 z a v False\n", "xxxx 13 16 z f a False\n", "xxxx 13 17 z f x False\n", "xxxx 13 18 z c f False\n", "xxxx 13 19 z a f False\n", "xxxx 13 20 z h v False\n", "seq1 14 0 v ! y False\n", "xxxx 14 1 v f b False\n", "xxxx 14 2 v f u False\n", "xxxx 14 3 v d d False\n", "xxxx 14 4 v d w False\n", "xxxx 14 5 v g u False\n", "xxxx 14 6 v g w False\n", "xxxx 14 7 v d u False\n", "xxxx 14 8 v h g False\n", "xxxx 14 9 v b c False\n", "xxxx 14 10 v d x False\n", "xxxx 14 11 v g z False\n", "xxxx 14 12 v c b False\n", "xxxx 14 13 v b a False\n", "seq1 14 14 v a v True\n", "seq2 14 15 v a a True\n", "xxxx 14 16 v f x False\n", "xxxx 14 17 v f f False\n", "xxxx 14 18 v c f False\n", "xxxx 14 19 v a v False\n", "xxxx 14 20 v h c False\n", "seq1 15 0 x ! b False\n", "xxxx 15 1 x f u False\n", "xxxx 15 2 x f d False\n", "xxxx 15 3 x d w False\n", "xxxx 15 4 x d u False\n", "xxxx 15 5 x g w False\n", "xxxx 15 6 x g u False\n", "xxxx 15 7 x d g False\n", "xxxx 15 8 x h c False\n", "xxxx 15 9 x b x False\n", "xxxx 15 10 x d z False\n", "xxxx 15 11 x g b False\n", "xxxx 15 12 x c a False\n", "xxxx 15 13 x b v False\n", "xxxx 15 14 x a a False\n", "seq1 15 15 x a x True\n", "seq2 15 16 x f f True\n", "seq2 15 17 x f f True\n", "xxxx 15 18 x c v False\n", "xxxx 15 19 x a c False\n", "xxxx 15 20 x h a False\n", "seq1 16 0 v ! u False\n", "xxxx 16 1 v f d False\n", "xxxx 16 2 v f w False\n", "xxxx 16 3 v d u False\n", "xxxx 16 4 v d w False\n", "xxxx 16 5 v g u False\n", "xxxx 16 6 v g g False\n", "xxxx 16 7 v d c False\n", "xxxx 16 8 v h x False\n", "xxxx 16 9 v b z False\n", "xxxx 16 10 v d b False\n", "xxxx 16 11 v g a False\n", "xxxx 16 12 v c v False\n", "xxxx 16 13 v b a False\n", "xxxx 16 14 v a x False\n", "xxxx 16 15 v a f False\n", "xxxx 16 16 v f f False\n", "seq1 16 17 v f v True\n", "seq2 16 18 v c c True\n", "seq2 16 19 v a a True\n", "seq2 16 20 v h h True\n", "seq1 17 0 v ! d False\n", "xxxx 17 1 v f w False\n", "xxxx 17 2 v f u False\n", "xxxx 17 3 v d w False\n", "xxxx 17 4 v d u False\n", "xxxx 17 5 v g g False\n", "xxxx 17 6 v g c False\n", "xxxx 17 7 v d x False\n", "xxxx 17 8 v h z False\n", "xxxx 17 9 v b b False\n", "xxxx 17 10 v d a False\n", "xxxx 17 11 v g v False\n", "xxxx 17 12 v c a False\n", "xxxx 17 13 v b x False\n", "xxxx 17 14 v a f False\n", "xxxx 17 15 v a f False\n", "xxxx 17 16 v f v False\n", "xxxx 17 17 v f c False\n", "xxxx 17 18 v c a False\n", "xxxx 17 19 v a h False\n", "seq1 17 20 v h v True\n", "seq1 18 0 z ! w False\n", "xxxx 18 1 z f u False\n", "xxxx 18 2 z f w False\n", "xxxx 18 3 z d u False\n", "xxxx 18 4 z d g False\n", "xxxx 18 5 z g c False\n", "xxxx 18 6 z g x False\n", "xxxx 18 7 z d z False\n", "xxxx 18 8 z h b False\n", "xxxx 18 9 z b a False\n", "xxxx 18 10 z d v False\n", "xxxx 18 11 z g a False\n", "xxxx 18 12 z c x False\n", "xxxx 18 13 z b f False\n", "xxxx 18 14 z a f False\n", "xxxx 18 15 z a v False\n", "xxxx 18 16 z f c False\n", "xxxx 18 17 z f a False\n", "xxxx 18 18 z c h False\n", "xxxx 18 19 z a v False\n", "seq1 18 20 z h z True\n", "seq1 19 0 x ! u False\n", "xxxx 19 1 x f w False\n", "xxxx 19 2 x f u False\n", "xxxx 19 3 x d g False\n", "xxxx 19 4 x d c False\n", "xxxx 19 5 x g x False\n", "xxxx 19 6 x g z False\n", "xxxx 19 7 x d b False\n", "xxxx 19 8 x h a False\n", "xxxx 19 9 x b v False\n", "xxxx 19 10 x d a False\n", "xxxx 19 11 x g x False\n", "xxxx 19 12 x c f False\n", "xxxx 19 13 x b f False\n", "xxxx 19 14 x a v False\n", "xxxx 19 15 x a c False\n", "xxxx 19 16 x f a False\n", "xxxx 19 17 x f h False\n", "xxxx 19 18 x c v False\n", "xxxx 19 19 x a z False\n", "seq1 19 20 x h x True\n", "seq1 20 0 y ! w False\n", "xxxx 20 1 y f u False\n", "xxxx 20 2 y f g False\n", "xxxx 20 3 y d c False\n", "xxxx 20 4 y d x False\n", "xxxx 20 5 y g z False\n", "xxxx 20 6 y g b False\n", "xxxx 20 7 y d a False\n", "xxxx 20 8 y h v False\n", "xxxx 20 9 y b a False\n", "xxxx 20 10 y d x False\n", "xxxx 20 11 y g f False\n", "xxxx 20 12 y c f False\n", "xxxx 20 13 y b v False\n", "xxxx 20 14 y a c False\n", "xxxx 20 15 y a a False\n", "xxxx 20 16 y f h False\n", "xxxx 20 17 y f v False\n", "xxxx 20 18 y c z False\n", "xxxx 20 19 y a x False\n", "seq1 20 20 y h y True\n", "T T T T . . . . . . . . . . . . . . . . .\n", ". . . T T T T . . . . . . . . . . . . . .\n", ". . . . . . T T . . . . . . . . . . . . .\n", ". . . . . . . T T . . . . . . . . . . . .\n", ". . . . . . . . T . . . . . . . . . . . .\n", ". . . . . . . . T . . . . . . . . . . . .\n", ". . . . . . . . T T . . . . . . . . . . .\n", ". . . . . . . . . T T . . . . . . . . . .\n", ". . . . . . . . . . T . . . . . . . . . .\n", ". . . . . . . . . . T . . . . . . . . . .\n", ". . . . . . . . . . T . . . . . . . . . .\n", ". . . . . . . . . . T T T . . . . . . . .\n", ". . . . . . . . . . . . T . . . . . . . .\n", ". . . . . . . . . . . . T T T . . . . . .\n", ". . . . . . . . . . . . . . T T . . . . .\n", ". . . . . . . . . . . . . . . T T T . . .\n", ". . . . . . . . . . . . . . . . . T T T T\n", ". . . . . . . . . . . . . . . . . . . . T\n", ". . . . . . . . . . . . . . . . . . . . T\n", ". . . . . . . . . . . . . . . . . . . . T\n", ". . . . . . . . . . . . . . . . . . . . T\n" ] } ], "source": [ "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True, debug=True)\n", "print(show_table(t))" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'ffdVdggVdZhWZYbUdWUWUgcXZbaVaXffVcahVZXY'" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "show_backtrace(bp)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T T T T . . . . . . . . . . . . . . . . .\n", ". . . T T T T . . . . . . . . . . . . . .\n", ". . . . . . T T . . . . . . . . . . . . .\n", ". . . . . . . T T . . . . . . . . . . . .\n", ". . . . . . . . T . . . . . . . . . . . .\n", ". . . . . . . . T . . . . . . . . . . . .\n", ". . . . . . . . T T . . . . . . . . . . .\n", ". . . . . . . . . T T . . . . . . . . . .\n", ". . . . . . . . . . T . . . . . . . . . .\n", ". . . . . . . . . . T . . . . . . . . . .\n", ". . . . . . . . . . T . . . . . . . . . .\n", ". . . . . . . . . . T T T . . . . . . . .\n", ". . . . . . . . . . . . T . . . . . . . .\n", ". . . . . . . . . . . . T T T . . . . . .\n", ". . . . . . . . . . . . . . T T . . . . .\n", ". . . . . . . . . . . . . . . T T T . . .\n", ". . . . . . . . . . . . . . . . . T T T T\n", ". . . . . . . . . . . . . . . . . . . . T\n", ". . . . . . . . . . . . . . . . . . . . T\n", ". . . . . . . . . . . . . . . . . . . . T\n", ". . . . . . . . . . . . . . . . . . . . T\n", "ffdVdggVdZhWZYbUdWUWUgcXZbaVaXffVcahVZXY\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n", "print(show_table(t))\n", "print(show_backtrace(bp))\n", "v" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "('fcbhdfdbgebhgbgbcbhceagfbfhedffbbbehbfbbgedbacecdg',\n", " 'dfbgbebeggbcdahfbddbfcgcehhffhgfhdfffbeedgcghhhaga',\n", " 'dfbfcbghbedbfedbggbcdgeahfbhbdgbgbcdbbfcghcehceahgfbffhgfhfedhdfffffbebbbedehgbfcbghbghehdbaacgecadg',\n", " 100)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s1 = make_string(50)\n", "s2 = make_string(50)\n", "il = interleave(s1, s2)\n", "s1, s2, il, len(il)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . T T . . T . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T\n", "DFBfcbGhBEdBfEdbGGBCDgeAHFbhBDgbgbcDbBFCGhCEHceaHgfbFFHGfhFedHDffFFFBEbbbEDehGbfCbGHbgHeHdbaAcGecAdg\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n", "print(show_table(t))\n", "print(show_backtrace(bp))\n", "v" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1000 loops, best of 3: 1.29 ms per loop\n" ] } ], "source": [ "%%timeit\n", "is_interleave(s2, s1, il)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . T T . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . T . . T . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . T . . T . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . T . T . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . T T . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n", "dfbFCBgHbeDbFeDBggbcdGEahfBHbdGBGBCdbBfcgHcehCEAhGFBffhgFHfEDhdfffFFbeBBBedEHgBFcBghBGhEhDBaACgECaDG\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n", "print(show_table(t))\n", "print(show_backtrace(bp))\n", "v" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "show_backtrace(bp).lower() == il" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "('dbgdadhhhhacehhbdfdcffdghcahbbceegebbfhabafecadhhe', False, False)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s3 = make_string(50)\n", "s3, is_interleave(s1, s3, il), is_interleave(s2, s3, il)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", "dFb\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n", "print(show_table(t))\n", "print(show_backtrace(bp))\n", "v" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def is_interleave_recursive(s1, s2, s3):\n", " if not s1:\n", " return s2 == s3\n", " elif not s2:\n", " return s1 == s3\n", " else:\n", " if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n", " return is_interleave_recursive(s1[:-1], s2, s3[:-1]) or is_interleave(s1, s2[:-1], s3[:-1])\n", " elif s1[-1] == s3[-1]:\n", " return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n", " elif s2[-1] == s3[-1]:\n", " return is_interleave(s1, s2[:-1], s3[:-1])\n", " else:\n", " return False" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import uuid" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def is_subseq_recursive_dot(s1, s2):\n", " node_id = uuid.uuid4().hex\n", " node_string = 'n{} [label=\"{}\\\\n{}\"];'.format(node_id, s1, s2)\n", "# print(s1, s2, node_string)\n", " if not s1:\n", " return node_id, ['n{} [label=\"-\\\\n{}\\\\nTrue\"];'.format(node_id, s2)]\n", " elif len(s1) > len(s2):\n", " return node_id, ['n{} [label=\"{}\\\\n{}\\\\nFalse\"];'.format(node_id, s1, s2)]\n", " else:\n", " if s1[-1] == s2[-1]:\n", " node1_id, node1_graph = is_subseq_recursive_dot(s1[:-1], s2[:-1])\n", " node2_id, node2_graph = is_subseq_recursive_dot(s1, s2[:-1])\n", " return node_id, ([node_string, \n", " 'n{} -> n{};'.format(node_id, node1_id), \n", " 'n{} -> n{};'.format(node_id, node2_id)] + \n", " node1_graph + node2_graph)\n", " else:\n", " node1_id, node1_graph = is_subseq_recursive_dot(s1, s2[:-1])\n", " return node_id, ([node_string, \n", " 'n{} -> n{};'.format(node_id, node1_id)] + \n", " node1_graph)" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def is_interleave_recursive_dot(s1, s2, s3):\n", " \n", "# print(s1, s2, s3)\n", " node_id = uuid.uuid4().hex\n", " node_string = 'n{} [label=\"{}\\\\n{}\\\\n{}\"];'.format(node_id, s1, s2, s3)\n", "\n", " if not s1:\n", " if s2 == s3:\n", " return node_id, ['n{} [label=\"-\\\\n{}\\\\n{}\\\\nTrue\"];'.format(node_id, s2, s3)]\n", " else:\n", " return node_id, ['n{} [label=\"-\\\\n{}\\\\n{}\\\\nFalse\"];'.format(node_id, s2, s3)]\n", " elif not s2:\n", " if s1 == s3:\n", " return node_id, ['n{} [label=\"{}\\\\n-\\\\n{}\\\\nTrue\"];'.format(node_id, s1, s3)]\n", " else:\n", " return node_id, ['n{} [label=\"{}\\\\n-\\\\n{}\\\\nFalse\"];'.format(node_id, s1, s3)]\n", " else:\n", " if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n", " node1_id, node1_graph = is_interleave_recursive_dot(s1[:-1], s2, s3[:-1])\n", " node2_id, node2_graph = is_interleave_recursive_dot(s1, s2[:-1], s3[:-1])\n", " return node_id, ([node_string, \n", " 'n{} -> n{};'.format(node_id, node1_id), \n", " 'n{} -> n{};'.format(node_id, node2_id)] + \n", " node1_graph + node2_graph)\n", " elif s1[-1] == s3[-1]:\n", " node1_id, node1_graph = is_interleave_recursive_dot(s1[:-1], s2, s3[:-1])\n", " return node_id, ([node_string, \n", " 'n{} -> n{};'.format(node_id, node1_id)] + \n", " node1_graph)\n", " elif s2[-1] == s3[-1]:\n", " node1_id, node1_graph = is_interleave_recursive_dot(s1, s2[:-1], s3[:-1])\n", " return node_id, ([node_string, \n", " 'n{} -> n{};'.format(node_id, node1_id)] + \n", " node1_graph)\n", " else:\n", " return node_id, ['n{} [label=\"{}\\\\n{}\\\\n{}\\\\nFalse\"];'.format(node_id, s1, s2, s3)]" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": true }, "outputs": [], "source": [ "s1 = \"aabcc\"\n", "s2 = \"dbbca\"\n", "\n", "s3t = \"aadbbcbcac\"\n", "s3f = \"aadbbbaccc\"" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n825af3fb1bf441a3b97d8fbfcdce6f3d [label=\"aabcc\\ndbbca\\naadbbcbcac\"];\n", "n825af3fb1bf441a3b97d8fbfcdce6f3d -> n944a00ca9b134f3c98aeef34526ff17d;\n", "n944a00ca9b134f3c98aeef34526ff17d [label=\"aabc\\ndbbca\\naadbbcbca\"];\n", "n944a00ca9b134f3c98aeef34526ff17d -> n1586862dcfb74b1a9e9f964b7de102ef;\n", "n1586862dcfb74b1a9e9f964b7de102ef [label=\"aabc\\ndbbc\\naadbbcbc\"];\n", "n1586862dcfb74b1a9e9f964b7de102ef -> nf59278631d8047e7b0cca670e412297b;\n", "n1586862dcfb74b1a9e9f964b7de102ef -> nd83e9c32d1fa43bab45dc21d46830924;\n", "nf59278631d8047e7b0cca670e412297b [label=\"aab\\ndbbc\\naadbbcb\"];\n", "nf59278631d8047e7b0cca670e412297b -> nb0424588e9354d2aa61b587a7edfb7f6;\n", "nb0424588e9354d2aa61b587a7edfb7f6 [label=\"aa\\ndbbc\\naadbbc\"];\n", "nb0424588e9354d2aa61b587a7edfb7f6 -> nb73d85cfb09e43d692de22a49de48b35;\n", "nb73d85cfb09e43d692de22a49de48b35 [label=\"aa\\ndbb\\naadbb\"];\n", "nb73d85cfb09e43d692de22a49de48b35 -> n9e34f866ae1746d797cebd4e1fc73af9;\n", "n9e34f866ae1746d797cebd4e1fc73af9 [label=\"aa\\ndb\\naadb\"];\n", "n9e34f866ae1746d797cebd4e1fc73af9 -> n5c7027bfea9f494894cea01fd5e25387;\n", "n5c7027bfea9f494894cea01fd5e25387 [label=\"aa\\nd\\naad\"];\n", "n5c7027bfea9f494894cea01fd5e25387 -> n650da0feb2624011a20e209bada2445c;\n", "n650da0feb2624011a20e209bada2445c [label=\"aa\\n-\\naa\\nTrue\"];\n", "nd83e9c32d1fa43bab45dc21d46830924 [label=\"aabc\\ndbb\\naadbbcb\"];\n", "nd83e9c32d1fa43bab45dc21d46830924 -> n1c4772b660f24d6da9194d16be602b3a;\n", "n1c4772b660f24d6da9194d16be602b3a [label=\"aabc\\ndb\\naadbbc\"];\n", "n1c4772b660f24d6da9194d16be602b3a -> n0393745322e447c79515cffb4afc4d5b;\n", "n0393745322e447c79515cffb4afc4d5b [label=\"aab\\ndb\\naadbb\"];\n", "n0393745322e447c79515cffb4afc4d5b -> na9ae42f3b7dd415886e78bb960b94184;\n", "n0393745322e447c79515cffb4afc4d5b -> nccaf23a4e311415cbe42bedd8a3727c2;\n", "na9ae42f3b7dd415886e78bb960b94184 [label=\"aa\\ndb\\naadb\"];\n", "na9ae42f3b7dd415886e78bb960b94184 -> nab2d4f76a75c4c6686166212cad4b4a3;\n", "nab2d4f76a75c4c6686166212cad4b4a3 [label=\"aa\\nd\\naad\"];\n", "nab2d4f76a75c4c6686166212cad4b4a3 -> nee8a56cc920943e0a2593a8ee863c53c;\n", "nee8a56cc920943e0a2593a8ee863c53c [label=\"aa\\n-\\naa\\nTrue\"];\n", "nccaf23a4e311415cbe42bedd8a3727c2 [label=\"aab\\nd\\naadb\"];\n", "nccaf23a4e311415cbe42bedd8a3727c2 -> ne1d3cf2b04074c10986fdefb464e5da8;\n", "ne1d3cf2b04074c10986fdefb464e5da8 [label=\"aa\\nd\\naad\"];\n", "ne1d3cf2b04074c10986fdefb464e5da8 -> n9091b74bc8a64b91a9e75aef6b016a64;\n", "n9091b74bc8a64b91a9e75aef6b016a64 [label=\"aa\\n-\\naa\\nTrue\"];\n" ] } ], "source": [ "root, graph = is_interleave_recursive_dot(s1, s2, s3t)\n", "print('\\n'.join(graph))" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n894a2781e978478699af2875308ec4ad [label=\"aaa\\naaa\\naaaaaa\"];\n", "n894a2781e978478699af2875308ec4ad -> n863e03f8030547bf9f4e7a4815c4e027;\n", "n894a2781e978478699af2875308ec4ad -> n4c492e6eb94741d2b11567b1b4c729fa;\n", "n863e03f8030547bf9f4e7a4815c4e027 [label=\"aa\\naaa\\naaaaa\"];\n", "n863e03f8030547bf9f4e7a4815c4e027 -> n8f044087a7324ef69d5cf2ae120c0902;\n", "n863e03f8030547bf9f4e7a4815c4e027 -> n5510c6a96018480ba0fc2315d34a69e6;\n", "n8f044087a7324ef69d5cf2ae120c0902 [label=\"a\\naaa\\naaaa\"];\n", "n8f044087a7324ef69d5cf2ae120c0902 -> n6f3153ef68384ebbbe5860a48c774d55;\n", "n8f044087a7324ef69d5cf2ae120c0902 -> n4d068ce52cf248adb3b537805a233dda;\n", "n6f3153ef68384ebbbe5860a48c774d55 [label=\"-\\naaa\\naaa\\nTrue\"];\n", "n4d068ce52cf248adb3b537805a233dda [label=\"a\\naa\\naaa\"];\n", "n4d068ce52cf248adb3b537805a233dda -> nb85aee31625f4998b596d9b6ea3b77fd;\n", "n4d068ce52cf248adb3b537805a233dda -> nec2837ce384246ffb06e3d4090adfb37;\n", "nb85aee31625f4998b596d9b6ea3b77fd [label=\"-\\naa\\naa\\nTrue\"];\n", "nec2837ce384246ffb06e3d4090adfb37 [label=\"a\\na\\naa\"];\n", "nec2837ce384246ffb06e3d4090adfb37 -> n9c395901af2d4e67a7e5a370f759bce6;\n", "nec2837ce384246ffb06e3d4090adfb37 -> nff84b0c784744901afb3ac8a5aef3c23;\n", "n9c395901af2d4e67a7e5a370f759bce6 [label=\"-\\na\\na\\nTrue\"];\n", "nff84b0c784744901afb3ac8a5aef3c23 [label=\"a\\n-\\na\\nTrue\"];\n", "n5510c6a96018480ba0fc2315d34a69e6 [label=\"aa\\naa\\naaaa\"];\n", "n5510c6a96018480ba0fc2315d34a69e6 -> n5eaaabd1caef4c3f8f6607a8bb254906;\n", "n5510c6a96018480ba0fc2315d34a69e6 -> n6041081af67d4f57968572aa2051d1bc;\n", "n5eaaabd1caef4c3f8f6607a8bb254906 [label=\"a\\naa\\naaa\"];\n", "n5eaaabd1caef4c3f8f6607a8bb254906 -> n6dd23a9ed026429fb57cbf94e6283364;\n", "n5eaaabd1caef4c3f8f6607a8bb254906 -> n3042bda75e7c4d8f8a9ccc464f0ba724;\n", "n6dd23a9ed026429fb57cbf94e6283364 [label=\"-\\naa\\naa\\nTrue\"];\n", "n3042bda75e7c4d8f8a9ccc464f0ba724 [label=\"a\\na\\naa\"];\n", "n3042bda75e7c4d8f8a9ccc464f0ba724 -> n5e702eeee87042deb3157b6663b1f07a;\n", "n3042bda75e7c4d8f8a9ccc464f0ba724 -> n37928d6516f942008c5e89b5c37098ee;\n", "n5e702eeee87042deb3157b6663b1f07a [label=\"-\\na\\na\\nTrue\"];\n", "n37928d6516f942008c5e89b5c37098ee [label=\"a\\n-\\na\\nTrue\"];\n", "n6041081af67d4f57968572aa2051d1bc [label=\"aa\\na\\naaa\"];\n", "n6041081af67d4f57968572aa2051d1bc -> nbb96e07d3c89450cb92ad725f6fc4845;\n", "n6041081af67d4f57968572aa2051d1bc -> n0dbe764d7e4a429298f2d3583e8c84b1;\n", "nbb96e07d3c89450cb92ad725f6fc4845 [label=\"a\\na\\naa\"];\n", "nbb96e07d3c89450cb92ad725f6fc4845 -> nbe5a7be2ec824370a293e7aa8f3a5467;\n", "nbb96e07d3c89450cb92ad725f6fc4845 -> ndc15a7d84b734bb793055e4712a82d5c;\n", "nbe5a7be2ec824370a293e7aa8f3a5467 [label=\"-\\na\\na\\nTrue\"];\n", "ndc15a7d84b734bb793055e4712a82d5c [label=\"a\\n-\\na\\nTrue\"];\n", "n0dbe764d7e4a429298f2d3583e8c84b1 [label=\"aa\\n-\\naa\\nTrue\"];\n", "n4c492e6eb94741d2b11567b1b4c729fa [label=\"aaa\\naa\\naaaaa\"];\n", "n4c492e6eb94741d2b11567b1b4c729fa -> n0e78dd2900a34a7297cc0ea2bb27e30c;\n", "n4c492e6eb94741d2b11567b1b4c729fa -> nc18fe2c53e9e4209a9af9c0678465b1f;\n", "n0e78dd2900a34a7297cc0ea2bb27e30c [label=\"aa\\naa\\naaaa\"];\n", "n0e78dd2900a34a7297cc0ea2bb27e30c -> n1b98c16a65994faaa980d9c530383c77;\n", "n0e78dd2900a34a7297cc0ea2bb27e30c -> n33dbe313802045f8895d0e904d588881;\n", "n1b98c16a65994faaa980d9c530383c77 [label=\"a\\naa\\naaa\"];\n", "n1b98c16a65994faaa980d9c530383c77 -> n5e7c6dff46ff49f7903eb543c02fa22b;\n", "n1b98c16a65994faaa980d9c530383c77 -> n33391a1fab3849cf9823ccc7396aa7d4;\n", "n5e7c6dff46ff49f7903eb543c02fa22b [label=\"-\\naa\\naa\\nTrue\"];\n", "n33391a1fab3849cf9823ccc7396aa7d4 [label=\"a\\na\\naa\"];\n", "n33391a1fab3849cf9823ccc7396aa7d4 -> n13b4732016804c3986853f6d2fe4a28b;\n", "n33391a1fab3849cf9823ccc7396aa7d4 -> n767be985e5a5469da7cfeea0272705b3;\n", "n13b4732016804c3986853f6d2fe4a28b [label=\"-\\na\\na\\nTrue\"];\n", "n767be985e5a5469da7cfeea0272705b3 [label=\"a\\n-\\na\\nTrue\"];\n", "n33dbe313802045f8895d0e904d588881 [label=\"aa\\na\\naaa\"];\n", "n33dbe313802045f8895d0e904d588881 -> nf59143762fc643f0bd58507b5097b837;\n", "n33dbe313802045f8895d0e904d588881 -> n30d968450bf147b68a8d7df49177722c;\n", "nf59143762fc643f0bd58507b5097b837 [label=\"a\\na\\naa\"];\n", "nf59143762fc643f0bd58507b5097b837 -> ncd2168bdc52c459d821427219fb885d1;\n", "nf59143762fc643f0bd58507b5097b837 -> nc6011f3f746f425ab01fd89e1f17cbb4;\n", "ncd2168bdc52c459d821427219fb885d1 [label=\"-\\na\\na\\nTrue\"];\n", "nc6011f3f746f425ab01fd89e1f17cbb4 [label=\"a\\n-\\na\\nTrue\"];\n", "n30d968450bf147b68a8d7df49177722c [label=\"aa\\n-\\naa\\nTrue\"];\n", "nc18fe2c53e9e4209a9af9c0678465b1f [label=\"aaa\\na\\naaaa\"];\n", "nc18fe2c53e9e4209a9af9c0678465b1f -> n38a7aa8aab21444d8b9d50ca71871b7e;\n", "nc18fe2c53e9e4209a9af9c0678465b1f -> n1ec1cf69ce3c4798b305338648a6e46b;\n", "n38a7aa8aab21444d8b9d50ca71871b7e [label=\"aa\\na\\naaa\"];\n", "n38a7aa8aab21444d8b9d50ca71871b7e -> nad5433a86522484e85d560ac7d202b3d;\n", "n38a7aa8aab21444d8b9d50ca71871b7e -> n6bfb83c32f9e46a19e9408fc087e74ae;\n", "nad5433a86522484e85d560ac7d202b3d [label=\"a\\na\\naa\"];\n", "nad5433a86522484e85d560ac7d202b3d -> n292f0206736a40ac8f6045ac0d8a0a07;\n", "nad5433a86522484e85d560ac7d202b3d -> n07c65e03d3bd473f97579a2c63f922c7;\n", "n292f0206736a40ac8f6045ac0d8a0a07 [label=\"-\\na\\na\\nTrue\"];\n", "n07c65e03d3bd473f97579a2c63f922c7 [label=\"a\\n-\\na\\nTrue\"];\n", "n6bfb83c32f9e46a19e9408fc087e74ae [label=\"aa\\n-\\naa\\nTrue\"];\n", "n1ec1cf69ce3c4798b305338648a6e46b [label=\"aaa\\n-\\naaa\\nTrue\"];\n" ] } ], "source": [ "root, graph = is_interleave_recursive_dot('aaa', 'aaa', 'aaaaaa')\n", "print('\\n'.join(graph))" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "s1 = make_string(500)\n", "s2 = make_string(500)\n", "s3 = make_string(500)\n", "s12 = interleave(s1, s2)\n", "s23 = interleave(s2, s3)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_interleave_recursive(s1, s2, s12)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_interleave_recursive(s1, s2, s23)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def show_annotated_table(table, bps):\n", " return '\\n'.join(' '.join('*' if (i, j) == (0, 0) else bps[i, j][2] if table[i, j] else '.' for j in sorted(set([k[1] for k in table])))\n", " for i in sorted(set([k[0] for k in table])))" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def show_backtrace_star(bps):\n", " i = max([0] + [k[0] for k in bps])\n", " j = max([0] + [k[1] for k in bps])\n", " chars = ''\n", " stars = ''\n", " if (i, j) in bps:\n", " while i != 0 or j != 0:\n", " chars += bps[i, j][2]\n", " if bps[i, j][3] == 'seq1':\n", " stars += '*'\n", " else:\n", " stars += ' '\n", " i, j = bps[i, j][0], bps[i, j][1] \n", " return ''.join(list(reversed(chars))) + '\\n' + ''.join(list(reversed(stars)))\n", " else:\n", " return ''" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: baddacaddb\n", "1: bcccacbacb\n", "2: cdcddbcccacbacbaabcc\n", "3: cdccdbadcaacbbcccaac\n", "4: bbacccdacdacadbdbacb\n", "5: cbaccbbcadadaaccaddb\n", "6: cbaccbcaac\n" ] }, { "data": { "text/plain": [ "['bbacccdacdacadbdbacb']" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s1 = make_string(10, alphabet='abcd')\n", "s2 = make_string(10, alphabet='abcd')\n", "s3 = make_string(10, alphabet='abcd')\n", "s4 = make_string(10, alphabet='abcd')\n", "il = interleave(s1, s2)\n", "bs = [s3, il, interleave(s3, s4), interleave(s2, s4), interleave(s1, s3)]\n", "random.shuffle(bs)\n", "bs = [s1, s2] + bs\n", "tg = [l for l in bs if is_interleave(s1, s2, l)]\n", "print('\\n'.join(['{}: {}'.format(i, s) for i, s in enumerate(bs)]))\n", "tg" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* b . . . . . . . . .\n", "b b . . . . . . . . .\n", ". a c c c . . . . . .\n", ". . . . d a c . . . .\n", ". . . . . . d . . . .\n", ". . . . . . a . . . .\n", ". . . . . . c . . . .\n", ". . . . . . a . . . .\n", ". . . . . . d b . . .\n", ". . . . . . . d . . .\n", ". . . . . . . b a c b\n", "bBAcccDacDACADbDBacb\n", "bbacccdacdacadbdbacb\n", " ** * ***** ** \n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v, bp, t = is_interleave(s1, s2, il, return_backpointers=True, return_table=True)\n", "print(show_annotated_table(t, bp))\n", "print(show_backtrace(bp))\n", "print(show_backtrace_star(bp))\n", "v" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cbaccbbcadadaaccaddb\n", " * ** * * *****\n" ] }, { "data": { "text/plain": [ "5" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ind = [i for i, b in enumerate(bs) if is_interleave(s1, s3, b)][0]\n", "v, bp = is_interleave(s1, s3, bs[ind], return_backpointers=True)\n", "print(show_backtrace_star(bp))\n", "ind" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* b . . . . . . . . .\n", "b b a . . . . . . . .\n", ". . c . . . . . . . .\n", ". . c . . . . . . . .\n", ". . c d . . . . . . .\n", ". . . a . . . . . . .\n", ". . . c d a c a d . .\n", ". . . . . . . . b d b\n", ". . . . . . . . . . a\n", ". . . . . . . . . . c\n", ". . . . . . . . . . b\n", "bBaCCCdACdacadBdbACB\n", "bbacccdacdacadbdbacb\n", " * *** ** * ***\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v, bp, t = is_interleave(s2, s1, il, return_backpointers=True, return_table=True)\n", "print(show_annotated_table(t, bp))\n", "print(show_backtrace(bp))\n", "print(show_backtrace_star(bp))\n", "v" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* . . . . . . . . . .\n", "b . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", "B\n", "b\n", "*\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v, bp, t = is_interleave(s1, s3, il, return_backpointers=True, return_table=True)\n", "print(show_annotated_table(t, bp))\n", "print(show_backtrace(bp))\n", "print(show_backtrace_star(bp))\n", "v" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* . . . . . . . . . .\n", "b . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", ". . . . . . . . . . .\n", "B\n", "b\n", "*\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v, bp, t = is_interleave(s2, s3, il, return_backpointers=True, return_table=True)\n", "print(show_annotated_table(t, bp))\n", "print(show_backtrace(bp))\n", "print(show_backtrace_star(bp))\n", "v" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Make puzzle data\n", "\n", "## Note to self\n", "Include some distractors in the test set, such that:\n", "* subsequence(my_bill, distractor) is true\n", "* subsequence(friend_bill, distractor) is true\n", "* interleave(my_bill, friend_bill, distractor) is false\n", "\n", "(i.e. characters are shared between my_bill and friend_bill)\n", "\n", "Students are taking a greedy approach to subsequence, and saying the interleave is true if both bills are subsequences of the distractor.\n", "\n", "i.e. \"aaa\" and \"aab\" are both subsequences of \"aaabbb\", but cannot be interleaved to form \"aaabbb\".\n" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": true }, "outputs": [], "source": [ "my_bill = make_string(200)\n", "friend_bill = make_string(200)\n", "other_bills = [make_string(200) for _ in range(98)]\n", "\n", "target_interleaved = interleave(my_bill, friend_bill)\n", "mine_interleaved = [interleave(my_bill, o) for o in random.sample(other_bills, 21)]\n", "friend_interleaved = [interleave(friend_bill, o) for o in random.sample(other_bills, 13)]\n", "other_interleaved = []\n", "for _ in range(103):\n", " s1, s2 = random.sample(other_bills, 2)\n", " other_interleaved += [interleave(s1, s2)]" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": true }, "outputs": [], "source": [ "all_targets = [target_interleaved] + mine_interleaved + friend_interleaved + other_interleaved" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 2.96 s, sys: 4 ms, total: 2.97 s\n", "Wall time: 2.97 s\n" ] }, { "data": { "text/plain": [ "[0]" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%time [i for i, s12 in enumerate(all_targets) if is_interleave(my_bill, friend_bill, s12)]" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 660 ms, sys: 0 ns, total: 660 ms\n", "Wall time: 658 ms\n" ] }, { "data": { "text/plain": [ "[0]" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%time [i for i, s12 in enumerate(all_targets) if is_interleave_recursive(my_bill, friend_bill, s12)]" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": true }, "outputs": [], "source": [ "bill_set = all_targets + random.sample(other_bills, 8)\n", "random.shuffle(bill_set)\n", "bill_set = [my_bill, friend_bill] + bill_set\n", "\n", "# with open('09-bills.txt', 'w') as f:\n", "# for i, b in enumerate(bill_set):\n", "# f.write('{}: {}\\n'.format(i, b))" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def is_subseq_greedy(s1, s2):\n", " i = j = 0\n", " while i < len(s1) and j < len(s2):\n", " if s1[i] == s2[j]:\n", " i += 1\n", " j += 1\n", " return i == len(s1)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def subseq_partition(s1, s2):\n", " i = j = 0\n", " remainder = ''\n", " while i < len(s1) and j < len(s2):\n", " if s1[i] == s2[j]:\n", " i += 1\n", " else:\n", " remainder += s2[j]\n", " j += 1\n", " return i == len(s1), remainder" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(40, 40, 20, 20)" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "common = make_string(10)\n", "padding = make_string(10)\n", "middle = interleave(common, padding)\n", "\n", "pre1 = make_string(5)\n", "suf1 = make_string(5)\n", "\n", "pre2 = make_string(5)\n", "suf2 = make_string(5)\n", "\n", "pre = interleave(pre1, pre2)\n", "suf = interleave(suf1, suf2)\n", "\n", "distractor = pre + middle + suf\n", "\n", "sub1 = pre1 + common + suf1\n", "sub2 = pre2 + common + suf2\n", "\n", "valid = interleave(sub1, sub2)\n", "\n", "len(distractor), len(valid), len(sub1), len(sub2)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(True, True)" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_subseq_greedy(sub1, distractor), is_subseq_greedy(sub2, distractor)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(True, True)" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_subseq_greedy(sub1, valid), is_subseq_greedy(sub2, valid)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(False, True)" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_interleave(sub1, sub2, distractor), is_interleave(sub1, sub2, valid)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "('echgeaeeefdcebeaahaf',\n", " 'eeahaaeeefdcebedghbg',\n", " 'eeecahahgeaaeeebafaadgceadabefdaghbgahaf',\n", " 'eecheagehaaaeeeeeefdcebefadahcaebfedghbg')" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sub1, sub2, distractor, valid" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a, b = subseq_partition(sub1, distractor)\n", "b == sub2" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "('eeahaaeeefdceb', 'eeahaaeeefdcebedghbg')" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a, b = subseq_partition(sub1, valid)\n", "b, sub2" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2+" } }, "nbformat": 4, "nbformat_minor": 1 }