{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Subsequence strings\n", "\n", "Given two strings `a` and `b`, is `a` a subsequence of `b`?\n", "\n", "For example,\n", "Given:\n", "a = \"aabcc\",\n", "b = \"dabaabcacb\",\n", "\n", "return True : dAbAaBCaCb\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import random" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": true }, "outputs": [], "source": [ "s1 = \"aabcc\"\n", "s2t = \"dabaabcacb\"\n", "s2f = \"dabacc\"\n", "\n", "s2 = s2t" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`dp_table[i, j]` is True if first `i` characters of `s1` can be found in first `j` characters of `s2`." ] }, { "cell_type": "code", "execution_count": 3, "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", " (0, 6): False,\n", " (0, 7): False,\n", " (0, 8): False,\n", " (0, 9): False,\n", " (0, 10): 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", " (1, 6): False,\n", " (1, 7): False,\n", " (1, 8): False,\n", " (1, 9): False,\n", " (1, 10): 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", " (2, 6): False,\n", " (2, 7): False,\n", " (2, 8): False,\n", " (2, 9): False,\n", " (2, 10): 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", " (3, 6): False,\n", " (3, 7): False,\n", " (3, 8): False,\n", " (3, 9): False,\n", " (3, 10): 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", " (4, 6): False,\n", " (4, 7): False,\n", " (4, 8): False,\n", " (4, 9): False,\n", " (4, 10): 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,\n", " (5, 6): False,\n", " (5, 7): False,\n", " (5, 8): False,\n", " (5, 9): False,\n", " (5, 10): False}" ] }, "execution_count": 3, "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": 4, "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": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "F F F F F F F F F F F\n", "F F F F F F F F F F F\n", "F F F F F F F F F F F\n", "F F F F F F F F F F F\n", "F F F F F F F F F F F\n", "F F F F F F F F F F F\n" ] } ], "source": [ "print(show_table(dp_table))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "aaaa aaababb\n", "aa 0 0 ! ! True\n", "aa 0 1 ! ! True\n", "aa 0 2 ! ! True\n", "aa 0 3 ! ! True\n", "aa 0 4 ! ! True\n", "aa 0 5 ! ! True\n", "aa 0 6 ! ! True\n", "aa 0 7 ! ! True\n", "s1 1 1 a a True\n", "s2 1 2 a a True\n", "s1 1 2 a a True\n", "s2 1 3 a a True\n", "s1 1 3 a a True\n", "s2 1 4 a b True\n", "s2 1 5 a a True\n", "s1 1 5 a a True\n", "s2 1 6 a b True\n", "s2 1 7 a b True\n", "s1 2 2 a a True\n", "s2 2 3 a a True\n", "s1 2 3 a a True\n", "s2 2 4 a b True\n", "s2 2 5 a a True\n", "s1 2 5 a a True\n", "s2 2 6 a b True\n", "s2 2 7 a b True\n", "s1 3 3 a a True\n", "s2 3 4 a b True\n", "s2 3 5 a a True\n", "s1 3 5 a a True\n", "s2 3 6 a b True\n", "s2 3 7 a b True\n", "xx 4 4 a b False\n", "s1 4 5 a a True\n", "s2 4 6 a b True\n", "s2 4 7 a b True\n", "T T T T T T T T\n", "F T T T T T T T\n", "F F T T T T T T\n", "F F F T T T T T\n", "F F F F F T T T\n" ] }, { "data": { "text/plain": [ "{(1, 1): (0, 0, 'a', 's1'),\n", " (1, 2): (0, 1, 'a', 's1'),\n", " (1, 3): (0, 2, 'a', 's1'),\n", " (1, 4): (1, 3, 'b', 's2'),\n", " (1, 5): (0, 4, 'a', 's1'),\n", " (1, 6): (1, 5, 'b', 's2'),\n", " (1, 7): (1, 6, 'b', 's2'),\n", " (2, 2): (1, 1, 'a', 's1'),\n", " (2, 3): (1, 2, 'a', 's1'),\n", " (2, 4): (2, 3, 'b', 's2'),\n", " (2, 5): (1, 4, 'a', 's1'),\n", " (2, 6): (2, 5, 'b', 's2'),\n", " (2, 7): (2, 6, 'b', 's2'),\n", " (3, 3): (2, 2, 'a', 's1'),\n", " (3, 4): (3, 3, 'b', 's2'),\n", " (3, 5): (2, 4, 'a', 's1'),\n", " (3, 6): (3, 5, 'b', 's2'),\n", " (3, 7): (3, 6, 'b', 's2'),\n", " (4, 5): (3, 4, 'a', 's1'),\n", " (4, 6): (4, 5, 'b', 's2'),\n", " (4, 7): (4, 6, 'b', 's2')}" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s2 = s2f\n", "\n", "s1 = 'aaaa'\n", "s2 = 'aaababb'\n", "\n", "print(s1, s2)\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(i, len(s2)+1):\n", " if i == 0 or j == 0:\n", " dp_table[i, j] = True\n", " print('aa', i, j, '!', '!', dp_table[i, j])\n", " else:\n", " # extend by character from s2\n", " if dp_table[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], dp_table[i, j]) \n", " # extend by character from s1\n", " if dp_table[i-1, j-1] and s1[i-1] == s2[j-1]:\n", " dp_table[i, j] = True\n", " backpointers[i, j] = (i-1, j-1, s1[i-1], 's1') \n", " print('s1', i, j, s1[i-1], s2[j-1], dp_table[i, j])\n", " if not dp_table[i, j]:\n", " print('xx', i, j, s1[i-1], s2[j-1], dp_table[i, j])\n", "\n", "print(show_table(dp_table))\n", "backpointers" ] }, { "cell_type": "code", "execution_count": 7, "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 and j != 0:\n", " if bps[i, j][3] == 's1':\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": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'AAAbAbb'" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "show_backtrace(backpointers)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def is_subseq(seq1, seq2, return_backpointers=False, return_table=False, debug=False):\n", " \"\"\"Return true if seq1 is a subsequence of seq2.\n", " If return_backpointers, also return the set of backpointers to\n", " reconstruct the subsequence\"\"\"\n", " \n", " # dp_table[i, j] is True if first i characters of seq1 can\n", " # be found in the first j characters of seq2\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(i, len(seq2)+1):\n", " if i == 0 or j == 0:\n", " dp_table[i, j] = True\n", " if debug: print('aa', i, j, '!', '!', dp_table[i, j])\n", " else:\n", " # extend by character from s2\n", " if dp_table[i, j-1]:\n", " dp_table[i, j] = True\n", " backpointers[i, j] = (i, j-1, seq2[j-1], 's2')\n", " if debug: print('s2', i, j, seq1[i-1], seq2[j-1], dp_table[i, j]) \n", " # extend by character from s1\n", " if dp_table[i-1, j-1] and seq1[i-1] == seq2[j-1]:\n", " dp_table[i, j] = True\n", " backpointers[i, j] = (i-1, j-1, seq1[i-1], 's1') \n", " if debug: print('s1', i, j, seq1[i-1], seq2[j-1], dp_table[i, j])\n", " if not dp_table[i, j]:\n", " if debug: print('xx', i, j, seq1[i-1], seq2[j-1], dp_table[i, j]) \n", " \n", "# if return_backpointers:\n", "# return dp_table[len(seq1), len(seq2)], backpointers\n", "# else:\n", "# return dp_table[len(seq1), len(seq2)]\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": 10, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "aa 0 0 ! ! True\n", "aa 0 1 ! ! True\n", "aa 0 2 ! ! True\n", "aa 0 3 ! ! True\n", "aa 0 4 ! ! True\n", "aa 0 5 ! ! True\n", "aa 0 6 ! ! True\n", "aa 0 7 ! ! True\n", "aa 0 8 ! ! True\n", "aa 0 9 ! ! True\n", "aa 0 10 ! ! True\n", "xx 1 1 a d False\n", "s1 1 2 a a True\n", "s2 1 3 a b True\n", "s2 1 4 a a True\n", "s1 1 4 a a True\n", "s2 1 5 a a True\n", "s1 1 5 a a True\n", "s2 1 6 a b True\n", "s2 1 7 a c True\n", "s2 1 8 a a True\n", "s1 1 8 a a True\n", "s2 1 9 a c True\n", "s2 1 10 a b True\n", "xx 2 2 a a False\n", "xx 2 3 a b False\n", "s1 2 4 a a True\n", "s2 2 5 a a True\n", "s1 2 5 a a True\n", "s2 2 6 a b True\n", "s2 2 7 a c True\n", "s2 2 8 a a True\n", "s1 2 8 a a True\n", "s2 2 9 a c True\n", "s2 2 10 a b True\n", "xx 3 3 a b False\n", "xx 3 4 a a False\n", "s1 3 5 a a True\n", "s2 3 6 a b True\n", "s2 3 7 a c True\n", "s2 3 8 a a True\n", "s1 3 8 a a True\n", "s2 3 9 a c True\n", "s2 3 10 a b True\n", "xx 4 4 a a False\n", "xx 4 5 a a False\n", "xx 4 6 a b False\n", "xx 4 7 a c False\n", "s1 4 8 a a True\n", "s2 4 9 a c True\n", "s2 4 10 a b True\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_subseq(s1, s2t, debug=True)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def show_annotated_table(table, bps):\n", " return '\\n'.join(' '.join('.' if (i, j) not in bps 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": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tf, bps, tb = is_subseq(s1, s2t, return_backpointers=True, return_table=True)\n", "tf" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'AbAAbcAcb'" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "show_backtrace(bps)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T T T T T T T T T T T\n", "F F T T T T T T T T T\n", "F F F F T T T T T T T\n", "F F F F F T T T T T T\n", "F F F F F F F F T T T\n" ] } ], "source": [ "print(show_table(tb))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ". . . . . . . . . . .\n", ". . a b a a b c a c b\n", ". . . . a a b c a c b\n", ". . . . . a b c a c b\n", ". . . . . . . . a c b\n" ] } ], "source": [ "print(show_annotated_table(tb, bps))" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(show_backtrace(bps)) == len(s2t)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "('aaaa', 'dabaabcacb')" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s1, s2t" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{(1, 2): (0, 1, 'a', 's1'),\n", " (1, 3): (1, 2, 'b', 's2'),\n", " (1, 4): (0, 3, 'a', 's1'),\n", " (1, 5): (0, 4, 'a', 's1'),\n", " (1, 6): (1, 5, 'b', 's2'),\n", " (1, 7): (1, 6, 'c', 's2'),\n", " (1, 8): (0, 7, 'a', 's1'),\n", " (1, 9): (1, 8, 'c', 's2'),\n", " (1, 10): (1, 9, 'b', 's2'),\n", " (2, 4): (1, 3, 'a', 's1'),\n", " (2, 5): (1, 4, 'a', 's1'),\n", " (2, 6): (2, 5, 'b', 's2'),\n", " (2, 7): (2, 6, 'c', 's2'),\n", " (2, 8): (1, 7, 'a', 's1'),\n", " (2, 9): (2, 8, 'c', 's2'),\n", " (2, 10): (2, 9, 'b', 's2'),\n", " (3, 5): (2, 4, 'a', 's1'),\n", " (3, 6): (3, 5, 'b', 's2'),\n", " (3, 7): (3, 6, 'c', 's2'),\n", " (3, 8): (2, 7, 'a', 's1'),\n", " (3, 9): (3, 8, 'c', 's2'),\n", " (3, 10): (3, 9, 'b', 's2'),\n", " (4, 8): (3, 7, 'a', 's1'),\n", " (4, 9): (4, 8, 'c', 's2'),\n", " (4, 10): (4, 9, 'b', 's2')}" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bps" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_subseq(s1, s2f)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "aa 0 0 ! ! True\n", "aa 0 1 ! ! True\n", "aa 0 2 ! ! True\n", "aa 0 3 ! ! True\n", "aa 0 4 ! ! True\n", "aa 0 5 ! ! True\n", "aa 0 6 ! ! True\n", "aa 0 7 ! ! True\n", "s1 1 1 a a True\n", "s2 1 2 a a True\n", "s1 1 2 a a True\n", "s2 1 3 a a True\n", "s1 1 3 a a True\n", "s2 1 4 a b True\n", "s2 1 5 a a True\n", "s1 1 5 a a True\n", "s2 1 6 a b True\n", "s2 1 7 a b True\n", "s1 2 2 a a True\n", "s2 2 3 a a True\n", "s1 2 3 a a True\n", "s2 2 4 a b True\n", "s2 2 5 a a True\n", "s1 2 5 a a True\n", "s2 2 6 a b True\n", "s2 2 7 a b True\n", "s1 3 3 a a True\n", "s2 3 4 a b True\n", "s2 3 5 a a True\n", "s1 3 5 a a True\n", "s2 3 6 a b True\n", "s2 3 7 a b True\n", "xx 4 4 a b False\n", "s1 4 5 a a True\n", "s2 4 6 a b True\n", "s2 4 7 a b True\n" ] }, { "data": { "text/plain": [ "(True,\n", " {(1, 1): (0, 0, 'a', 's1'),\n", " (1, 2): (0, 1, 'a', 's1'),\n", " (1, 3): (0, 2, 'a', 's1'),\n", " (1, 4): (1, 3, 'b', 's2'),\n", " (1, 5): (0, 4, 'a', 's1'),\n", " (1, 6): (1, 5, 'b', 's2'),\n", " (1, 7): (1, 6, 'b', 's2'),\n", " (2, 2): (1, 1, 'a', 's1'),\n", " (2, 3): (1, 2, 'a', 's1'),\n", " (2, 4): (2, 3, 'b', 's2'),\n", " (2, 5): (1, 4, 'a', 's1'),\n", " (2, 6): (2, 5, 'b', 's2'),\n", " (2, 7): (2, 6, 'b', 's2'),\n", " (3, 3): (2, 2, 'a', 's1'),\n", " (3, 4): (3, 3, 'b', 's2'),\n", " (3, 5): (2, 4, 'a', 's1'),\n", " (3, 6): (3, 5, 'b', 's2'),\n", " (3, 7): (3, 6, 'b', 's2'),\n", " (4, 5): (3, 4, 'a', 's1'),\n", " (4, 6): (4, 5, 'b', 's2'),\n", " (4, 7): (4, 6, 'b', 's2')})" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_subseq('aaaa', 'aaababb', return_backpointers=True, debug=True)" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def is_subseq_recursive(s1, s2):\n", "# print(s1, s2)\n", " if not s1:\n", " return True\n", " elif len(s1) > len(s2):\n", " return False\n", " else:\n", " if s1[-1] == s2[-1]:\n", " return is_subseq_recursive(s1, s2[:-1]) or is_subseq_recursive(s1[:-1], s2[:-1])\n", " else:\n", " return is_subseq_recursive(s1, s2[:-1])" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def is_subseq_recursive_2(s1, s2):\n", " if not s1:\n", " return True\n", " elif len(s1) > len(s2):\n", " return False\n", " else:\n", " if s1[-1] == s2[-1]:\n", " return is_subseq_recursive(s1[:-1], s2[:-1]) or is_subseq_recursive(s1, s2[:-1])\n", " else:\n", " return is_subseq_recursive(s1, s2[:-1])" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import uuid" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_subseq_recursive(s1, s2t)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_subseq_recursive(s1, s2f)" ] }, { "cell_type": "code", "execution_count": 76, "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": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'ae50b62c418f4ba8902bfa8bab4948e0'" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uuid.uuid4().hex" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "nd5092f0e2ba047ba9b662e17a650791a [label=\"daabcc\\ndabaabcacb\"];\n", "nd5092f0e2ba047ba9b662e17a650791a -> nc243f60568164ba495d5f89dc1075a85;\n", "nc243f60568164ba495d5f89dc1075a85 [label=\"daabcc\\ndabaabcac\"];\n", "nc243f60568164ba495d5f89dc1075a85 -> n933e3a2ebca34034866b98ab19ee3f90;\n", "nc243f60568164ba495d5f89dc1075a85 -> n3c49af7ea69340f2a97827a0547f73db;\n", "n933e3a2ebca34034866b98ab19ee3f90 [label=\"daabc\\ndabaabca\"];\n", "n933e3a2ebca34034866b98ab19ee3f90 -> n8d50442e9d704d7a8e9f0ba2f38e73fc;\n", "n8d50442e9d704d7a8e9f0ba2f38e73fc [label=\"daabc\\ndabaabc\"];\n", "n8d50442e9d704d7a8e9f0ba2f38e73fc -> n942c205bd0994681bf159f01fc42d0f5;\n", "n8d50442e9d704d7a8e9f0ba2f38e73fc -> n8aab1aa30e494cef8895ff177a1d0623;\n", "n942c205bd0994681bf159f01fc42d0f5 [label=\"daab\\ndabaab\"];\n", "n942c205bd0994681bf159f01fc42d0f5 -> na797ca966ed045d5a14888ef06ae64ba;\n", "n942c205bd0994681bf159f01fc42d0f5 -> nd7ea02b3fb6348e49929c458903e1c66;\n", "na797ca966ed045d5a14888ef06ae64ba [label=\"daa\\ndabaa\"];\n", "na797ca966ed045d5a14888ef06ae64ba -> nfc8f27c7ea3b45f69d3e28ff7397c211;\n", "na797ca966ed045d5a14888ef06ae64ba -> nfc96ed80812342958197f351bf4bb6c4;\n", "nfc8f27c7ea3b45f69d3e28ff7397c211 [label=\"da\\ndaba\"];\n", "nfc8f27c7ea3b45f69d3e28ff7397c211 -> n0fba1674138c4ee2a437ec3bfe3c0c34;\n", "nfc8f27c7ea3b45f69d3e28ff7397c211 -> n214435af4c204b2bac186c6bc7fd4b43;\n", "n0fba1674138c4ee2a437ec3bfe3c0c34 [label=\"d\\ndab\"];\n", "n0fba1674138c4ee2a437ec3bfe3c0c34 -> nbbbca27c4d794d3396c58908f36ad8b1;\n", "nbbbca27c4d794d3396c58908f36ad8b1 [label=\"d\\nda\"];\n", "nbbbca27c4d794d3396c58908f36ad8b1 -> n4a39eb3283ba4896bd0ae98e695a5e78;\n", "n4a39eb3283ba4896bd0ae98e695a5e78 [label=\"d\\nd\"];\n", "n4a39eb3283ba4896bd0ae98e695a5e78 -> n0f69ba31cb9341b8a0e01b58e94ecc3e;\n", "n4a39eb3283ba4896bd0ae98e695a5e78 -> n01a1efd1fe0148409aa9ae19a57a1c11;\n", "n0f69ba31cb9341b8a0e01b58e94ecc3e [label=\"-\\n\\nTrue\"];\n", "n01a1efd1fe0148409aa9ae19a57a1c11 [label=\"d\\n\\nFalse\"];\n", "n214435af4c204b2bac186c6bc7fd4b43 [label=\"da\\ndab\"];\n", "n214435af4c204b2bac186c6bc7fd4b43 -> n7f75729c74d944199866bc8242166a15;\n", "n7f75729c74d944199866bc8242166a15 [label=\"da\\nda\"];\n", "n7f75729c74d944199866bc8242166a15 -> nfe2ac3cf290844a686eb20c8a1419632;\n", "n7f75729c74d944199866bc8242166a15 -> n99dabcab19424f76aade00e10b247e28;\n", "nfe2ac3cf290844a686eb20c8a1419632 [label=\"d\\nd\"];\n", "nfe2ac3cf290844a686eb20c8a1419632 -> n4ef4c358f84b44f0816ee6c23bc87c23;\n", "nfe2ac3cf290844a686eb20c8a1419632 -> n0fcf711c28b84e869cd5b1ad29147b79;\n", "n4ef4c358f84b44f0816ee6c23bc87c23 [label=\"-\\n\\nTrue\"];\n", "n0fcf711c28b84e869cd5b1ad29147b79 [label=\"d\\n\\nFalse\"];\n", "n99dabcab19424f76aade00e10b247e28 [label=\"da\\nd\\nFalse\"];\n", "nfc96ed80812342958197f351bf4bb6c4 [label=\"daa\\ndaba\"];\n", "nfc96ed80812342958197f351bf4bb6c4 -> n6f68fb9a9f774752ada474efa377f60e;\n", "nfc96ed80812342958197f351bf4bb6c4 -> ne0abe88f3d764703a75eed757cc316bf;\n", "n6f68fb9a9f774752ada474efa377f60e [label=\"da\\ndab\"];\n", "n6f68fb9a9f774752ada474efa377f60e -> n9c89649fee58407db0ff5d0ba2eb4f2d;\n", "n9c89649fee58407db0ff5d0ba2eb4f2d [label=\"da\\nda\"];\n", "n9c89649fee58407db0ff5d0ba2eb4f2d -> n34738b8c332d4e559f9aa7c7eec42e72;\n", "n9c89649fee58407db0ff5d0ba2eb4f2d -> n446a9bd7fa264edcb2bf289b4fe55f71;\n", "n34738b8c332d4e559f9aa7c7eec42e72 [label=\"d\\nd\"];\n", "n34738b8c332d4e559f9aa7c7eec42e72 -> n73e44dd0c7f248a3bd4aa11de6040c5f;\n", "n34738b8c332d4e559f9aa7c7eec42e72 -> n7af9d67feb864b8ea552f84d64b3e610;\n", "n73e44dd0c7f248a3bd4aa11de6040c5f [label=\"-\\n\\nTrue\"];\n", "n7af9d67feb864b8ea552f84d64b3e610 [label=\"d\\n\\nFalse\"];\n", "n446a9bd7fa264edcb2bf289b4fe55f71 [label=\"da\\nd\\nFalse\"];\n", "ne0abe88f3d764703a75eed757cc316bf [label=\"daa\\ndab\"];\n", "ne0abe88f3d764703a75eed757cc316bf -> n639c085cdfa84e26a754dd4aa56a044e;\n", "n639c085cdfa84e26a754dd4aa56a044e [label=\"daa\\nda\\nFalse\"];\n", "nd7ea02b3fb6348e49929c458903e1c66 [label=\"daab\\ndabaa\"];\n", "nd7ea02b3fb6348e49929c458903e1c66 -> nbfa7d3dbec204c328749c3db14b668ea;\n", "nbfa7d3dbec204c328749c3db14b668ea [label=\"daab\\ndaba\"];\n", "nbfa7d3dbec204c328749c3db14b668ea -> nabacc0aef05041c5998655b5e68b6d94;\n", "nabacc0aef05041c5998655b5e68b6d94 [label=\"daab\\ndab\\nFalse\"];\n", "n8aab1aa30e494cef8895ff177a1d0623 [label=\"daabc\\ndabaab\"];\n", "n8aab1aa30e494cef8895ff177a1d0623 -> nd04c429a65b74db8902b1a2725254549;\n", "nd04c429a65b74db8902b1a2725254549 [label=\"daabc\\ndabaa\"];\n", "nd04c429a65b74db8902b1a2725254549 -> nff340dd0af774bf0818a959dad441b84;\n", "nff340dd0af774bf0818a959dad441b84 [label=\"daabc\\ndaba\\nFalse\"];\n", "n3c49af7ea69340f2a97827a0547f73db [label=\"daabcc\\ndabaabca\"];\n", "n3c49af7ea69340f2a97827a0547f73db -> n5f1bfeaf12e247d9bc9ca4641cb72fb5;\n", "n5f1bfeaf12e247d9bc9ca4641cb72fb5 [label=\"daabcc\\ndabaabc\"];\n", "n5f1bfeaf12e247d9bc9ca4641cb72fb5 -> na504494b1bc842bd800600c18478723a;\n", "n5f1bfeaf12e247d9bc9ca4641cb72fb5 -> n13e17edfcd5a4128996ba5dd2473f244;\n", "na504494b1bc842bd800600c18478723a [label=\"daabc\\ndabaab\"];\n", "na504494b1bc842bd800600c18478723a -> n78a73478b48c43d594e6a04a79c61946;\n", "n78a73478b48c43d594e6a04a79c61946 [label=\"daabc\\ndabaa\"];\n", "n78a73478b48c43d594e6a04a79c61946 -> na3c9f1e44c6546ba9b4c49c48ae842ba;\n", "na3c9f1e44c6546ba9b4c49c48ae842ba [label=\"daabc\\ndaba\\nFalse\"];\n", "n13e17edfcd5a4128996ba5dd2473f244 [label=\"daabcc\\ndabaab\"];\n", "n13e17edfcd5a4128996ba5dd2473f244 -> n5624db7a63c643bcafb2ba6797348bba;\n", "n5624db7a63c643bcafb2ba6797348bba [label=\"daabcc\\ndabaa\\nFalse\"];\n" ] } ], "source": [ "root, graph = is_subseq_recursive_dot('daabcc', 'dabaabcacb')\n", "print('\\n'.join(graph))" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "bdabcc dabaabcacb\n", "bdabcc dabaabcac\n", "bdabcc dabaabca\n", "bdabcc dabaabc\n", "bdabcc dabaab\n", "bdabcc dabaa\n", "bdabc dabaab\n", "bdabc dabaa\n", "bdabc daba\n", "bdabc dabaabca\n", "bdabc dabaabc\n", "bdabc dabaab\n", "bdabc dabaa\n", "bdabc daba\n", "bdab dabaab\n", "bdab dabaa\n", "bdab daba\n", "bdab dab\n", "bda dabaa\n", "bda daba\n", "bda dab\n", "bda da\n", "bd dab\n", "bd da\n", "bd d\n", "bd daba\n", "bd dab\n", "bd da\n", "bd d\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_subseq_recursive('bdabcc', 'dabaabcacb')" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "bdabcc dabaabcacb nae20c69b2c4d4ea2a239af485ca10f16 [label=\"bdabcc\\ndabaabcacb\"];\n", "bdabcc dabaabcac nac3868f0d46645ca8bf1b02110448236 [label=\"bdabcc\\ndabaabcac\"];\n", "bdabc dabaabca nf5a124f6b457426eaa13f9d58a716fe1 [label=\"bdabc\\ndabaabca\"];\n", "bdabc dabaabc nf82bf143985849a9a14d7272ab8be040 [label=\"bdabc\\ndabaabc\"];\n", "bdab dabaab nf5694edb16d84740ad75d3c3a9dc33f4 [label=\"bdab\\ndabaab\"];\n", "bda dabaa n7734cd7f92a34a3bbb223dac592bd496 [label=\"bda\\ndabaa\"];\n", "bd daba nf51d59c7071c4725a4e961fd017fd0b6 [label=\"bd\\ndaba\"];\n", "bd dab n48a2b0c66af943439d0c9767e9181c50 [label=\"bd\\ndab\"];\n", "bd da nfee98ef394994c0b9664921c73ae7882 [label=\"bd\\nda\"];\n", "bd d n077956a8b783437ba5a65c3fd3380e2f [label=\"bd\\nd\"];\n", "bda daba nd7f11536d8df400d860ac372d1c3e9f8 [label=\"bda\\ndaba\"];\n", "bd dab nb1bf7b9e21a64b30a7a536a9b8649e56 [label=\"bd\\ndab\"];\n", "bd da nb0329d485ca14bfaa79caa33670a8699 [label=\"bd\\nda\"];\n", "bd d ne91eaaeffb1443639b733682718f4092 [label=\"bd\\nd\"];\n", "bda dab n115e972256cc4394a1eba134f114e4ab [label=\"bda\\ndab\"];\n", "bda da na78115224d9f4e37b4045f6c30e4ceb1 [label=\"bda\\nda\"];\n", "bdab dabaa nad799597664c441f9ccedc62f06247bb [label=\"bdab\\ndabaa\"];\n", "bdab daba n55c3278b1aea4bdc92b3d5eb3c09366c [label=\"bdab\\ndaba\"];\n", "bdab dab n5d2503b1d062482b898e4682240dcc78 [label=\"bdab\\ndab\"];\n", "bdabc dabaab nd6bf8394c44b4af79b2a91534ba13317 [label=\"bdabc\\ndabaab\"];\n", "bdabc dabaa ne856116c734a46b1967bddb73c56140f [label=\"bdabc\\ndabaa\"];\n", "bdabc daba ne0497380dcb04eb9b64499dca04e370b [label=\"bdabc\\ndaba\"];\n", "bdabcc dabaabca na1b07d40913a48a89651e06846c27489 [label=\"bdabcc\\ndabaabca\"];\n", "bdabcc dabaabc nf7b9fd837f974551b0795d7492210e52 [label=\"bdabcc\\ndabaabc\"];\n", "bdabc dabaab n753dfbdd86b543cbb9b246e976d31406 [label=\"bdabc\\ndabaab\"];\n", "bdabc dabaa na21720c117704e02910b868caeddb9a9 [label=\"bdabc\\ndabaa\"];\n", "bdabc daba nb1bec31f0ddf4a888f941702a407906f [label=\"bdabc\\ndaba\"];\n", "bdabcc dabaab n556f3f77789b40f0b332b55e20828606 [label=\"bdabcc\\ndabaab\"];\n", "bdabcc dabaa n5b6173aea18d41f8b4a2c5ce99cc4d7a [label=\"bdabcc\\ndabaa\"];\n", "nae20c69b2c4d4ea2a239af485ca10f16 [label=\"bdabcc\\ndabaabcacb\"];\n", "nae20c69b2c4d4ea2a239af485ca10f16 -> nac3868f0d46645ca8bf1b02110448236;\n", "nac3868f0d46645ca8bf1b02110448236 [label=\"bdabcc\\ndabaabcac\"];\n", "nac3868f0d46645ca8bf1b02110448236 -> nf5a124f6b457426eaa13f9d58a716fe1;\n", "nac3868f0d46645ca8bf1b02110448236 -> na1b07d40913a48a89651e06846c27489;\n", "nf5a124f6b457426eaa13f9d58a716fe1 [label=\"bdabc\\ndabaabca\"];\n", "nf5a124f6b457426eaa13f9d58a716fe1 -> nf82bf143985849a9a14d7272ab8be040;\n", "nf82bf143985849a9a14d7272ab8be040 [label=\"bdabc\\ndabaabc\"];\n", "nf82bf143985849a9a14d7272ab8be040 -> nf5694edb16d84740ad75d3c3a9dc33f4;\n", "nf82bf143985849a9a14d7272ab8be040 -> nd6bf8394c44b4af79b2a91534ba13317;\n", "nf5694edb16d84740ad75d3c3a9dc33f4 [label=\"bdab\\ndabaab\"];\n", "nf5694edb16d84740ad75d3c3a9dc33f4 -> n7734cd7f92a34a3bbb223dac592bd496;\n", "nf5694edb16d84740ad75d3c3a9dc33f4 -> nad799597664c441f9ccedc62f06247bb;\n", "n7734cd7f92a34a3bbb223dac592bd496 [label=\"bda\\ndabaa\"];\n", "n7734cd7f92a34a3bbb223dac592bd496 -> nf51d59c7071c4725a4e961fd017fd0b6;\n", "n7734cd7f92a34a3bbb223dac592bd496 -> nd7f11536d8df400d860ac372d1c3e9f8;\n", "nf51d59c7071c4725a4e961fd017fd0b6 [label=\"bd\\ndaba\"];\n", "nf51d59c7071c4725a4e961fd017fd0b6 -> n48a2b0c66af943439d0c9767e9181c50;\n", "n48a2b0c66af943439d0c9767e9181c50 [label=\"bd\\ndab\"];\n", "n48a2b0c66af943439d0c9767e9181c50 -> nfee98ef394994c0b9664921c73ae7882;\n", "nfee98ef394994c0b9664921c73ae7882 [label=\"bd\\nda\"];\n", "nfee98ef394994c0b9664921c73ae7882 -> n077956a8b783437ba5a65c3fd3380e2f;\n", "n077956a8b783437ba5a65c3fd3380e2f [label=\"bd\\nd\\nFalse\"];\n", "nd7f11536d8df400d860ac372d1c3e9f8 [label=\"bda\\ndaba\"];\n", "nd7f11536d8df400d860ac372d1c3e9f8 -> nb1bf7b9e21a64b30a7a536a9b8649e56;\n", "nd7f11536d8df400d860ac372d1c3e9f8 -> n115e972256cc4394a1eba134f114e4ab;\n", "nb1bf7b9e21a64b30a7a536a9b8649e56 [label=\"bd\\ndab\"];\n", "nb1bf7b9e21a64b30a7a536a9b8649e56 -> nb0329d485ca14bfaa79caa33670a8699;\n", "nb0329d485ca14bfaa79caa33670a8699 [label=\"bd\\nda\"];\n", "nb0329d485ca14bfaa79caa33670a8699 -> ne91eaaeffb1443639b733682718f4092;\n", "ne91eaaeffb1443639b733682718f4092 [label=\"bd\\nd\\nFalse\"];\n", "n115e972256cc4394a1eba134f114e4ab [label=\"bda\\ndab\"];\n", "n115e972256cc4394a1eba134f114e4ab -> na78115224d9f4e37b4045f6c30e4ceb1;\n", "na78115224d9f4e37b4045f6c30e4ceb1 [label=\"bda\\nda\\nFalse\"];\n", "nad799597664c441f9ccedc62f06247bb [label=\"bdab\\ndabaa\"];\n", "nad799597664c441f9ccedc62f06247bb -> n55c3278b1aea4bdc92b3d5eb3c09366c;\n", "n55c3278b1aea4bdc92b3d5eb3c09366c [label=\"bdab\\ndaba\"];\n", "n55c3278b1aea4bdc92b3d5eb3c09366c -> n5d2503b1d062482b898e4682240dcc78;\n", "n5d2503b1d062482b898e4682240dcc78 [label=\"bdab\\ndab\\nFalse\"];\n", "nd6bf8394c44b4af79b2a91534ba13317 [label=\"bdabc\\ndabaab\"];\n", "nd6bf8394c44b4af79b2a91534ba13317 -> ne856116c734a46b1967bddb73c56140f;\n", "ne856116c734a46b1967bddb73c56140f [label=\"bdabc\\ndabaa\"];\n", "ne856116c734a46b1967bddb73c56140f -> ne0497380dcb04eb9b64499dca04e370b;\n", "ne0497380dcb04eb9b64499dca04e370b [label=\"bdabc\\ndaba\\nFalse\"];\n", "na1b07d40913a48a89651e06846c27489 [label=\"bdabcc\\ndabaabca\"];\n", "na1b07d40913a48a89651e06846c27489 -> nf7b9fd837f974551b0795d7492210e52;\n", "nf7b9fd837f974551b0795d7492210e52 [label=\"bdabcc\\ndabaabc\"];\n", "nf7b9fd837f974551b0795d7492210e52 -> n753dfbdd86b543cbb9b246e976d31406;\n", "nf7b9fd837f974551b0795d7492210e52 -> n556f3f77789b40f0b332b55e20828606;\n", "n753dfbdd86b543cbb9b246e976d31406 [label=\"bdabc\\ndabaab\"];\n", "n753dfbdd86b543cbb9b246e976d31406 -> na21720c117704e02910b868caeddb9a9;\n", "na21720c117704e02910b868caeddb9a9 [label=\"bdabc\\ndabaa\"];\n", "na21720c117704e02910b868caeddb9a9 -> nb1bec31f0ddf4a888f941702a407906f;\n", "nb1bec31f0ddf4a888f941702a407906f [label=\"bdabc\\ndaba\\nFalse\"];\n", "n556f3f77789b40f0b332b55e20828606 [label=\"bdabcc\\ndabaab\"];\n", "n556f3f77789b40f0b332b55e20828606 -> n5b6173aea18d41f8b4a2c5ce99cc4d7a;\n", "n5b6173aea18d41f8b4a2c5ce99cc4d7a [label=\"bdabcc\\ndabaa\\nFalse\"];\n" ] } ], "source": [ "root, graph = is_subseq_recursive_dot('bdabcc', 'dabaabcacb')\n", "print('\\n'.join(graph))" ] }, { "cell_type": "code", "execution_count": 30, "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": 31, "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)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "sl1 = make_string(200)\n", "sl2 = make_string(200)\n", "sl3 = make_string(200)\n", "sl12 = interleave(sl1, sl2)\n", "sl23 = interleave(sl2, sl3)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(True, False)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "is_subseq(sl1, sl12), is_subseq(sl1, sl23)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "ename": "KeyboardInterrupt", "evalue": "", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msl1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msl12\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msl1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msl23\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mis_subseq_recursive\u001b[0;34m(s1, s2)\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mis_subseq_recursive\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mKeyboardInterrupt\u001b[0m: " ] } ], "source": [ "is_subseq_recursive(sl1, sl12), is_subseq_recursive(sl1, sl23)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import timeit" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 128 6.601971108466387e-06\n", "2 128 1.1173018720000982e-05\n", "3 128 1.7676036804914474e-05\n", "4 128 2.5538960471749306e-05\n", "5 128 3.5266566555947065e-05\n", "6 128 4.612101474776864e-05\n", "7 128 5.9491489082574844e-05\n", "8 128 7.708946941420436e-05\n", "9 128 9.241350926458836e-05\n", "10 128 0.00011261552572250366\n", "11 128 0.00013369298540055752\n", "12 128 0.00015364354476332664\n", "13 128 0.00018264143727719784\n", "14 128 0.00021015095990151167\n", "15 128 0.0002313450095243752\n", "16 128 0.0002656164579093456\n", "17 128 0.00030093902023509145\n", "18 128 0.00034747645258903503\n", "19 128 0.00038037047488614917\n", "20 128 0.00039016600931063294\n", "21 128 0.0004141985555179417\n", "22 128 0.0004589990130625665\n", "23 128 0.0005071259802207351\n", "24 128 0.000558166007976979\n", "25 128 0.0006022494635544717\n", "26 128 0.000670306442771107\n", "27 128 0.0007114085019566119\n", "28 128 0.0007825554930604994\n", "29 128 0.0008297829772345722\n", "30 128 0.0009118785383179784\n", "31 128 0.0009387695463374257\n", "32 128 0.0010290474747307599\n", "33 128 0.0010991995804943144\n", "34 128 0.001162782427854836\n", "35 128 0.0012630489654839039\n", "36 128 0.0013626019936054945\n", "37 128 0.0013828364899381995\n", "38 128 0.0014394805184565485\n", "39 128 0.0015522410394623876\n", "40 128 0.0016528905252926052\n", "41 128 0.001752416486851871\n", "42 128 0.0018637359025888145\n", "43 128 0.0019305709865875542\n", "44 128 0.0019937875331379473\n", "45 128 0.002114867966156453\n", "46 128 0.0021349010639823973\n", "47 128 0.0022526634857058525\n", "48 128 0.002346995985135436\n", "49 128 0.0024804204585961998\n", "50 128 0.0026001944206655025\n", "51 128 0.0026794440345838666\n", "52 128 0.002824594499543309\n", "53 128 0.0030016429373063147\n", "54 128 0.003160015563480556\n", "55 128 0.00318777997745201\n", "56 128 0.003325541445519775\n", "57 128 0.0034704965073615313\n", "58 128 0.0036058140103705227\n", "59 128 0.0037392310332506895\n", "60 128 0.0037602405063807964\n", "61 128 0.003874778456520289\n", "62 128 0.004084868531208485\n", "63 128 0.004155766975600272\n", "64 128 0.004267089010681957\n", "65 128 0.004337636521086097\n", "66 128 0.0044974255142733455\n", "67 128 0.004694238479714841\n", "68 128 0.004869959433563054\n", "69 128 0.004944236483424902\n", "70 128 0.005068219965323806\n", "71 128 0.005291507521178573\n", "72 128 0.005452780984342098\n", "73 128 0.005550310015678406\n", "74 128 0.005827677552588284\n", "75 128 0.005954194464720786\n", "76 128 0.006162200937978923\n", "77 128 0.006293880462180823\n", "78 128 0.006430666020605713\n", "79 128 0.006628004543017596\n", "80 128 0.006773526547476649\n", "81 128 0.006877631531096995\n", "82 128 0.007066302059683949\n", "83 128 0.007277273049112409\n", "84 128 0.0074174615438096225\n", "85 128 0.007571773545350879\n", "86 128 0.007751822471618652\n", "87 128 0.007897154020611197\n", "88 128 0.008157184987794608\n", "89 128 0.008307107957080007\n", "90 128 0.008498225477524102\n", "91 128 0.008694847987499088\n", "92 128 0.008919386542402208\n", "93 128 0.009161543508525938\n", "94 128 0.00944519997574389\n", "95 128 0.00951321900356561\n", "96 128 0.009540809493046254\n", "97 128 0.010032013524323702\n", "98 128 0.010202373494394124\n", "99 128 0.010228634462691844\n", "100 128 0.010533473512623459\n", "101 128 0.01096995797706768\n", "102 128 0.011132450483273715\n", "103 128 0.01138017192715779\n", "104 128 0.011960987467318773\n", "105 128 0.012275321991182864\n", "106 128 0.01236614998197183\n", "107 128 0.012787212966941297\n", "108 128 0.013005171960685402\n", "109 128 0.013409941457211971\n", "110 128 0.013808032497763634\n" ] } ], "source": [ "times_recorded_dp = {}\n", "cont = True\n", "reps = 128\n", "l = 1\n", "\n", "setup_code = \"\"\"sl1 = make_string(l) ;\n", "sl2 = make_string(l) ;\n", "sl3 = make_string(l) ;\n", "sl12 = interleave(sl1, sl2) ;\n", "sl23 = interleave(sl2, sl3)\"\"\"\n", "\n", "while cont:\n", "\n", " t = timeit.Timer('is_subseq(sl1, sl12)', \n", " 'l = {} ; '.format(l) + setup_code, \n", " globals=globals())\n", " stime = min(t.repeat(reps, number=1))\n", " t = timeit.Timer('is_subseq(sl1, sl23)', \n", " 'l = {} ; '.format(l) + setup_code, \n", " globals=globals())\n", " ftime = min(t.repeat(reps, number=1)) \n", " times_recorded_dp[l] = (stime + ftime ) / 2\n", " print(l, reps, times_recorded_dp[l])\n", " l += 1\n", " if stime * reps > 10:\n", " reps = reps // 2\n", " if reps <= 1:\n", " cont = False\n", " if l > 110:\n", " cont = False\n", " " ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 128 1.4614779502153397e-06\n", "2 128 2.2249878384172916e-06\n", "3 128 3.04199056699872e-06\n", "4 128 3.817433025687933e-06\n", "5 128 4.5790220610797405e-06\n", "6 128 5.405454430729151e-06\n", "7 128 6.143003702163696e-06\n", "8 128 7.1534886956214905e-06\n", "9 128 7.709488272666931e-06\n", "10 128 9.231502190232277e-06\n", "11 128 9.659503120929003e-06\n", "12 128 1.1146999895572662e-05\n", "13 128 1.3675540685653687e-05\n", "14 128 1.4537479728460312e-05\n", "15 128 1.726200571283698e-05\n", "16 128 2.175051486119628e-05\n", "17 128 2.642604522407055e-05\n", "18 128 2.882845001295209e-05\n", "19 128 3.30429757013917e-05\n", "20 128 3.415101673454046e-05\n", "21 128 4.3374544475227594e-05\n", "22 128 4.3387000914663076e-05\n", "23 128 5.406048148870468e-05\n", "24 128 7.064553210511804e-05\n", "25 128 6.675999611616135e-05\n", "26 128 7.653201464563608e-05\n", "27 128 8.046295261010528e-05\n", "28 128 8.30040080472827e-05\n", "29 128 9.860144928097725e-05\n", "30 128 0.00012834451626986265\n", "31 128 0.00012909498764202\n", "32 128 0.00015940150478854775\n", "33 128 0.00017911155009642243\n", "34 128 0.00015924405306577682\n", "35 128 0.00019503897055983543\n", "36 128 0.0002618280122987926\n", "37 128 0.00027317157946527004\n", "38 128 0.0003093755221925676\n", "39 128 0.0003216919722035527\n", "40 128 0.0004375210264697671\n", "41 128 0.000429175968747586\n", "42 128 0.0004322319873608649\n", "43 128 0.00047204853035509586\n", "44 128 0.0005446930299513042\n", "45 128 0.0005909049650654197\n", "46 128 0.0006897440180182457\n", "47 128 0.0006101980106905103\n", "48 128 0.0009493179968558252\n", "49 128 0.0010656820377334952\n", "50 128 0.0010958575294353068\n", "51 128 0.0011784244561567903\n", "52 128 0.0015215784660540521\n", "53 128 0.0016730880015529692\n", "54 128 0.0018497870187275112\n", "55 128 0.0019531224970705807\n", "56 128 0.002047635498456657\n", "57 128 0.002590053016319871\n", "58 128 0.00282047048676759\n", "59 128 0.0028463290072977543\n", "60 128 0.003852981433738023\n", "61 128 0.003954462939873338\n", "62 128 0.005894984060432762\n", "63 128 0.003989071468822658\n", "64 128 0.005397962988354266\n", "65 128 0.005613878485746682\n", "66 128 0.006631733034737408\n", "67 128 0.006388595968019217\n", "68 128 0.008692775038070977\n", "69 128 0.011248551483731717\n", "70 128 0.01025481807300821\n", "71 128 0.012467472988646477\n", "72 128 0.012154755007941276\n", "73 128 0.01328759198077023\n", "74 128 0.014517615491058677\n", "75 128 0.014188894943799824\n", "76 128 0.02000475104432553\n", "77 128 0.008263764902949333\n", "78 128 0.027680979983415455\n", "79 128 0.026263607025612146\n", "80 128 0.029358336003497243\n", "81 128 0.019039819424506277\n", "82 128 0.030424615542870015\n", "83 128 0.05704057845287025\n", "84 64 0.054549605934880674\n", "85 64 0.10833553707925603\n", "86 32 0.07274995249463245\n", "87 32 0.1189103105571121\n", "88 32 0.11648729699663818\n", "89 32 0.08882703294511884\n", "90 32 0.16369645803933963\n", "91 16 0.37688057048944756\n", "92 8 0.20311490900348872\n", "93 8 0.13178699905984104\n", "94 8 0.6466444740071893\n", "95 4 0.9140647805761546\n", "96 4 1.9596780224819668\n", "97 2 2.149461797962431\n", "98 2 1.419025840528775\n", "99 2 0.9921340015134774\n", "100 2 0.9624096675543115\n", "101 2 1.5941892554983497\n", "102 2 1.6760708974907175\n", "103 2 2.177948990953155\n", "104 2 12.678528299031314\n" ] } ], "source": [ "times_recorded_r = {}\n", "cont = True\n", "reps = 128\n", "l = 1\n", "\n", "setup_code = \"\"\"sl1 = make_string(l) ;\n", "sl2 = make_string(l) ;\n", "sl3 = make_string(l) ;\n", "sl12 = interleave(sl1, sl2) ;\n", "sl23 = interleave(sl2, sl3)\"\"\"\n", "\n", "while cont:\n", "# stime = timeit.timeit('is_subseq_recursive(sl1, sl12)', \n", "# 'l = {} ; '.format(l) + setup_code, \n", "# globals=globals(), number=reps) / reps\n", "# ftime = timeit.timeit('is_subseq_recursive(sl1, sl23)', \n", "# 'l = {} ; '.format(l) + setup_code, \n", "# globals=globals(), number=reps) / reps\n", " t = timeit.Timer('is_subseq_recursive(sl1, sl12)', \n", " 'l = {} ; '.format(l) + setup_code, \n", " globals=globals())\n", " stime = min(t.repeat(reps,number=1))\n", " t = timeit.Timer('is_subseq_recursive(sl1, sl23)', \n", " 'l = {} ; '.format(l) + setup_code, \n", " globals=globals())\n", " ftime = min(t.repeat(reps, number=1)) \n", " times_recorded_r[l] = (stime + ftime ) / 2\n", " print(l, reps, times_recorded_r[l])\n", " l += 1\n", " if stime * reps > 10:\n", " reps = reps // 2\n", " if reps <= 1:\n", " cont = False\n", " " ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 128 8.884817361831665e-07\n", "2 128 2.034998033195734e-06\n", "3 128 2.758519258350134e-06\n", "4 128 3.492517862468958e-06\n", "5 128 4.411558620631695e-06\n", "6 128 4.7970679588615894e-06\n", "7 128 5.636480636894703e-06\n", "8 128 6.429501809179783e-06\n", "9 128 8.435978088527918e-06\n", "10 128 8.897040970623493e-06\n", "11 128 9.417475666850805e-06\n", "12 128 1.0774005204439163e-05\n", "13 128 1.4505523722618818e-05\n", "14 128 1.56490714289248e-05\n", "15 128 1.618947135284543e-05\n", "16 128 2.0946492440998554e-05\n", "17 128 2.3907457944005728e-05\n", "18 128 2.4928071070462465e-05\n", "19 128 2.8219015803188086e-05\n", "20 128 3.5653007216751575e-05\n", "21 128 3.706448478624225e-05\n", "22 128 4.079949576407671e-05\n", "23 128 4.724744940176606e-05\n", "24 128 5.7765981182456017e-05\n", "25 128 7.110205478966236e-05\n", "26 128 6.68570282869041e-05\n", "27 128 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min(t.repeat(reps, number=1))\n", " t = timeit.Timer('is_subseq_recursive_2(sl1, sl23)', \n", " 'l = {} ; '.format(l) + setup_code, \n", " globals=globals())\n", " ftime = min(t.repeat(reps, number=1))\n", " times_recorded_r2[l] = (stime + ftime ) / 2\n", " print(l, reps, times_recorded_r2[l])\n", " l += 1\n", " if stime * reps > 10:\n", " reps = reps // 2\n", " if reps <= 1:\n", " cont = False\n", " " ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "{1: 8.884817361831665e-07,\n", " 2: 2.034998033195734e-06,\n", " 3: 2.758519258350134e-06,\n", " 4: 3.492517862468958e-06,\n", " 5: 4.411558620631695e-06,\n", " 6: 4.7970679588615894e-06,\n", " 7: 5.636480636894703e-06,\n", " 8: 6.429501809179783e-06,\n", " 9: 8.435978088527918e-06,\n", " 10: 8.897040970623493e-06,\n", " 11: 9.417475666850805e-06,\n", " 12: 1.0774005204439163e-05,\n", " 13: 1.4505523722618818e-05,\n", " 14: 1.56490714289248e-05,\n", " 15: 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}, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pandas as pd\n", "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline " ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " dp r1 r2\n", "1 0.000006 0.000001 8.884817e-07\n", "2 0.000010 0.000002 2.034998e-06\n", "3 0.000016 0.000003 2.758519e-06\n", "4 0.000024 0.000004 3.492518e-06\n", "5 0.000032 0.000005 4.411559e-06\n", "6 0.000041 0.000005 4.797068e-06\n", "7 0.000053 0.000006 5.636481e-06\n", "8 0.000067 0.000007 6.429502e-06\n", "9 0.000085 0.000008 8.435978e-06\n", "10 0.000100 0.000009 8.897041e-06\n", "11 0.000115 0.000010 9.417476e-06\n", "12 0.000140 0.000011 1.077401e-05\n", "13 0.000162 0.000014 1.450552e-05\n", "14 0.000183 0.000015 1.564907e-05\n", "15 0.000215 0.000017 1.618947e-05\n", "16 0.000242 0.000022 2.094649e-05\n", "17 0.000266 0.000026 2.390746e-05\n", "18 0.000306 0.000029 2.492807e-05\n", "19 0.000346 0.000033 2.821902e-05\n", "20 0.000385 0.000034 3.565301e-05\n", "21 0.000415 0.000043 3.706448e-05\n", "22 0.000463 0.000043 4.079950e-05\n", "23 0.000494 0.000054 4.724745e-05\n", "24 0.000523 0.000071 5.776598e-05\n", "25 0.000582 0.000067 7.110205e-05\n", "26 0.000651 0.000077 6.685703e-05\n", "27 0.000710 0.000080 7.095095e-05\n", "28 0.000752 0.000083 9.183702e-05\n", "29 0.000825 0.000099 9.083998e-05\n", "30 0.000878 0.000128 1.272025e-04\n", ".. ... ... ...\n", "75 0.005947 0.014189 1.939319e-02\n", "76 0.006030 0.020005 2.004181e-02\n", "77 0.006158 0.008264 2.844302e-02\n", "78 0.006392 0.027681 1.740247e-02\n", "79 0.006637 0.026264 2.905736e-02\n", "80 0.006664 0.029358 2.609148e-02\n", "81 0.006705 0.019040 2.800373e-02\n", "82 0.006991 0.030425 3.854370e-02\n", "83 0.007352 0.057041 4.743193e-02\n", "84 0.007388 0.054550 5.365823e-02\n", "85 0.007670 0.108336 7.952621e-02\n", "86 0.007745 0.072750 1.124436e-01\n", "87 0.008001 0.118910 8.979999e-02\n", "88 0.008151 0.116487 1.257425e-01\n", "89 0.008254 0.088827 1.086573e-01\n", "90 0.008464 0.163696 1.978011e-01\n", "91 0.008546 0.376881 2.107999e-01\n", "92 0.008675 0.203115 2.024802e-01\n", "93 0.009046 0.131787 4.154621e-01\n", "94 0.009209 0.646644 2.825372e-01\n", "95 0.009408 0.914065 3.404359e-01\n", "96 0.009638 1.959678 9.467042e-01\n", "97 0.009727 2.149462 2.073050e+00\n", "98 0.009999 1.419026 9.190455e-01\n", "99 0.010274 0.992134 5.788109e-01\n", "100 0.010565 0.962410 2.735283e+00\n", "101 NaN 1.594189 1.871398e+00\n", "102 NaN 1.676071 2.684198e+00\n", "103 NaN 2.177949 1.615787e+00\n", "104 NaN 12.678528 4.937538e+00\n", "\n", "[104 rows x 3 columns]" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "time_df = pd.DataFrame([times_recorded_dp, times_recorded_r, times_recorded_r2]).T\n", "time_df.columns = ['dp', 'r1', 'r2']\n", "time_df" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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