--- /dev/null
+{
+ "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": 54,
+ "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": 4,
+ "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": 4,
+ "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": 5,
+ "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": 6,
+ "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": 47,
+ "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": 47,
+ "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": 59,
+ "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] == '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": 60,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'AAAbAbb'"
+ ]
+ },
+ "execution_count": 60,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "show_backtrace(backpointers)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 49,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def is_subseq(seq1, seq2, return_backpointers=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)]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 39,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "True"
+ ]
+ },
+ "execution_count": 39,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "is_subseq(s1, s2t)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 55,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "True"
+ ]
+ },
+ "execution_count": 55,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "tf, bps = is_subseq(s1, s2t, return_backpointers=True)\n",
+ "tf"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 56,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "'AABCaCb'"
+ ]
+ },
+ "execution_count": 56,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "show_backtrace(bps)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "False"
+ ]
+ },
+ "execution_count": 42,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "is_subseq(s1, s2f)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {},
+ "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, 1, 'a', 's1'),\n",
+ " (1, 2): (0, 2, 'a', 's1'),\n",
+ " (1, 3): (0, 3, 'a', 's1'),\n",
+ " (1, 4): (1, 3, 'b', 's2'),\n",
+ " (1, 5): (0, 5, 'a', 's1'),\n",
+ " (1, 6): (1, 5, 'b', 's2'),\n",
+ " (1, 7): (1, 6, 'b', 's2'),\n",
+ " (2, 2): (1, 2, 'a', 's1'),\n",
+ " (2, 3): (1, 3, 'a', 's1'),\n",
+ " (2, 4): (2, 3, 'b', 's2'),\n",
+ " (2, 5): (1, 5, 'a', 's1'),\n",
+ " (2, 6): (2, 5, 'b', 's2'),\n",
+ " (2, 7): (2, 6, 'b', 's2'),\n",
+ " (3, 3): (2, 3, 'a', 's1'),\n",
+ " (3, 4): (3, 3, 'b', 's2'),\n",
+ " (3, 5): (2, 5, 'a', 's1'),\n",
+ " (3, 6): (3, 5, 'b', 's2'),\n",
+ " (3, 7): (3, 6, 'b', 's2'),\n",
+ " (4, 5): (3, 5, 'a', 's1'),\n",
+ " (4, 6): (4, 5, 'b', 's2'),\n",
+ " (4, 7): (4, 6, 'b', 's2')})"
+ ]
+ },
+ "execution_count": 43,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "is_subseq('aaaa', 'aaababb', return_backpointers=True, debug=True)"
+ ]
+ },
+ {
+ "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
+}
projects / ou-summer-of-code-2017.git / blobdiff