},
{
"cell_type": "code",
- "execution_count": 54,
+ "execution_count": 33,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "import random"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
"metadata": {
"collapsed": true
},
},
{
"cell_type": "code",
- "execution_count": 47,
+ "execution_count": 7,
"metadata": {},
"outputs": [
{
" (4, 7): (4, 6, 'b', 's2')}"
]
},
- "execution_count": 47,
+ "execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
},
{
"cell_type": "code",
- "execution_count": 59,
+ "execution_count": 8,
"metadata": {
"collapsed": true
},
" 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",
+ " while i != 0 and j != 0:\n",
" if bps[i, j][3] == 's1':\n",
" chars += bps[i, j][2].upper()\n",
" else:\n",
},
{
"cell_type": "code",
- "execution_count": 60,
+ "execution_count": 9,
"metadata": {},
"outputs": [
{
"'AAAbAbb'"
]
},
- "execution_count": 60,
+ "execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
},
{
"cell_type": "code",
- "execution_count": 49,
- "metadata": {},
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": true
+ },
"outputs": [],
"source": [
- "def is_subseq(seq1, seq2, return_backpointers=False, debug=False):\n",
+ "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",
" 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",
+ "# 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": 39,
- "metadata": {},
+ "execution_count": 12,
+ "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": 39,
+ "execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "is_subseq(s1, s2t)"
+ "is_subseq(s1, s2t, debug=True)"
]
},
{
"cell_type": "code",
- "execution_count": 55,
+ "execution_count": 13,
+ "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": 14,
"metadata": {},
"outputs": [
{
"True"
]
},
- "execution_count": 55,
+ "execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "tf, bps = is_subseq(s1, s2t, return_backpointers=True)\n",
+ "tf, bps, tb = is_subseq(s1, s2t, return_backpointers=True, return_table=True)\n",
"tf"
]
},
{
"cell_type": "code",
- "execution_count": 56,
+ "execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
- "'AABCaCb'"
+ "'AbAAbcAcb'"
]
},
- "execution_count": 56,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
},
{
"cell_type": "code",
- "execution_count": 42,
+ "execution_count": 16,
+ "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": 17,
+ "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": 18,
"metadata": {},
"outputs": [
{
"False"
]
},
- "execution_count": 42,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "is_subseq(s1, s2f)"
+ "len(show_backtrace(bps)) == len(s2t)"
]
},
{
"cell_type": "code",
- "execution_count": 43,
+ "execution_count": 19,
"metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "('aaaa', 'dabaabcacb')"
+ ]
+ },
+ "execution_count": 19,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "s1, s2t"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "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": 20,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "bps"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "False"
+ ]
+ },
+ "execution_count": 21,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "is_subseq(s1, s2f)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "scrolled": true
+ },
"outputs": [
{
"name": "stdout",
"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, 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, 5, 'a', 's1'),\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, 2, 'a', 's1'),\n",
- " (2, 3): (1, 3, 'a', 's1'),\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, 5, 'a', 's1'),\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, 3, 'a', 's1'),\n",
+ " (3, 3): (2, 2, 'a', 's1'),\n",
" (3, 4): (3, 3, 'b', 's2'),\n",
- " (3, 5): (2, 5, 'a', 's1'),\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, 5, 'a', 's1'),\n",
+ " (4, 5): (3, 4, 'a', 's1'),\n",
" (4, 6): (4, 5, 'b', 's2'),\n",
" (4, 7): (4, 6, 'b', 's2')})"
]
},
- "execution_count": 43,
+ "execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
"is_subseq('aaaa', 'aaababb', return_backpointers=True, debug=True)"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def is_subseq_recursive(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": 29,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "True"
+ ]
+ },
+ "execution_count": 29,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "is_subseq_recursive(s1, s2t)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "False"
+ ]
+ },
+ "execution_count": 28,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "is_subseq_recursive(s1, s2f)"
+ ]
+ },
+ {
+ "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": 40,
+ "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": 41,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(True, False)"
+ ]
+ },
+ "execution_count": 41,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "is_subseq(sl1, sl12), is_subseq(sl1, sl23)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "is_subseq_recursive(sl1, sl12), is_subseq_recursive(sl1, sl23)"
+ ]
+ },
{
"cell_type": "code",
"execution_count": null,
projects / ou-summer-of-code-2017.git / blobdiff