lcs

lcs.ipynb

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   "metadata": {},
   "source": [
    "Modified from http://rosettacode.org/wiki/Longest_common_subsequence#Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "def lcsRF(xstr, ystr):\n",
    "    if not xstr or not ystr:\n",
    "        return \"\"\n",
    "    x, xs, y, ys = xstr[0], xstr[1:], ystr[0], ystr[1:]\n",
    "    if x == y:\n",
    "        return x + lcsRF(xs, ys)\n",
    "    else:\n",
    "        return max(lcsRF(xstr, ys), lcsRF(xs, ystr), key=len)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tsitest'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lcsRF('thisisatest', 'testing123testing')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def lcsRB(xstr, ystr):\n",
    "    if not xstr or not ystr:\n",
    "        return \"\"\n",
    "    x, xs, y, ys = xstr[len(xstr)-1], xstr[:len(xstr)-1], ystr[len(ystr)-1], ystr[:len(ystr)-1]\n",
    "    if x == y:\n",
    "        return lcsRB(xs, ys) +  x \n",
    "    else:\n",
    "        return max(lcsRB(xstr, ys), lcsRB(xs, ystr), key=len)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tsitest'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lcsRB('thisisatest', 'testing123testing')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def lcsDP(a, b):\n",
    "    lengths = [[0 for j in range(len(b)+1)] for i in range(len(a)+1)]\n",
    "    # row 0 and column 0 are initialized to 0 already\n",
    "    for i, x in enumerate(a):\n",
    "        for j, y in enumerate(b):\n",
    "            if x == y:\n",
    "                lengths[i+1][j+1] = lengths[i][j] + 1\n",
    "            else:\n",
    "                lengths[i+1][j+1] = \\\n",
    "                    max(lengths[i+1][j], lengths[i][j+1])\n",
    "    # read one the substring out from the matrix\n",
    "    result = \"\"\n",
    "    x, y = len(a), len(b)\n",
    "    while x != 0 and y != 0:\n",
    "        if lengths[x][y] == lengths[x-1][y]:\n",
    "            x -= 1\n",
    "        elif lengths[x][y] == lengths[x][y-1]:\n",
    "            y -= 1\n",
    "        else:\n",
    "            assert a[x-1] == b[y-1]\n",
    "            result = a[x-1] + result\n",
    "            x -= 1\n",
    "            y -= 1\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tsitest'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lcsDP('thisisatest', 'testing123testing')"
   ]
  }
 ],
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