algorithms/longest-string-that-is-substring-of-x-and-subsequence-of-y.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lcs(x: str, y: str) -> int:\n",
    "    n = len(x)\n",
    "    m = len(y)\n",
    "    \n",
    "    # initialize table to zeros\n",
    "    l = np.zeros((n + 1, m + 1))\n",
    "    \n",
    "    for i in range(1, n + 1):\n",
    "        for j in range(1, m + 1):\n",
    "            if x[i - 1] == y[j - 1]:\n",
    "                l[i, j] = 1 + l[i - 1, j - 1]\n",
    "            else:\n",
    "                l[i, j] = l[i, j - 1]\n",
    "    \n",
    "    # return the max of the last column\n",
    "    return l[:, m].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lcs('abdbabfgd', 'betfdbfafr')"
   ]
  }
 ],
 "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}