[chore] replace py file with notebook

dynamic-programming/levenshtein_distance.ipynb

@@ -0,0 +1,147 @@
+{
+ "metadata": {
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.0-final"
+  },
+  "orig_nbformat": 2,
+  "kernelspec": {
+   "name": "python3",
+   "display_name": "Python 3.9.0 64-bit",
+   "metadata": {
+    "interpreter": {
+     "hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49"
+    }
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2,
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\"\"\"\n",
+    "Write a function that takes in two strings and returns the minimal number of edit\n",
+    "operations that need to be performed on the first string to get the second string.\n",
+    "Edit Operations include: insertion, deletion and substitition.\n",
+    "\n",
+    "\n",
+    "Sample input: str1: \"abc\", str2: \"yabd\"\n",
+    "Sample output: 2\n",
+    "Explanation: insert \"y\", substitute: \"c\" for \"d\"\n",
+    "\n",
+    "\"\"\"\n",
+    "\n",
+    "def levenshtein_distance(str1, str2):\n",
+    "    \"\"\"\n",
+    "    Complexity:\n",
+    "        Time: O(nm)\n",
+    "        Space: O(nm), We can use dynamic programming to improve on the space\n",
+    "        complexity.\n",
+    "    \"\"\"\n",
+    "    edits = [[col for col in range(len(str2) + 1)] for row in range(len(str1) + 1)]\n",
+    "    # [\n",
+    "    #  [0, 1, 2, 3, 4]\n",
+    "    #  [ ... ]\n",
+    "    # ]\n",
+    "\n",
+    "\n",
+    "    for row in range(1, len(str1) + 1):\n",
+    "    # make the first value of each row to be 1, 2, 3, 4, ...\n",
+    "    # [ [0, 1, 2, ..],\n",
+    "    #   [1, ...]\n",
+    "    #   [2, ...]\n",
+    "    #   [3, ...] ]\n",
+    "\n",
+    "        edits[row][0] = edits[row - 1][0] + 1\n",
+    "\n",
+    "    # iterate through the 2 dimensional array\n",
+    "    for row in range(1, len(str1) + 1):\n",
+    "        for col in range(1, len(str2) + 1):\n",
+    "            if str1[row - 1] == str2[col - 1]:\n",
+    "                edits[row][col] = edits[row - 1][col - 1]\n",
+    "            else:\n",
+    "                edits[row][col] = 1 + min(\n",
+    "                    edits[row - 1][col],\n",
+    "                    edits[row][col - 1],\n",
+    "                    edits[row - 1][col - 1]\n",
+    "                )\n",
+    "\n",
+    "    # return the bottom right value of the two-dim array\n",
+    "    return edits[-1][-1]\n",
+    "\n",
+    "\n",
+    "def levenshtein_distance_efficient(str1, str2):\n",
+    "    \"\"\"\n",
+    "        Complexity:\n",
+    "            Time: O(nm) where n = length of str1, and m = length of str2\n",
+    "            Space: O(min(m, n))\n",
+    "    \"\"\"\n",
+    "    small = str1 if len(str1) < len(str2) else str2\n",
+    "    big = str1 if len(str1) >= len(str2) else str2\n",
+    "\n",
+    "    even_edits = [x for x in range(len(small) + 1)]\n",
+    "    odd_edits = [None for x in range(len(small) + 1)]\n",
+    "\n",
+    "    for i in range(len(big) + 1):\n",
+    "        if i % 2 == 1:\n",
+    "            # current edits are odd edits\n",
+    "            current_edits, previous_edits = odd_edits, even_edits\n",
+    "        else:\n",
+    "            # curent_edits are even edits\n",
+    "            current_edits, previous_edits = even_edits, odd_edits\n",
+    "\n",
+    "        # for the first element, make it each equal to i\n",
+    "        current_edits[0] = i\n",
+    "\n",
+    "        for j in range(1, len(small) + 1):\n",
+    "            if big[i - 1] == small[j - 1]:\n",
+    "                current_edits[j] = previous_edits[j - 1]\n",
+    "            else:\n",
+    "                current_edits[j] = 1 + min(\n",
+    "                    previous_edits[j - 1], previous_edits[j], current_edits[j - 1]\n",
+    "                )\n",
+    "    return even_edits[-1] if len(big) % 2 == 0 else odd_edits[-1]\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "2"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 2
+    }
+   ],
+   "source": [
+    "levenshtein_distance(\"abc\", \"yabd\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ]
+}