Edit Distance

Author: ignacio-chiazzo

LeetcodeProblems/Edit_Distance.js

@@ -0,0 +1,118 @@
+/*
+Edit Distance
+https://leetcode.com/problems/edit-distance/
+
+Given two words word1 and word2, find the minimum number of operations required to convert word1 to word2.
+
+You have the following 3 operations permitted on a word:
+
+Insert a character
+Delete a character
+Replace a character
+Example 1:
+
+Input: word1 = "horse", word2 = "ros"
+Output: 3
+Explanation: 
+horse -> rorse (replace 'h' with 'r')
+rorse -> rose (remove 'r')
+rose -> ros (remove 'e')
+Example 2:
+
+Input: word1 = "intention", word2 = "execution"
+Output: 5
+Explanation: 
+intention -> inention (remove 't')
+inention -> enention (replace 'i' with 'e')
+enention -> exention (replace 'n' with 'x')
+exention -> exection (replace 'n' with 'c')
+exection -> execution (insert 'u')
+
+*/
+
+// Optimal solution
+var minDistance = function(word1, word2) {
+  var matrix = [];
+  for(var i = 0; i <= word1.length; i++) {
+      matrix[i] = [];
+      for(var j = 0; j <= word2.length; j++) {
+          if(i === 0) {
+              matrix[i][j] = j;
+          } else if(j === 0){
+              matrix[i][j] = i;
+          } else {
+              matrix[i][j] = 0;
+          }
+      }
+  };
+  
+  for(var i = 1; i <= word1.length; i++) {
+      for(var j = 1; j <= word2.length; j++) {
+          if(word1.charAt(i - 1) === word2.charAt(j - 1)) {
+              matrix[i][j] = matrix[i - 1][j - 1];
+          } else {
+              matrix[i][j] = 1 + min(
+                  matrix[i - 1][j - 1],
+                  matrix[i - 1][j], // add
+                  matrix[i][j - 1]  // remove
+              );   
+          }
+      }
+  }
+  
+  return matrix[word1.length][word2.length];
+};
+
+var min = function(a, b, c) {
+  if(a < b) {
+      return (a < c) ? a : c;
+  }
+  return (b < c) ? b : c;
+}
+
+//Solution 2
+var minDistance2 = function(word1, word2) {
+  return minDistanceAux(word1, word2, 0, 0);
+}
+
+var minDistanceAux = function(word1, word2, iter1, iter2) {
+ if(word1.length === iter1) {
+     return word2.length - iter2;
+ }
+  
+ if(word2.length === iter2) {
+     return word1.length - iter1;
+ }
+  
+ if(word1.charAt(iter1) === word2.charAt(iter2)) {
+     return minDistanceAux(word1, word2, iter1 + 1, iter2 + 1);
+ }
+  
+ return 1 + min(
+     minDistanceAux(word1, word2, iter1 + 1, iter2 + 1),
+     minDistanceAux(word1, word2, iter1, iter2 + 1), // add
+     minDistanceAux(word1, word2, iter1 + 1, iter2 ) // delete
+ )
+};
+
+var min = function(a, b, c) {
+  if(a < b) {
+      return (a < c) ? a : c;
+  }
+  return (b < c) ? b : c;
+}
+
+var main = function() {
+  console.log("-------------");
+  console.log("Approach 1");
+  console.log(minDistance("ros", "horse"));
+  console.log(minDistance("intention", "execution"));
+  console.log("-------------");
+  console.log("Approach 2");
+  console.log(minDistance2("ros", "horse"));
+  console.log(minDistance2("intention", "execution"));
+}
+
+main();
+
+module.exports.main = main;