diff --git a/Dynamic-Programming/EditDistance.js b/Dynamic-Programming/EditDistance.js new file mode 100644 index 0000000000..ac554d8b56 --- /dev/null +++ b/Dynamic-Programming/EditDistance.js @@ -0,0 +1,61 @@ +/* +Wikipedia -> https://en.wikipedia.org/wiki/Edit_distance + +Q. -> Given two strings `word1` and `word2`. You can perform these operations on any of the string to make both strings similar. + - Insert + - Remove + - Replace +Find the minimum operation cost required to make both same. Each operation cost is 1. + +Algorithm details -> +time complexity - O(n*m) +space complexity - O(n*m) +*/ + +const minimumEditDistance = (word1, word2) => { + const n = word1.length + const m = word2.length + const dp = new Array(m + 1).fill(0).map(item => []) + + /* + fill dp matrix with default values - + - first row is filled considering no elements in word2. + - first column filled considering no elements in word1. + */ + + for (let i = 0; i < n + 1; i++) { + dp[0][i] = i + } + + for (let i = 0; i < m + 1; i++) { + dp[i][0] = i + } + + /* + indexing is 1 based for dp matrix as we defined some known values at first row and first column/ + */ + + for (let i = 1; i < m + 1; i++) { + for (let j = 1; j < n + 1; j++) { + const letter1 = word1[j - 1] + const letter2 = word2[i - 1] + + if (letter1 === letter2) { + dp[i][j] = dp[i - 1][j - 1] + } else { + dp[i][j] = Math.min(dp[i - 1][j], dp[i - 1][j - 1], dp[i][j - 1]) + 1 + } + } + } + + return dp[m][n] +} + +const main = () => { + console.log(minimumEditDistance('horse', 'ros')) + console.log(minimumEditDistance('cat', 'cut')) + console.log(minimumEditDistance('', 'abc')) + console.log(minimumEditDistance('google', 'glgool')) +} + +main()