Given two words *word1* and *word2*, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.)

You have the following 3 operations permitted on a word:

- Insert a character
- Delete a character
- Replace a character

**Example**

Given word1 = `"mart"`

and word2 = `"karma"`

, return `3`

.

Solution: Dynamic Programming

f[i][j] = MIN(f[i-1][j-1], f[i-1][j]+1, f[i][j-1]+1) // a[i] == b[j]

= MIN(f[i-1][j], f[i][j-1], f[i-1][j-1]) + 1 // a[i] != b[j]

intialize: f[i][0] = i, f[0][j] = j

answer: f[a.length()][b.length()]

public int minDistance(String word1, String word2) { if (word1 == null || word2 == null) { return -1; } //minDistance[i][j] = minimum distance to convert first i chars of word 1 //to first j chars of word 2 int[][] minDistance = new int[word1.length() + 1][word2.length() + 1]; //init the first column -- word2 is empty for (int i = 0; i < minDistance.length; i++) { minDistance[i][0] = i; } //init the first row -- word1 is empty for (int j = 0; j < minDistance[0].length; j++) { minDistance[0][j] = j; } for (int i = 1; i <= word1.length(); i++) { for (int j = 1; j <= word2.length(); j++) { if (word1.charAt(i - 1) == word2.charAt(j - 1)) { minDistance[i][j] = Math.min(Math.min(minDistance[i - 1][j - 1], minDistance[i - 1][j] + 1), minDistance[i][j - 1] + 1); } else { minDistance[i][j] = Math.min(Math.min(minDistance[i - 1][j - 1], minDistance[i - 1][j]), minDistance[i][j - 1]) + 1; } } } return minDistance[word1.length()][word2.length()]; }