# Edit Distance

Edit distance is a classic alogrithm, it uses dynamic programming method. Let to be the minimum edit distance to modify str1[0..i] to str2[0..j]. Then we will have four iteration case in this problem:

1. If we insert a character,
2. If we delete a character,
3. If we replace a character,
4. If the next character is the same,

We pick the minimum of the four cases at last. The final result will be .

public class EditDistance {
public int minDistance(String word1, String word2) {
char[] w1 = word1.toCharArray();
char[] w2 = word2.toCharArray();

int[][] dp = new int[w1.length + 1][w2.length + 1];

for (int i = 0; i <= w1.length; i++) {
for (int j = 0; j <= w2.length; j++) {
if (i == 0 && j == 0) {
continue;
} else if (i == 0) {
dp[i][j] = dp[i][j - 1] + 1;
} else if (j == 0) {
dp[i][j] = dp[i - 1][j] + 1;
} else {
int replace = (w1[i - 1] == w2[j - 1] ? 0 : 1);
dp[i][j] = Math.min(dp[i - 1][j - 1] + replace, Math.min(dp[i - 1][j], dp[i][j - 1]) + 1);
}
}
}

return dp[w1.length][w2.length];
}
}