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:
a) Insert a character
b) Delete a character
c) Replace a character
reference: https://www.youtube.com/watch?v=Uv9dNpHlSY4
Solution：DP
思路：
Screen Shot 2017-11-23 at 17.23.58.png
Time Complexity: O(mn) Space Complexity: O(mn)
Solution Code：
class Solution {
public int minDistance(String word1, String word2) {
int m = word1.length();
int n = word2.length();
int[][] dist = new int[m + 1][n + 1];
// init
for(int i = 0; i <= m; i++) dist[i][0] = i;
for(int j = 0; j <= n; j++) dist[0][j] = j;
for(int i = 1; i <= m; i++) {
for(int j = 1; j <= n; j++) {
dist[i][j] = Integer.MAX_VALUE;
}
}
// start dp
for(int i = 1; i <= m; i++) {
for(int j = 1; j <= n; j++) {
// (1) and (2)
dist[i][j] = Math.min(dist[i][j - 1], dist[i - 1][j]) + 1;
// (3)
if(word1.charAt(i - 1) == word2.charAt(j - 1)) {
dist[i][j] = Math.min(dist[i][j], dist[i - 1][j - 1]);
}
else {
dist[i][j] = Math.min(dist[i][j], dist[i - 1][j - 1] + 1);
}
}
}
return dist[m][n];
}
}
