Edit Distance

Description:

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:

class Solution {
public:    
	/**
	 * @param word1 & word2: Two string.
	 * @return: The minimum number of steps.
	 */
	int minDistance(string word1, string word2) {
		auto len1 = (int)word1.length();
		auto len2 = (int)word2.length();
		if (len1 == 0) return len2;
		if (len2 == 0) return len1;
		vector<int> pre(len2+1, 0);
		vector<int> cur(len2+1, 0);
		for (int i = 0; i <= len2; ++i) pre[i] = i;
		for (int i = 1; i <= len1; ++i) {
			cur[0] = i;
			for (int j = 1; j <= len2; ++j) {
				if (word1[i-1] == word2[j-1]) cur[j] = pre[j-1];
				else cur[j] = min(cur[j-1], min(pre[j], pre[j-1]))+1;
				pre[j-1] = cur[j-1];
			}
			pre[len2] = cur[len2];
		}
		return cur[len2];
	}
};