Edit Distance

于 2015-06-29 18:23:58 发布 · 59 阅读

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本文介绍了一种求解两字符串间转换所需的最小操作步骤的算法。通过插入、删除或替换字符实现转换，利用动态规划的方法高效计算出最短路径。

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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

public class Solution {
    public int minDistance(String word1, String word2) {
        if (word1 == null || word2 == null) {
        	return 0;
        }
        int row = word1.length() + 1;
        int col = word2.length() + 1;
        int[][] dp = new int[row][col];
        for (int i = 1; i < row; i++) {
			dp[i][0] = i;
		}
        for (int i = 1; i < col; i++) {
			dp[0][i] = i;
		}
        for (int i = 1; i < row; i++) {
			for (int j = 1; j < col; j++) {
				if (word1.charAt(i-1) == word2.charAt(j-1)) {
					dp[i][j] = dp[i-1][j-1];
				} else {
					dp[i][j] = dp[i-1][j-1] + 1;
				}
				dp[i][j] = Math.min(dp[i][j], dp[i][j-1] + 1);
				dp[i][j] = Math.min(dp[i][j], dp[i-1][j] + 1);
			}
		}
        return dp[row-1][col-1];
    }
}