Leetcode 72. Edit Distance

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题目描述

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

输入：两个字符串word1, word2
输出：需要修改、删除、插入的次数

思路

动态规划：用L(i,j)表示word1[0:i]与word2[0:j]的编辑距离

for i = 0，1, 2, ..., m:    L(i,0) = ifor j = 0，1, 2, ..., n:    L(0,j) = jfor i = 0，1, 2, ..., m:    for j = 0，1, 2, ..., n:        L(i,j) = min(L(i-1,j)+1, L(i,j-1)+1, diff+L(i-1,j-1))return L(m,n)

代码

class Solution {public:    int minDistance(string word1, string word2) {        if(word2.length()==0||word1.length()==0) return max(word2.length(),word1.length());        int L[word1.length()+1][word2.length()+1];        for(int i =0;i<=word1.length();i++)            L[i][0] = i;        for(int j =0;j<=word2.length();j++)            L[0][j] = j;        for(int i = 1;i<=word1.length();i++){            for(int j =1;j<=word2.length();j++){                if(j>=1&&i>=1){                    int diff = (word1[i-1]!=word2[j-1]);                    L[i][j] = min(min(1+L[i-1][j],1+L[i][j-1]),diff+L[i-1][j-1]);                }            }        }        return L[word1.length()][word2.length()];    }};