leetcode Edit Distance
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题目
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
题目来源:https://leetcode.com/problems/edit-distance/
分析
动态规划。既然允许三种操作:插入、删除和替换,那么就三个操作都做然后选取一种最小的。dp[i][j]表示word1前i个字符和word2前j个字符之间的最小距离,递推公式就是:
如果word1的第i个字符和word2的第j个字符相同;
dp[i][j] = dp[i-1][j-1]
否则
dp[i][j] = min(dp[i-1][j-1]+1, dp[i-1][j] + 1, dp[i][j-1] + 1)
dp[i-1][j-1]+1表示增加一次替换操作;
dp[i-1][j]+1表示word2执行insert操作或者word1执行delete操作;
dp[i][j-1]+1表示word1执行insert操作或者word2执行delete操作。
代码
class Solution {public: int minDistance(string word1, string word2) { int len1 = word1.length() + 1; int len2 = word2.length() + 1; vector<vector<int> > dp(len1, vector<int>(len2, 0)); for(int i = 0; i < len1; i++){ dp[i][0] = i; } for(int i = 0; i < len2; i++){ dp[0][i] = i; } for(int i = 1; i < len1; i++){ for(int j = 1; j < len2; j++){ if(word1.at(i-1) == word2.at(j-1)) dp[i][j] = dp[i-1][j-1]; else dp[i][j] = min(dp[i-1][j-1]+1, min(dp[i-1][j] + 1, dp[i][j-1] + 1)); } } return dp[len1-1][len2-1]; }};
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