1 class Solution { 2 private: 3 int d[100][100]; 4 5 public: 6 int minDistance(string word1, string word2) 7 { 8 int len1 = word1.length(); 9 int len2 = word2.length(); 10 11 for(int i=0;i<=len1;i++) 12 d[i][0]= i; 13 14 for(int j=0;j<=len2;j++) 15 d[0][j]=j; 16 17 for(int i=1;i <=len1;i++) 18 { 19 for(int j=1;j<=len2;j++) 20 { 21 int diff; 22 if(word1[i-1] == word2[j-1]) 23 diff = 0 ; 24 else 25 diff = 1 ; 26 int temp = min(d[i-1][j] + 1, d[i][j-1] + 1); 27 d[i][j] = min(temp, d[i-1][j-1] + diff); 28 } 29 } 30 return d[len1][len2]; 31 } 32 };
这是《趣学算法》一书中4-4节提供的代码，在leetcode上运行，速度比较慢，392ms（5.16%），12.9mb（5.22%）。
补充一个python的实现：
1 class Solution: 2 def minDistance(self, word1: str, word2: str) -> int: 3 m = len(word1) 4 n = len(word2) 5 dp = [[0 for _ in range(n+1)]for _ in range(m+1)] 6 for j in range(n+1): 7 dp[0][j] = j 8 for i in range(m+1): 9 dp[i][0] = i 10 for i in range(1,m+1): 11 for j in range(1,n+1): 12 diff = 1 if word1[i-1] != word2[j-1] else 0 13 minval = min(dp[i-1][j]+1,dp[i][j-1]+1) 14 minval = min(minval,dp[i-1][j-1]+diff) 15 dp[i][j] = minval 16 return dp[m][n]
240ms，16.4mb
下面提供leetcode中一个12ms，8.5mb的解决方案：
1 class Solution { 2 public: 3 int minDistance(string word1, string word2) { 4 int m = word1.length(); 5 int n = word2.length(); 6 vector<int> dp(m+1, 0); 7 int i, j; 8 int temp, min; 9 for(i=0;i<=m;i++) 10 dp[i] = i; 11 for(j=1;j<=n;j++) 12 { 13 temp = dp[0]; 14 dp[0]++; 15 for(i=1;i<=m;i++) 16 { 17 min = temp + (word1[i-1]!=word2[j-1]); 18 min = (dp[i-1]+1)<min?(dp[i-1]+1):min; 19 min = (dp[i]+1)<min?(dp[i]+1):min; 20 temp = dp[i]; 21 dp[i] = min; 22 } 23 } 24 return dp[m]; 25 } 26 };
将第二种写法，转化为python语法：
1 class Solution: 2 def minDistance(self, word1: str, word2: str) -> int: 3 m = len(word1) 4 n = len(word2) 5 dp = list(range(m+1)) 6 for j in range(1,n+1): 7 temp = dp[0] 8 dp[0] += 1 9 for i in range(1,m+1): 10 diff = 1 if word1[i-1] != word2[j-1] else 0 11 minval = temp + diff 12 minval = min(minval,dp[i-1]+1) 13 minval = min(minval,dp[i]+1) 14 temp = dp[i] 15 dp[i] = minval 16 return dp[m]
204ms，12.9mb