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41 | 41 |
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42 | 42 | <!-- 这里可写通用的实现逻辑 -->
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43 | 43 |
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| 44 | +**方法一:动态规划** |
| 45 | + |
| 46 | +类似[1143. 最长公共子序列](/solution/1100-1199/1143.Longest%20Common%20Subsequence/README.md)。 |
| 47 | + |
| 48 | +定义 `dp[i][j]` 表示使得 `word1[0:i-1]` 和 `word1[0:j-1]` 两个字符串相同所需执行的删除操作次数。 |
| 49 | + |
| 50 | +时间复杂度 O(mn)。 |
| 51 | + |
| 52 | + |
44 | 53 | <!-- tabs:start -->
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45 | 54 |
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46 | 55 | ### **Python3**
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47 | 56 |
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48 | 57 | <!-- 这里可写当前语言的特殊实现逻辑 -->
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49 | 58 |
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50 | 59 | ```python
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51 |
| - |
| 60 | +class Solution: |
| 61 | + def minDistance(self, word1: str, word2: str) -> int: |
| 62 | + m, n = len(word1), len(word2) |
| 63 | + dp = [[0] * (n + 1) for _ in range(m + 1)] |
| 64 | + for i in range(1, m + 1): |
| 65 | + dp[i][0] = i |
| 66 | + for j in range(1, n + 1): |
| 67 | + dp[0][j] = j |
| 68 | + for i in range(1, m + 1): |
| 69 | + for j in range(1, n + 1): |
| 70 | + if word1[i - 1] == word2[j - 1]: |
| 71 | + dp[i][j] = dp[i - 1][j - 1] |
| 72 | + else: |
| 73 | + dp[i][j] = 1 + min(dp[i - 1][j], dp[i][j - 1]) |
| 74 | + return dp[-1][-1] |
52 | 75 | ```
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53 | 76 |
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54 | 77 | ### **Java**
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55 | 78 |
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56 | 79 | <!-- 这里可写当前语言的特殊实现逻辑 -->
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57 | 80 |
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58 | 81 | ```java
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| 82 | +class Solution { |
| 83 | + public int minDistance(String word1, String word2) { |
| 84 | + int m = word1.length(), n = word2.length(); |
| 85 | + int[][] dp = new int[m + 1][n + 1]; |
| 86 | + for (int i = 1; i <= m; ++i) { |
| 87 | + dp[i][0] = i; |
| 88 | + } |
| 89 | + for (int j = 1; j <= n; ++j) { |
| 90 | + dp[0][j] = j; |
| 91 | + } |
| 92 | + for (int i = 1; i <= m; ++i) { |
| 93 | + for (int j = 1; j <= n; ++j) { |
| 94 | + if (word1.charAt(i - 1) == word2.charAt(j - 1)) { |
| 95 | + dp[i][j] = dp[i - 1][j - 1]; |
| 96 | + } else { |
| 97 | + dp[i][j] = 1 + Math.min(dp[i - 1][j], dp[i][j - 1]); |
| 98 | + } |
| 99 | + } |
| 100 | + } |
| 101 | + return dp[m][n]; |
| 102 | + } |
| 103 | +} |
| 104 | +``` |
| 105 | + |
| 106 | +### **C++** |
| 107 | + |
| 108 | +```cpp |
| 109 | +class Solution { |
| 110 | +public: |
| 111 | + int minDistance(string word1, string word2) { |
| 112 | + int m = word1.size(), n = word2.size(); |
| 113 | + vector<vector<int>> dp(m + 1, vector<int>(n + 1)); |
| 114 | + for (int i = 1; i <= m; ++i) dp[i][0] = i; |
| 115 | + for (int j = 1; j <= n; ++j) dp[0][j] = j; |
| 116 | + for (int i = 1; i <= m; ++i) |
| 117 | + { |
| 118 | + for (int j = 1; j <= n; ++j) |
| 119 | + { |
| 120 | + if (word1[i - 1] == word2[j - 1]) dp[i][j] = dp[i - 1][j - 1]; |
| 121 | + else dp[i][j] = 1 + min(dp[i - 1][j], dp[i][j - 1]); |
| 122 | + } |
| 123 | + } |
| 124 | + return dp[m][n]; |
| 125 | + } |
| 126 | +}; |
| 127 | +``` |
59 | 128 |
|
| 129 | +### **Go** |
| 130 | +
|
| 131 | +```go |
| 132 | +func minDistance(word1 string, word2 string) int { |
| 133 | + m, n := len(word1), len(word2) |
| 134 | + dp := make([][]int, m+1) |
| 135 | + for i := range dp { |
| 136 | + dp[i] = make([]int, n+1) |
| 137 | + dp[i][0] = i |
| 138 | + } |
| 139 | + for j := range dp[0] { |
| 140 | + dp[0][j] = j |
| 141 | + } |
| 142 | + for i := 1; i <= m; i++ { |
| 143 | + for j := 1; j <= n; j++ { |
| 144 | + if word1[i-1] == word2[j-1] { |
| 145 | + dp[i][j] = dp[i-1][j-1] |
| 146 | + } else { |
| 147 | + dp[i][j] = 1 + min(dp[i-1][j], dp[i][j-1]) |
| 148 | + } |
| 149 | + } |
| 150 | + } |
| 151 | + return dp[m][n] |
| 152 | +} |
| 153 | +
|
| 154 | +func min(a, b int) int { |
| 155 | + if a < b { |
| 156 | + return a |
| 157 | + } |
| 158 | + return b |
| 159 | +} |
60 | 160 | ```
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61 | 161 |
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62 | 162 | ### **...**
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