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48 | 48 | <li><code>s</code> 仅由数字和英文字母(大写和/或小写)组成</li>
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49 | 49 | </ul>
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50 | 50 |
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51 |
| - |
52 | 51 | ## 解法
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53 | 52 |
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54 | 53 | <!-- 这里可写通用的实现逻辑 -->
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55 | 54 |
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| 55 | +动态规划法。 |
| 56 | + |
| 57 | +设 `dp[i][j]` 表示字符串 `s[i..j]` 是否为回文串。 |
| 58 | + |
| 59 | +- 当 `j - i < 2`,即字符串长度为 2 时,只要 `s[i] == s[j]`,`dp[i][j]` 就为 true。 |
| 60 | +- 当 `j - i >= 2`,`dp[i][j] = dp[i + 1][j - 1] && s[i] == s[j]`。 |
| 61 | + |
56 | 62 | <!-- tabs:start -->
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57 | 63 |
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58 | 64 | ### **Python3**
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59 | 65 |
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60 | 66 | <!-- 这里可写当前语言的特殊实现逻辑 -->
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61 | 67 |
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62 | 68 | ```python
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63 |
| - |
| 69 | +class Solution: |
| 70 | + def longestPalindrome(self, s: str) -> str: |
| 71 | + n = len(s) |
| 72 | + dp = [[False] * n for _ in range(n)] |
| 73 | + start, mx = 0, 1 |
| 74 | + for j in range(n): |
| 75 | + for i in range(j + 1): |
| 76 | + if j - i < 2: |
| 77 | + dp[i][j] = s[i] == s[j] |
| 78 | + else: |
| 79 | + dp[i][j] = dp[i + 1][j - 1] and s[i] == s[j] |
| 80 | + if dp[i][j] and mx < j - i + 1: |
| 81 | + start, mx = i, j - i + 1 |
| 82 | + return s[start:start+mx] |
64 | 83 | ```
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65 | 84 |
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66 | 85 | ### **Java**
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67 | 86 |
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68 | 87 | <!-- 这里可写当前语言的特殊实现逻辑 -->
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69 | 88 |
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70 | 89 | ```java
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| 90 | +class Solution { |
| 91 | + public String longestPalindrome(String s) { |
| 92 | + int n = s.length(); |
| 93 | + boolean[][] dp = new boolean[n][n]; |
| 94 | + int mx = 1, start = 0; |
| 95 | + for (int j = 0; j < n; ++j) { |
| 96 | + for (int i = 0; i <= j; ++i) { |
| 97 | + if (j - i < 2) { |
| 98 | + dp[i][j] = s.charAt(i) == s.charAt(j); |
| 99 | + } else { |
| 100 | + dp[i][j] = dp[i + 1][j - 1] && s.charAt(i) == s.charAt(j); |
| 101 | + } |
| 102 | + if (dp[i][j] && mx < j - i + 1) { |
| 103 | + mx = j - i + 1; |
| 104 | + start = i; |
| 105 | + } |
| 106 | + } |
| 107 | + } |
| 108 | + return s.substring(start, start + mx); |
| 109 | + } |
| 110 | +} |
| 111 | +``` |
| 112 | + |
| 113 | +### **C++** |
| 114 | + |
| 115 | +```cpp |
| 116 | +class Solution { |
| 117 | +public: |
| 118 | + string longestPalindrome(string s) { |
| 119 | + int n = s.size(); |
| 120 | + vector<vector<bool>> dp(n, vector<bool>(n, false)); |
| 121 | + int start = 0, mx = 1; |
| 122 | + for (int j = 0; j < n; ++j) { |
| 123 | + for (int i = 0; i <= j; ++i) { |
| 124 | + if (j - i < 2) { |
| 125 | + dp[i][j] = s[i] == s[j]; |
| 126 | + } else { |
| 127 | + dp[i][j] = dp[i + 1][j - 1] && s[i] == s[j]; |
| 128 | + } |
| 129 | + if (dp[i][j] && mx < j - i + 1) { |
| 130 | + start = i; |
| 131 | + mx = j - i + 1; |
| 132 | + } |
| 133 | + } |
| 134 | + } |
| 135 | + return s.substr(start, mx); |
| 136 | + } |
| 137 | +}; |
| 138 | +``` |
| 139 | +
|
| 140 | +### **Go** |
| 141 | +
|
| 142 | +```go |
| 143 | +func longestPalindrome(s string) string { |
| 144 | + n := len(s) |
| 145 | + dp := make([][]bool, n) |
| 146 | + for i := 0; i < n; i++ { |
| 147 | + dp[i] = make([]bool, n) |
| 148 | + } |
| 149 | + mx, start := 1, 0 |
| 150 | + for j := 0; j < n; j++ { |
| 151 | + for i := 0; i <= j; i++ { |
| 152 | + if j-i < 2 { |
| 153 | + dp[i][j] = s[i] == s[j] |
| 154 | + } else { |
| 155 | + dp[i][j] = dp[i+1][j-1] && s[i] == s[j] |
| 156 | + } |
| 157 | + if dp[i][j] && mx < j-i+1 { |
| 158 | + mx, start = j-i+1, i |
| 159 | + } |
| 160 | + } |
| 161 | + } |
| 162 | + return s[start : start+mx] |
| 163 | +} |
| 164 | +``` |
71 | 165 |
|
| 166 | +### **C#** |
| 167 | + |
| 168 | +```cs |
| 169 | +public class Solution{ |
| 170 | + public string LongestPalindrome(string s) { |
| 171 | + int n = s.Length; |
| 172 | + bool[,] dp = new bool[n, n]; |
| 173 | + int mx = 1, start = 0; |
| 174 | + for (int j = 0; j < n; ++j) |
| 175 | + { |
| 176 | + for (int i = 0; i <= j; ++i) |
| 177 | + { |
| 178 | + if (j - i < 2) |
| 179 | + { |
| 180 | + dp[i, j] = s[i] == s[j]; |
| 181 | + } |
| 182 | + else |
| 183 | + { |
| 184 | + dp[i, j] = dp[i + 1, j - 1] && s[i] == s[j]; |
| 185 | + } |
| 186 | + if (dp[i, j] && mx < j - i + 1) |
| 187 | + { |
| 188 | + mx = j - i + 1; |
| 189 | + start = i; |
| 190 | + } |
| 191 | + } |
| 192 | + } |
| 193 | + return s.Substring(start, mx); |
| 194 | + } |
| 195 | +} |
72 | 196 | ```
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73 | 197 |
|
74 | 198 | ### **...**
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