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45 | 45 |
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46 | 46 | <!-- 这里可写通用的实现逻辑 -->
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47 | 47 |
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| 48 | +**方法一:动态规划** |
| 49 | + |
| 50 | +定义 `dp[i][j]` 表示打印区间 `[i, j]` 所需的最少打印次数。当 `i == j` 时,`dp[i][j] = 1`,即只有一个字符,只需打印一次。答案为 `dp[0][n - 1]`。 |
| 51 | + |
| 52 | +如果 `s[i] == s[j]`,则 `dp[i][j] = dp[i][j - 1]`;否则,`dp[i][j] = min(dp[i][k] + dp[k + 1][j])`,其中 `i <= k < j`。 |
| 53 | + |
| 54 | +时间复杂度 $O(n^3)$,空间复杂度 $O(n^2)$。其中 $n$ 为字符串 `s` 的长度。 |
| 55 | + |
48 | 56 | <!-- tabs:start -->
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49 | 57 |
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50 | 58 | ### **Python3**
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51 | 59 |
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52 | 60 | <!-- 这里可写当前语言的特殊实现逻辑 -->
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53 | 61 |
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54 | 62 | ```python
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55 |
| - |
| 63 | +class Solution: |
| 64 | + def strangePrinter(self, s: str) -> int: |
| 65 | + n = len(s) |
| 66 | + dp = [[inf] * n for _ in range(n)] |
| 67 | + for i in range(n - 1, -1, -1): |
| 68 | + dp[i][i] = 1 |
| 69 | + for j in range(i + 1, n): |
| 70 | + if s[i] == s[j]: |
| 71 | + dp[i][j] = dp[i][j - 1] |
| 72 | + else: |
| 73 | + for k in range(i, j): |
| 74 | + dp[i][j] = min(dp[i][j], dp[i][k] + dp[k + 1][j]) |
| 75 | + return dp[0][-1] |
56 | 76 | ```
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57 | 77 |
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58 | 78 | ### **Java**
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59 | 79 |
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60 | 80 | <!-- 这里可写当前语言的特殊实现逻辑 -->
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61 | 81 |
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62 | 82 | ```java
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| 83 | +class Solution { |
| 84 | + public int strangePrinter(String s) { |
| 85 | + int n = s.length(); |
| 86 | + int[][] f = new int[n + 1][n + 1]; |
| 87 | + for (int i = 0; i < n; ++i) { |
| 88 | + f[i][i] = 1; |
| 89 | + } |
| 90 | + for (int i = n - 2; i >= 0; --i) { |
| 91 | + for (int j = i + 1; j < n; ++j) { |
| 92 | + f[i][j] = 1 + f[i + 1][j]; |
| 93 | + for (int k = i + 1; k <= j; ++k) { |
| 94 | + if (s.charAt(i) == s.charAt(k)) { |
| 95 | + f[i][j] = Math.min(f[i][j], f[i + 1][k] + f[k + 1][j]); |
| 96 | + } |
| 97 | + } |
| 98 | + } |
| 99 | + } |
| 100 | + return f[0][n - 1]; |
| 101 | + } |
| 102 | +} |
| 103 | +``` |
| 104 | + |
| 105 | +```java |
| 106 | +class Solution { |
| 107 | + public int strangePrinter(String s) { |
| 108 | + int n = s.length(); |
| 109 | + int[][] dp = new int[n][n]; |
| 110 | + for (int i = n - 1; i >= 0; --i) { |
| 111 | + dp[i][i] = 1; |
| 112 | + for (int j = i + 1; j < n; ++j) { |
| 113 | + if (s.charAt(i) == s.charAt(j)) { |
| 114 | + dp[i][j] = dp[i][j - 1]; |
| 115 | + } else { |
| 116 | + dp[i][j] = 10000; |
| 117 | + for (int k = i; k < j; ++k) { |
| 118 | + dp[i][j] = Math.min(dp[i][j], dp[i][k] + dp[k + 1][j]); |
| 119 | + } |
| 120 | + } |
| 121 | + } |
| 122 | + } |
| 123 | + return dp[0][n - 1]; |
| 124 | + } |
| 125 | +} |
| 126 | +``` |
| 127 | + |
| 128 | +### **C++** |
| 129 | + |
| 130 | +```cpp |
| 131 | +class Solution { |
| 132 | +public: |
| 133 | + int strangePrinter(string s) { |
| 134 | + int n = s.size(); |
| 135 | + vector<vector<int>> dp(n, vector<int>(n, INT_MAX)); |
| 136 | + for (int i = n - 1; i >= 0; --i) { |
| 137 | + dp[i][i] = 1; |
| 138 | + for (int j = i + 1; j < n; ++j) { |
| 139 | + if (s[i] == s[j]) { |
| 140 | + dp[i][j] = dp[i][j - 1]; |
| 141 | + } else { |
| 142 | + for (int k = i; k < j; ++k) { |
| 143 | + dp[i][j] = min(dp[i][j], dp[i][k] + dp[k + 1][j]); |
| 144 | + } |
| 145 | + } |
| 146 | + } |
| 147 | + } |
| 148 | + return dp[0][n - 1]; |
| 149 | + } |
| 150 | +}; |
| 151 | +``` |
63 | 152 |
|
| 153 | +### **Go** |
| 154 | +
|
| 155 | +```go |
| 156 | +func strangePrinter(s string) int { |
| 157 | + n := len(s) |
| 158 | + dp := make([][]int, n) |
| 159 | + for i := range dp { |
| 160 | + dp[i] = make([]int, n) |
| 161 | + } |
| 162 | + for i := n - 1; i >= 0; i-- { |
| 163 | + dp[i][i] = 1 |
| 164 | + for j := i + 1; j < n; j++ { |
| 165 | + if s[i] == s[j] { |
| 166 | + dp[i][j] = dp[i][j-1] |
| 167 | + } else { |
| 168 | + dp[i][j] = 10000 |
| 169 | + for k := i; k < j; k++ { |
| 170 | + dp[i][j] = min(dp[i][j], dp[i][k]+dp[k+1][j]) |
| 171 | + } |
| 172 | + } |
| 173 | + } |
| 174 | + } |
| 175 | + return dp[0][n-1] |
| 176 | +} |
| 177 | +
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| 178 | +func min(a, b int) int { |
| 179 | + if a < b { |
| 180 | + return a |
| 181 | + } |
| 182 | + return b |
| 183 | +} |
64 | 184 | ```
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65 | 185 |
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66 | 186 | ### **...**
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