|
51 | 51 | <li><code>0 <= initial[i] < graph.length</code></li>
|
52 | 52 | </ul>
|
53 | 53 |
|
54 |
| - |
55 | 54 | ## 解法
|
56 | 55 |
|
57 | 56 | <!-- 这里可写通用的实现逻辑 -->
|
58 | 57 |
|
| 58 | +并查集。 |
| 59 | + |
| 60 | +模板 1——朴素并查集: |
| 61 | + |
| 62 | +```python |
| 63 | +# 初始化,p存储每个点的祖宗节点 |
| 64 | +p = [i for i in range(n)] |
| 65 | +# 返回x的祖宗节点 |
| 66 | +def find(x): |
| 67 | + if p[x] != x: |
| 68 | + # 路径压缩 |
| 69 | + p[x] = find(p[x]) |
| 70 | + return p[x] |
| 71 | +# 合并a和b所在的两个集合 |
| 72 | +p[find(a)] = find(b) |
| 73 | +``` |
| 74 | + |
| 75 | +模板 2——维护 size 的并查集: |
| 76 | + |
| 77 | +```python |
| 78 | +# 初始化,p存储每个点的祖宗节点,size只有当节点是祖宗节点时才有意义,表示祖宗节点所在集合中,点的数量 |
| 79 | +p = [i for i in range(n)] |
| 80 | +size = [1] * n |
| 81 | +# 返回x的祖宗节点 |
| 82 | +def find(x): |
| 83 | + if p[x] != x: |
| 84 | + # 路径压缩 |
| 85 | + p[x] = find(p[x]) |
| 86 | + return p[x] |
| 87 | +# 合并a和b所在的两个集合 |
| 88 | +size[find(b)] += size[find(a)] |
| 89 | +p[find(a)] = find(b) |
| 90 | +``` |
| 91 | + |
| 92 | +模板 3——维护到祖宗节点距离的并查集: |
| 93 | + |
| 94 | +```python |
| 95 | +# 初始化,p存储每个点的祖宗节点,d[x]存储x到p[x]的距离 |
| 96 | +p = [i for i in range(n)] |
| 97 | +d = [0] * n |
| 98 | +# 返回x的祖宗节点 |
| 99 | +def find(x): |
| 100 | + if p[x] != x: |
| 101 | + t = find(p[x]) |
| 102 | + d[x] += d[p[x]] |
| 103 | + p[x] = t |
| 104 | + return p[x] |
| 105 | +# 合并a和b所在的两个集合 |
| 106 | +p[find(a)] = find(b) |
| 107 | +d[find(a)] = dinstance |
| 108 | +``` |
| 109 | + |
59 | 110 | <!-- tabs:start -->
|
60 | 111 |
|
61 | 112 | ### **Python3**
|
62 | 113 |
|
63 | 114 | <!-- 这里可写当前语言的特殊实现逻辑 -->
|
64 | 115 |
|
65 | 116 | ```python
|
66 |
| - |
| 117 | +class Solution: |
| 118 | + def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int: |
| 119 | + n = len(graph) |
| 120 | + p = list(range(n)) |
| 121 | + size = [1] * n |
| 122 | + |
| 123 | + def find(x): |
| 124 | + if p[x] != x: |
| 125 | + p[x] = find(p[x]) |
| 126 | + return p[x] |
| 127 | + |
| 128 | + for i in range(n): |
| 129 | + for j in range(i + 1, n): |
| 130 | + if graph[i][j] == 1: |
| 131 | + pa, pb = find(i), find(j) |
| 132 | + if pa == pb: |
| 133 | + continue |
| 134 | + p[pa] = pb |
| 135 | + size[pb] += size[pa] |
| 136 | + |
| 137 | + mi = float('inf') |
| 138 | + res = initial[0] |
| 139 | + initial.sort() |
| 140 | + for i in range(len(initial)): |
| 141 | + t = 0 |
| 142 | + s = set() |
| 143 | + for j in range(len(initial)): |
| 144 | + if i == j: |
| 145 | + continue |
| 146 | + if find(initial[j]) in s: |
| 147 | + continue |
| 148 | + s.add(find(initial[j])) |
| 149 | + t += size[find(initial[j])] |
| 150 | + if mi > t: |
| 151 | + mi = t |
| 152 | + res = initial[i] |
| 153 | + return res |
67 | 154 | ```
|
68 | 155 |
|
69 | 156 | ### **Java**
|
70 | 157 |
|
71 | 158 | <!-- 这里可写当前语言的特殊实现逻辑 -->
|
72 | 159 |
|
73 | 160 | ```java
|
| 161 | +class Solution { |
| 162 | + private int[] p; |
| 163 | + |
| 164 | + public int minMalwareSpread(int[][] graph, int[] initial) { |
| 165 | + int n = graph.length; |
| 166 | + p = new int[n]; |
| 167 | + for (int i = 0; i < n; ++i) { |
| 168 | + p[i] = i; |
| 169 | + } |
| 170 | + int[] size = new int[n]; |
| 171 | + Arrays.fill(size, 1); |
| 172 | + for (int i = 0; i < n; ++i) { |
| 173 | + for (int j = i + 1; j < n; ++j) { |
| 174 | + if (graph[i][j] == 1) { |
| 175 | + int pa = find(i), pb = find(j); |
| 176 | + if (pa == pb) { |
| 177 | + continue; |
| 178 | + } |
| 179 | + p[pa] = pb; |
| 180 | + size[pb] += size[pa]; |
| 181 | + } |
| 182 | + } |
| 183 | + } |
| 184 | + int mi = Integer.MAX_VALUE; |
| 185 | + int res = initial[0]; |
| 186 | + Arrays.sort(initial); |
| 187 | + for (int i = 0; i < initial.length; ++i) { |
| 188 | + int t = 0; |
| 189 | + Set<Integer> s = new HashSet<>(); |
| 190 | + for (int j = 0; j < initial.length; ++j) { |
| 191 | + if (i == j) { |
| 192 | + continue; |
| 193 | + } |
| 194 | + if (s.contains(find(initial[j]))) { |
| 195 | + continue; |
| 196 | + } |
| 197 | + s.add(find(initial[j])); |
| 198 | + t += size[find(initial[j])]; |
| 199 | + } |
| 200 | + if (mi > t) { |
| 201 | + mi = t; |
| 202 | + res = initial[i]; |
| 203 | + } |
| 204 | + } |
| 205 | + return res; |
| 206 | + } |
| 207 | + |
| 208 | + private int find(int x) { |
| 209 | + if (p[x] != x) { |
| 210 | + p[x] = find(p[x]); |
| 211 | + } |
| 212 | + return p[x]; |
| 213 | + } |
| 214 | +} |
| 215 | +``` |
| 216 | + |
| 217 | +### **C++** |
| 218 | + |
| 219 | +```cpp |
| 220 | +class Solution { |
| 221 | +public: |
| 222 | + vector<int> p; |
| 223 | + |
| 224 | + int minMalwareSpread(vector<vector<int>>& graph, vector<int>& initial) { |
| 225 | + int n = graph.size(); |
| 226 | + p.resize(n); |
| 227 | + for (int i = 0; i < n; ++i) p[i] = i; |
| 228 | + vector<int> size(n, 1); |
| 229 | + for (int i = 0; i < n; ++i) |
| 230 | + { |
| 231 | + for (int j = i + 1; j < n; ++j) |
| 232 | + { |
| 233 | + if (graph[i][j]) |
| 234 | + { |
| 235 | + int pa = find(i), pb = find(j); |
| 236 | + if (pa == pb) continue; |
| 237 | + p[pa] = pb; |
| 238 | + size[pb] += size[pa]; |
| 239 | + } |
| 240 | + } |
| 241 | + } |
| 242 | + int mi = 400; |
| 243 | + int res = initial[0]; |
| 244 | + sort(initial.begin(), initial.end()); |
| 245 | + for (int i = 0; i < initial.size(); ++i) |
| 246 | + { |
| 247 | + int t = 0; |
| 248 | + unordered_set<int> s; |
| 249 | + for (int j = 0; j < initial.size(); ++j) |
| 250 | + { |
| 251 | + if (i == j) continue; |
| 252 | + if (s.count(find(initial[j]))) continue; |
| 253 | + s.insert(find(initial[j])); |
| 254 | + t += size[find(initial[j])]; |
| 255 | + } |
| 256 | + if (mi > t) |
| 257 | + { |
| 258 | + mi = t; |
| 259 | + res = initial[i]; |
| 260 | + } |
| 261 | + } |
| 262 | + return res; |
| 263 | + } |
| 264 | + |
| 265 | + int find(int x) { |
| 266 | + if (p[x] != x) p[x] = find(p[x]); |
| 267 | + return p[x]; |
| 268 | + } |
| 269 | +}; |
| 270 | +``` |
74 | 271 |
|
| 272 | +### **Go** |
| 273 | +
|
| 274 | +```go |
| 275 | +var p []int |
| 276 | +
|
| 277 | +func minMalwareSpread(graph [][]int, initial []int) int { |
| 278 | + n := len(graph) |
| 279 | + p = make([]int, n) |
| 280 | + size := make([]int, n) |
| 281 | + for i := 0; i < n; i++ { |
| 282 | + p[i] = i |
| 283 | + size[i] = 1 |
| 284 | + } |
| 285 | + for i := 0; i < n; i++ { |
| 286 | + for j := i + 1; j < n; j++ { |
| 287 | + if graph[i][j] == 1 { |
| 288 | + pa, pb := find(i), find(j) |
| 289 | + if pa == pb { |
| 290 | + continue |
| 291 | + } |
| 292 | + p[pa] = pb |
| 293 | + size[pb] += size[pa] |
| 294 | + } |
| 295 | + } |
| 296 | + } |
| 297 | + mi := 400 |
| 298 | + res := initial[0] |
| 299 | + sort.Ints(initial) |
| 300 | + for i := 0; i < len(initial); i++ { |
| 301 | + t := 0 |
| 302 | + s := make(map[int]bool) |
| 303 | + for j := 0; j < len(initial); j++ { |
| 304 | + if i == j { |
| 305 | + continue |
| 306 | + } |
| 307 | + if s[find(initial[j])] { |
| 308 | + continue |
| 309 | + } |
| 310 | + s[find(initial[j])] = true |
| 311 | + t += size[find(initial[j])] |
| 312 | + } |
| 313 | + if mi > t { |
| 314 | + mi = t |
| 315 | + res = initial[i] |
| 316 | + } |
| 317 | + } |
| 318 | + return res |
| 319 | +} |
| 320 | +
|
| 321 | +func find(x int) int { |
| 322 | + if p[x] != x { |
| 323 | + p[x] = find(p[x]) |
| 324 | + } |
| 325 | + return p[x] |
| 326 | +} |
75 | 327 | ```
|
76 | 328 |
|
77 | 329 | ### **...**
|
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