|
69 | 69 |
|
70 | 70 | <!-- 这里可写通用的实现逻辑 --> |
71 | 71 |
|
| 72 | +**方法一:并查集** |
| 73 | + |
| 74 | +正向遍历 $arr,ドル利用并查集动态维护每组 1ドル$ 的长度。 |
| 75 | + |
| 76 | +时间复杂度 $O(nlogn)$。 |
| 77 | + |
| 78 | +类似题目:[2334. 元素值大于变化阈值的子数组](/solution/2300-2399/2334.Subarray%20With%20Elements%20Greater%20Than%20Varying%20Threshold/README.md) |
| 79 | + |
| 80 | +**方法二:动态维护区间端点的长度** |
| 81 | + |
| 82 | +我们其实并不需要去通过查找并查集来获取每个区间长度,我们只需要在每个区间端点处记录每个区间长度,由于合并的时候**只会访问区间端点**,所以合并区间的时候修改端点区间长度即可。 |
| 83 | + |
| 84 | +时间复杂度 $O(n)$。 |
| 85 | + |
72 | 86 | <!-- tabs:start --> |
73 | 87 |
|
74 | 88 | ### **Python3** |
75 | 89 |
|
76 | 90 | <!-- 这里可写当前语言的特殊实现逻辑 --> |
77 | 91 |
|
78 | 92 | ```python |
| 93 | +class Solution: |
| 94 | + def findLatestStep(self, arr: List[int], m: int) -> int: |
| 95 | + def find(x): |
| 96 | + if p[x] != x: |
| 97 | + p[x] = find(p[x]) |
| 98 | + return p[x] |
| 99 | + |
| 100 | + def union(a, b): |
| 101 | + pa, pb = find(a), find(b) |
| 102 | + if pa == pb: |
| 103 | + return |
| 104 | + p[pa] = pb |
| 105 | + size[pb] += size[pa] |
| 106 | + |
| 107 | + n = len(arr) |
| 108 | + if m == n: |
| 109 | + return n |
| 110 | + vis = [False] * n |
| 111 | + p = list(range(n)) |
| 112 | + size = [1] * n |
| 113 | + ans = -1 |
| 114 | + for i, v in enumerate(arr): |
| 115 | + v -= 1 |
| 116 | + if v and vis[v - 1]: |
| 117 | + if size[find(v - 1)] == m: |
| 118 | + ans = i |
| 119 | + union(v, v - 1) |
| 120 | + if v < n - 1 and vis[v + 1]: |
| 121 | + if size[find(v + 1)] == m: |
| 122 | + ans = i |
| 123 | + union(v, v + 1) |
| 124 | + vis[v] = True |
| 125 | + return ans |
| 126 | +``` |
79 | 127 |
|
| 128 | +```python |
| 129 | +class Solution: |
| 130 | + def findLatestStep(self, arr: List[int], m: int) -> int: |
| 131 | + n = len(arr) |
| 132 | + if m == n: |
| 133 | + return n |
| 134 | + cnt = [0] * (n + 2) |
| 135 | + ans = -1 |
| 136 | + for i, v in enumerate(arr): |
| 137 | + v -= 1 |
| 138 | + l, r = cnt[v - 1], cnt[v + 1] |
| 139 | + if l == m or r == m: |
| 140 | + ans = i |
| 141 | + cnt[v - l] = cnt[v + r] = l + r + 1 |
| 142 | + return ans |
80 | 143 | ``` |
81 | 144 |
|
82 | 145 | ### **Java** |
83 | 146 |
|
84 | 147 | <!-- 这里可写当前语言的特殊实现逻辑 --> |
85 | 148 |
|
86 | 149 | ```java |
| 150 | +class Solution { |
| 151 | + private int[] p; |
| 152 | + private int[] size; |
| 153 | + |
| 154 | + public int findLatestStep(int[] arr, int m) { |
| 155 | + int n = arr.length; |
| 156 | + if (m == n) { |
| 157 | + return n; |
| 158 | + } |
| 159 | + boolean[] vis = new boolean[n]; |
| 160 | + p = new int[n]; |
| 161 | + size = new int[n]; |
| 162 | + for (int i = 0; i < n; ++i) { |
| 163 | + p[i] = i; |
| 164 | + size[i] = 1; |
| 165 | + } |
| 166 | + int ans = -1; |
| 167 | + for (int i = 0; i < n; ++i) { |
| 168 | + int v = arr[i] - 1; |
| 169 | + if (v > 0 && vis[v - 1]) { |
| 170 | + if (size[find(v - 1)] == m) { |
| 171 | + ans = i; |
| 172 | + } |
| 173 | + union(v, v - 1); |
| 174 | + } |
| 175 | + if (v < n - 1 && vis[v + 1]) { |
| 176 | + if (size[find(v + 1)] == m) { |
| 177 | + ans = i; |
| 178 | + } |
| 179 | + union(v, v + 1); |
| 180 | + } |
| 181 | + vis[v] = true; |
| 182 | + } |
| 183 | + return ans; |
| 184 | + } |
| 185 | + |
| 186 | + private int find(int x) { |
| 187 | + if (p[x] != x) { |
| 188 | + p[x] = find(p[x]); |
| 189 | + } |
| 190 | + return p[x]; |
| 191 | + } |
| 192 | + |
| 193 | + private void union(int a, int b) { |
| 194 | + int pa = find(a), pb = find(b); |
| 195 | + if (pa == pb) { |
| 196 | + return; |
| 197 | + } |
| 198 | + p[pa] = pb; |
| 199 | + size[pb] += size[pa]; |
| 200 | + } |
| 201 | +} |
| 202 | +``` |
| 203 | + |
| 204 | +```java |
| 205 | +class Solution { |
| 206 | + public int findLatestStep(int[] arr, int m) { |
| 207 | + int n = arr.length; |
| 208 | + if (m == n) { |
| 209 | + return n; |
| 210 | + } |
| 211 | + int[] cnt = new int[n + 2]; |
| 212 | + int ans = -1; |
| 213 | + for (int i = 0; i < n; ++i) { |
| 214 | + int v = arr[i]; |
| 215 | + int l = cnt[v - 1], r = cnt[v + 1]; |
| 216 | + if (l == m || r == m) { |
| 217 | + ans = i; |
| 218 | + } |
| 219 | + cnt[v - l] = l + r + 1; |
| 220 | + cnt[v + r] = l + r + 1; |
| 221 | + } |
| 222 | + return ans; |
| 223 | + } |
| 224 | +} |
| 225 | +``` |
| 226 | + |
| 227 | +### **C++** |
| 228 | + |
| 229 | +```cpp |
| 230 | +class Solution { |
| 231 | +public: |
| 232 | + vector<int> p; |
| 233 | + vector<int> size; |
| 234 | + |
| 235 | + int findLatestStep(vector<int>& arr, int m) { |
| 236 | + int n = arr.size(); |
| 237 | + if (m == n) return n; |
| 238 | + p.resize(n); |
| 239 | + size.assign(n, 1); |
| 240 | + for (int i = 0; i < n; ++i) p[i] = i; |
| 241 | + int ans = -1; |
| 242 | + vector<int> vis(n); |
| 243 | + for (int i = 0; i < n; ++i) |
| 244 | + { |
| 245 | + int v = arr[i] - 1; |
| 246 | + if (v && vis[v - 1]) |
| 247 | + { |
| 248 | + if (size[find(v - 1)] == m) ans = i; |
| 249 | + unite(v, v - 1); |
| 250 | + } |
| 251 | + if (v < n - 1 && vis[v + 1]) |
| 252 | + { |
| 253 | + if (size[find(v + 1)] == m) ans = i; |
| 254 | + unite(v, v + 1); |
| 255 | + } |
| 256 | + vis[v] = true; |
| 257 | + } |
| 258 | + return ans; |
| 259 | + } |
| 260 | + |
| 261 | + int find(int x) { |
| 262 | + if (p[x] != x) p[x] = find(p[x]); |
| 263 | + return p[x]; |
| 264 | + } |
| 265 | + |
| 266 | + void unite(int a, int b) { |
| 267 | + int pa = find(a), pb = find(b); |
| 268 | + if (pa == pb) return; |
| 269 | + p[pa] = pb; |
| 270 | + size[pb] += size[pa]; |
| 271 | + } |
| 272 | +}; |
| 273 | +``` |
| 274 | + |
| 275 | +```cpp |
| 276 | +class Solution { |
| 277 | +public: |
| 278 | + int findLatestStep(vector<int>& arr, int m) { |
| 279 | + int n = arr.size(); |
| 280 | + if (m == n) return n; |
| 281 | + vector<int> cnt(n + 2); |
| 282 | + int ans = -1; |
| 283 | + for (int i = 0; i < n; ++i) |
| 284 | + { |
| 285 | + int v = arr[i]; |
| 286 | + int l = cnt[v - 1], r = cnt[v + 1]; |
| 287 | + if (l == m || r == m) ans = i; |
| 288 | + cnt[v - l] = cnt[v + r] = l + r + 1; |
| 289 | + } |
| 290 | + return ans; |
| 291 | + } |
| 292 | +}; |
| 293 | +``` |
| 294 | + |
| 295 | +### **Go** |
| 296 | + |
| 297 | +```go |
| 298 | +func findLatestStep(arr []int, m int) int { |
| 299 | + n := len(arr) |
| 300 | + if m == n { |
| 301 | + return n |
| 302 | + } |
| 303 | + p := make([]int, n) |
| 304 | + size := make([]int, n) |
| 305 | + vis := make([]bool, n) |
| 306 | + for i := range p { |
| 307 | + p[i] = i |
| 308 | + size[i] = 1 |
| 309 | + } |
| 310 | + var find func(int) int |
| 311 | + find = func(x int) int { |
| 312 | + if p[x] != x { |
| 313 | + p[x] = find(p[x]) |
| 314 | + } |
| 315 | + return p[x] |
| 316 | + } |
| 317 | + union := func(a, b int) { |
| 318 | + pa, pb := find(a), find(b) |
| 319 | + if pa == pb { |
| 320 | + return |
| 321 | + } |
| 322 | + p[pa] = pb |
| 323 | + size[pb] += size[pa] |
| 324 | + } |
| 325 | + |
| 326 | + ans := -1 |
| 327 | + for i, v := range arr { |
| 328 | + v-- |
| 329 | + if v > 0 && vis[v-1] { |
| 330 | + if size[find(v-1)] == m { |
| 331 | + ans = i |
| 332 | + } |
| 333 | + union(v, v-1) |
| 334 | + } |
| 335 | + if v < n-1 && vis[v+1] { |
| 336 | + if size[find(v+1)] == m { |
| 337 | + ans = i |
| 338 | + } |
| 339 | + union(v, v+1) |
| 340 | + } |
| 341 | + vis[v] = true |
| 342 | + } |
| 343 | + return ans |
| 344 | +} |
| 345 | +``` |
87 | 346 |
|
| 347 | +```go |
| 348 | +func findLatestStep(arr []int, m int) int { |
| 349 | + n := len(arr) |
| 350 | + if m == n { |
| 351 | + return n |
| 352 | + } |
| 353 | + cnt := make([]int, n+2) |
| 354 | + ans := -1 |
| 355 | + for i, v := range arr { |
| 356 | + l, r := cnt[v-1], cnt[v+1] |
| 357 | + if l == m || r == m { |
| 358 | + ans = i |
| 359 | + } |
| 360 | + cnt[v-l], cnt[v+r] = l+r+1, l+r+1 |
| 361 | + } |
| 362 | + return ans |
| 363 | +} |
88 | 364 | ``` |
89 | 365 |
|
90 | 366 | ### **...** |
|
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