diff --git a/TangDou/AcWing_TiGao/T1/LIS/1014.md b/TangDou/AcWing_TiGao/T1/LIS/1014.md index 9b442b1..321012a 100644 --- a/TangDou/AcWing_TiGao/T1/LIS/1014.md +++ b/TangDou/AcWing_TiGao/T1/LIS/1014.md @@ -107,44 +107,49 @@ int res; int main() { cin >> n; - for (int i = 1; i <= n; i++) cin >> a[i]; + for (int i = 0; i < n; i++) cin >> a[i]; // 正向 - f[++fl] = a[1]; - p1[1] = 1; + f[0] = a[0]; + p1[0] = 1; - for (int i = 2; i <= n; i++) + for (int i = 0; i < n; i++) if (a[i] > f[fl]) { f[++fl] = a[i]; p1[i] = fl; } else { - int t = lower_bound(f + 1, f + fl + 1, a[i]) - f; + int t = lower_bound(f, f + fl, a[i]) - f; f[t] = a[i]; p1[i] = t; } // 反向 - g[++gl] = a[n]; - p2[n] = 1; + g[0] = a[n - 1]; + p2[n - 1] = 1; - for (int i = n - 1; i >= 1; i--) + for (int i = n - 1; i >= 0; i--) if (a[i] > g[gl]) { g[++gl] = a[i]; p2[i] = gl; } else { - int t = lower_bound(g + 1, g + gl + 1, a[i]) - g; + int t = lower_bound(g, g + gl, a[i]) - g; g[t] = a[i]; p2[i] = t; } - for (int i = 1; i <= n; i++) res = max(res, p2[i] + p1[i] - 1); + for (int i = 0; i < n; i++) res = max(res, p2[i] + p1[i] + 2 - 1); printf("%d\n", res); return 0; } ``` -### 六、状态机分析法 +>**总结**: +① 朴素版本性能较差$O(N^2)$,但有一个先天的优势:可以知道每个数字作为最高点时,左边有多少个,右边有多少个,对于求左右最长这样的题目不用再拐弯了。 +② 贪心+二分版本的性能好$O(LogN*N)$,但有一个缺点,就是只能获取到最长上升序列的长度,不知道 **以每个数字为最高点时,左边有多少个,右边有多少个**,如果非得用这个算法不可的话,那么就需要对贪心+二分版本的代码进行改造:用数组记录第几个数字在上升序列中应该是排在第几位的,显得麻烦一些。 + + +### 六、状态机分析法【选读$O(N^2)$】 这是我做过 $AcWing$第二场热身赛的$C$题——[$AcWing$ $3549$. 最长非递减子序列](https://www.acwing.com/problem/content/3552/) 后总结出来的一类模型 那就是,**利用状态机模型$DP$解决最长$xxx$子序列模型** 的方法 diff --git a/TangDou/AcWing_TiGao/T1/LIS/1014_2.cpp b/TangDou/AcWing_TiGao/T1/LIS/1014_2.cpp index ae3bead..4a9310c 100644 --- a/TangDou/AcWing_TiGao/T1/LIS/1014_2.cpp +++ b/TangDou/AcWing_TiGao/T1/LIS/1014_2.cpp @@ -16,37 +16,37 @@ int res; int main() { cin >> n; - for (int i = 1; i <= n; i++) cin >> a[i]; + for (int i = 0; i < n; i++) cin >> a[i]; // 正向 - f[++fl] = a[1]; - p1[1] = 1; + f[0] = a[0]; + p1[0] = 1; - for (int i = 2; i <= n; i++) + for (int i = 0; i < n; i++) if (a[i] > f[fl]) { f[++fl] = a[i]; p1[i] = fl; } else { - int t = lower_bound(f + 1, f + fl + 1, a[i]) - f; + int t = lower_bound(f, f + fl, a[i]) - f; f[t] = a[i]; p1[i] = t; } // 反向 - g[++gl] = a[n]; - p2[n] = 1; + g[0] = a[n - 1]; + p2[n - 1] = 1; - for (int i = n - 1; i >= 1; i--) + for (int i = n - 1; i >= 0; i--) if (a[i] > g[gl]) { g[++gl] = a[i]; p2[i] = gl; } else { - int t = lower_bound(g + 1, g + gl + 1, a[i]) - g; + int t = lower_bound(g, g + gl, a[i]) - g; g[t] = a[i]; p2[i] = t; } - for (int i = 1; i <= n; i++) res = max(res, p2[i] + p1[i] - 1); + for (int i = 0; i < n; i++) res = max(res, p2[i] + p1[i] + 2 - 1); printf("%d\n", res); return 0;