http://codeforces.com/contest/583/problem/D
原題:You are given an array of positive integers?a1,?a2,?...,?an?×?T?of length?n?×?T. We know that for any?i?>?n?it is true that?ai?=?ai?-?n. Find the length of the longest non-decreasing sequence of the given array.
題目大意:有長度為n的數組a(n <= 100),其中a[i] <= 300,這個a數組可以重復T次,問他的最長上升子序列是多少?
思路:我們可以發現,這個數組如果要全部都算上的,那么在t<=n的情況下,他的最長上升子序列一定會遍歷一次a數組。所以我們就只需要把原來的數組擴大n倍,然后求他的LIS。
這樣以后我們發現,后面的重復的次數一定是原來數組里面出現次數(假定重復次數k為最多)最多的數值,所以ans = Lis的長度 + k * T - min(n, T);
復雜度 O(n*n*logn)
//看看會不會爆int!數組會不會少了一維! //取物問題一定要小心先手勝利的條件 #include <bits/stdc++.h> using namespace std; #pragma comment(linker,"/STACK:102400000,102400000") #define LL long long #define ALL(a) a.begin(), a.end() #define pb push_back #define mk make_pair #define fi first #define se second #define haha printf("haha\n") const int maxn = 100 + 5; int a[maxn * maxn]; int n, T; vector<int> ve;int solve(int t){int len = t * n;for (int i = 1; i < t; i++){for (int j = 1; j <= n; j++){a[n * i + j] = a[j];}}for (int i = 1; i <= n * t; i++){int pos = upper_bound(ve.begin(), ve.end(), a[i]) - ve.begin();if (pos == ve.size()) ve.push_back(a[i]);else ve[pos] = a[i];}return ve.size(); }int cnt[maxn * maxn]; int main(){cin >> n >> T;int maxval = 0, k = 0;for (int i = 1; i <= n; i++){scanf("%d", a + i);cnt[a[i]]++;k = max(cnt[a[i]], k);}int ans = solve(min(n, T));//printf("ans = %d k = %d T - min(n, T) = %d\n", ans, k, T - min(n, T));printf("%d\n", ans + k * (T - min(n, T)));return 0; }
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