[CodeForces940E]Cashback（set+DP）

Description

Since you are the best Wraith King, Nizhniy Magazin «Mir» at the centre of Vinnytsia is offering you a discount.

You are given an array a of length n and an integer c.

The value of some array b of length k is the sum of its elements except for the smallest. For example, the value of the array [3, 1, 6, 5, 2] with c = 2 is 3 + 6 + 5 = 14.

Among all possible partitions of a into contiguous subarrays output the smallest possible sum of the values of these subarrays.

Solution

这里有一个贪心的思想，就是只需要划分长度为1或者长度为c的区间，其他的不会比这两种更优

首先裸的DP，\(dp[i]=min\{dp[j]+Cost_{j+1,i}\}\)

然后只要对长度为c的区间进行更新，可以用multiset进行存储数据

（STL中的multiset与set的区别在于可以存储相同的元素）

具体见代码

Code

#include <cstdio>
#include <algorithm>
#include <set>
#define ll long long
#define N 100010
using namespace std;

int n,c;
ll A[N],dp[N],sum;
multiset<ll> q;//默认升序排列

int main(){
	scanf("%d%d",&n,&c);
	for(int i=1;i<=n;i++)scanf("%I64d",&A[i]);
	for(int i=1;i<=n;i++){
		sum+=A[i];
		dp[i]=dp[i-1]+A[i];
		q.insert(A[i]);
		if(i>c){q.erase(q.find(A[i-c]));sum-=A[i-c];}//删除最小的元素
		if(i>=c){dp[i]=min(dp[i],dp[i-c]+sum-*q.begin());}//转移
	}
	printf("%I64d\n",dp[n]);
	return 0;
}