第八届河南省赛G.Interference Signal（dp）

Dr.Kong’s laboratory monitor some interference signals. The interference signals can be digitized into a series of positive integer. May be, there are N integers a1,a2,…,an.

Dr.Kong wants to know the average strength of a contiguous interference signal block. the block must contain at least M integers.

Please help Dr.Kong to calculate the maximum average strength, given the constraint.

The input contains K test cases. Each test case specifies:

* Line 1: Two space-separated integers, N and M.

* Lines2~line N+1:  ai  (i=1,2,…,N)

1 ≤ K≤ 8,  5 ≤ N≤ 2000,   1 ≤ M ≤ N,  0 ≤ ai ≤9999

The input contains K test cases. Each test case specifies:

* Line 1: Two space-separated integers, N and M.

* Lines2~line N+1:  ai  (i=1,2,…,N)

1 ≤ K≤ 8,  5 ≤ N≤ 2000,   1 ≤ M ≤ N,  0 ≤ ai ≤9999

第八届河南省赛

题解：让找长度大于等于M的连续子序列的最大平均值；

思路：简单dp，dp[i][j]=dp[i-1][j-1]+m[j];代表在j处前i个数的序列和；

然后判断找平均值；

代码：

#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<algorithm>
#include<set>
using namespace std;
#define mem(x,y) memset(x,y,sizeof(x))
#define SI(x) scanf("%d",&x)
#define SL(x) scanf("%lld",&x)
#define  PI(x) printf("%d",x)
#define  PL(x) printf("%lld",x)
#define P_ printf(" ")
const int INF=0x3f3f3f3f;
const double PI=acos(-1.0);
typedef long long LL;
const int MAXN=2020;
int m[MAXN];
int dp[MAXN][MAXN];
double pp[MAXN][MAXN];
int main(){
	int T,N,M;
	SI(T);
	while(T--){
		SI(N);SI(M);
		for(int i=1;i<=N;i++)SI(m[i]);
		mem(dp,0);
		for(int i=1;i<=N;i++){
			for(int j=1;j<=N;j++){
				dp[i][j]=dp[i-1][j-1]+m[j];
			}
		}
		double x=0;
		for(int i=M;i<=N;i++)
			for(int j=M;j<=N;j++)
				x=max(x,1.0*dp[i][j]/i);
		printf("%d\n",(int)(1000*x));
	}
	return 0;
}