The heat during the last few days has been really intense. Scientists from all over the Berland study how the temperatures and weather change, and they claim that this summer is abnormally hot. But any scientific claim sounds a lot more reasonable if there are some numbers involved, so they have decided to actually calculate some value which would represent how high the temperatures are.
Mathematicians of Berland State University came up with a special heat intensity value. This value is calculated as follows:
Suppose we want to analyze the segment of nn consecutive days. We have measured the temperatures during these nn days; the temperature during ii-th day equals aiai.
We denote the average temperature of a segment of some consecutive days as the arithmetic mean of the temperature measures during this segment of days. So, if we want to analyze the average temperature from day xx to day yy, we calculate it as y∑i=xaiy−x+1∑i=xyaiy−x+1 (note that division is performed without any rounding). The heat intensity value is the maximum of average temperatures over all segments of not less than kkconsecutive days. For example, if analyzing the measures [3,4,1,2][3,4,1,2] and k=3k=3, we are interested in segments [3,4,1][3,4,1], [4,1,2][4,1,2] and [3,4,1,2][3,4,1,2] (we want to find the maximum value of average temperature over these segments).
You have been hired by Berland State University to write a program that would compute the heat intensity value of a given period of days. Are you up to this task?
The first line contains two integers nn and kk (1≤k≤n≤50001≤k≤n≤5000) — the number of days in the given period, and the minimum number of days in a segment we consider when calculating heat intensity value, respectively.
The second line contains nn integers a1a1, a2a2, ..., anan (1≤ai≤50001≤ai≤5000) — the temperature measures during given nn days.
Print one real number — the heat intensity value, i. e., the maximum of average temperatures over all segments of not less than kkconsecutive days.
Your answer will be considered correct if the following condition holds: |res−res0|<10−6|res−res0|<10−6, where resres is your answer, and res0res0 is the answer given by the jury's solution.
4 3 3 4 1 2
2.666666666666667
Codeforces (c) Copyright 2010-2018 Mike Mirzay
題意:給出長爲n的數列,表示有連續的n天,每天的溫度爲ai,現在,定義平均熱度爲∑i=xyaiy−x+1
x,y表示任意從x天開始,到y天結束。k表是最短的連續天數,即y-x+1>=k。數列可能有多個平均熱度,求出最大的平均熱度
思路:如果直接暴力直接枚舉所有的情況的話是5000的立方,所以考慮用前綴和來做,先處理出前i天的溫度和。
#include "iostream" #include "cstring" #include "algorithm" using namespace std; #define esp 1e-6 int n,k,a[5005]; int main(){ scanf("%d%d",&n,&k); for (int i=1;i<=n;i++) scanf("%d",&a[i]),a[i]+=a[i-1]; double ans=0; for(int i=0;i<=n;i++) for(int j=i+k;j<=n;j++) ans=(1.0*(a[j]-a[i])/(j-i))-ans>esp?(1.0*(a[j]-a[i])/(j-i)):ans; printf("%.15lf",ans); return 0; }