問題 K: Best Cow Fences

時間限制: 1 Sec  記憶體限制: 128 MB
提交: 61  解決: 27
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題目描述

Farmer John's farm consists of a long row of N (1 <= N <= 100,000)fields. Each field contains a certain number of cows, 1 <= ncows <= 2000. 
FJ wants to build a fence around a contiguous group of these fields in order to maximize the average number of cows per field within that block. The block must contain at least F (1 <= F <= N) fields, where F given as input. 
Calculate the fence placement that maximizes the average, given the constraint. 

輸入

* Line 1: Two space-separated integers, N and F. 
* Lines 2..N+1: Each line contains a single integer, the number of cows in a field. Line 2 gives the number of cows in field 1,line 3 gives the number in field 2, and so on. 

輸出

* Line 1: A single integer that is 1000 times the maximal average.Do not perform rounding, just print the integer that is 1000*ncows/nfields. 

樣例輸入

10 6
6 
4
2
10
3
8
5
9
4
1

樣例輸出

6500

題意：給你n個牛的自身價值，讓你找出連續的且數量大於等於F的一段區間，使這段區間內的牛的平均價值最大。

分析：一個簡單的二分，再加一個經典的處理。

1、首先二分割槽間的平均值為多少，讓陣列中的所有數都減去平均值。

2、再從陣列中找出一段長度大於等於F的區間，看區間和是否會大於等於0。

3、要找這段區間需要維護左端點最小值，列舉右端點。先把減去平均值的陣列求一個字首和，再設K，對於當前列舉到的 i 位置，我們想讓a[i]-a[k]，儘量大，那麼a[k]，就必須儘量小，所以一直維護最小值就可以了minn=（minn，sum[i-m]）。