HDU 2993 MAX Average Problem （斜率优化）

ACM

题目地址： 
HDU 2993 MAX Average Problem

题意： 
给一个长度为 n 的序列，找出长度 >= k 的平均值最大的连续子序列。

分析： 
斜率优化的例题。 
这里有篇博客给论文里面的分析部分上色了，还不错：http://www.cnblogs.com/Free-rein/archive/2012/08/09/2630190.html

数据有点多，得用输入外挂才能过。

代码：

/**  Author:      illuz <iilluzen[at]gmail.com>*  File:        2993.cpp*  Create Date: 2014-09-17 23:56:17*  Descripton:  dp*/#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>using namespace std;#define repf(i,a,b) for(int i=(a);i<=(b);i++)typedef long long ll;const int N = 1e5 + 5;ll sum[N];int q[N], front, rear;int n, k;inline bool check(int a, int b, int c) {return (sum[c] - sum[b]) * (b - a) <= (sum[b] - sum[a]) * (c - b);}int Scan() {int res = 0, ch, flag = 0;if((ch = getchar()) == '-')flag = 1;else if(ch >= '0' && ch <= '9')res = ch - '0';while ((ch = getchar()) >= '0' && ch <= '9' )res = res * 10 + ch - '0';return flag ? -res : res;}int main() {while (~scanf("%d%d", &n, &k)) {repf (i, 1, n) {sum[i] = sum[i - 1] + Scan();}front = 0;rear = -1;double ans = 0;repf (i, k, n) {while (front < rear && check(q[rear - 1], q[rear], i - k))rear--;q[++rear] = i - k;while (front < rear && check(q[front + 1], q[front], i))front++;ans = max(ans, (sum[i] - sum[q[front]]) * 1. / (i - q[front]));}printf("%.2f\n", ans);}return 0;}