[USACO11JAN]利润Profits

题目描述

The cows have opened a new business, and Farmer John wants to see how well they are doing. The business has been running for N (1 <= N <= 100,000) days, and every day i the cows recorded their net profit P_i (-1,000 <= P_i <= 1,000).

Farmer John wants to find the largest total profit that the cows have made during any consecutive time period. (Note that a consecutive time period can range in length from one day through N days.) Help him by writing a program to calculate the largest sum of consecutive profits.

牛们开了家新公司，这家公司已经运作了N天，财务报表显示第i天获得的利润为Pi ， 有些天的利润可能是个负数。约翰想给奶牛公司写个新闻报道，以吹嘘她们的业绩。于是他 想知道，这家公司在哪一段连续的日子里，利润总和是最大的。

输入输出格式

输入格式：

• Line 1: A single integer: N

• Lines 2..N+1: Line i+1 contains a single integer: P_i

输出格式：

• Line 1: A single integer representing the value of the maximum sum of profits for any consecutive time period.

输入输出样例

输入样例#1：

7
-3
4
9
-2
-5
8
-3

输出样例#1：

14

说明

The maximum sum is obtained by taking the sum from the second through the sixth number (4, 9, -2, -5, 8) => 14.

簡單動規。（因為方程沒法應付全負的情況，加了個l特判）

代碼實現：

 #include<cstdio>
 #include<iostream>
 using namespace std;
 int n,a,b,c,l=-,f[][];
 int main(){
     scanf("%d",&n);
     for(int i=;i<=n;i++){
         scanf("%d",&a);
         b=i%;c=(b+)%;l=max(l,a);
         f[b][]=max(f[c][],f[c][]);
         f[b][]=max(f[c][]+a,a);
     }
     if(l>=) printf("%d\n",max(f[n%][],f[n%][]));
     else printf("%d\n",l);
     return ;
 }

還記得某種數列問題嗎？