• 洛谷-P3009 [USACO11JAN]Profits S


    洛谷-P3009 [USACO11JAN]Profits S

    原题链接:https://www.luogu.com.cn/problem/P3009


    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.

    奶牛们开始了新的生意,它们的主人约翰想知道它们到底能做得多好。这笔生意已经做了N(1≤N≤100,000)天,每天奶牛们都会记录下这一天的利润Pi(-1,000≤Pi≤1,000)。

    约翰想要找到奶牛们在连续的时间期间所获得的最大的总利润。(注:连续时间的周期长度范围从第一天到第N天)。

    请你写一个计算最大利润的程序来帮助他。

    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 #1

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

    输出 #1

    14 
    

    说明/提示

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

    感谢@smartzzh 提供的翻译。

    C++代码

    #include <iostream>
    using namespace std;
    
    int dp[100005];
    
    int main() {
        int n, ans=0;
        cin >> n;
        int p[n];
        for (int i=0; i<n; ++i)
            cin >> p[i];
        dp[0] = p[0]>0?p[0]:0;
        for (int i=1; i<n; ++i) {
            dp[i] += dp[i-1] + p[i];
            if (dp[i] < 0)
                dp[i] = 0;
            if (ans < dp[i])
                ans = dp[i];
        }
        if (ans == 0) {
            ans = p[0];
            for (int i=1; i<n; ++i)
                if (ans < p[i])
                    ans = p[i];
        }
        cout << ans << endl;
        return 0;
    }
    
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  • 原文地址:https://www.cnblogs.com/yuzec/p/14270344.html
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