poj 3273Monthly Expense(经典二分枚举)

最新推荐文章于 2021-02-04 04:07:46 发布

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本文介绍了一个预算规划问题，农民John需要为接下来的每一天设定预算，并将其划分为若干个“fajomonth”周期，以确保每月的最大支出最小化。文章提供了一个解决此问题的C语言程序示例。

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Monthly Expense

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 22175		Accepted: 8681

Description

Farmer John is an astounding(令人震惊的) accounting wizard(男巫) and has realized he might run out of money to run the farm. He has already calculated(计算) and recorded the exactamount(数量) of money (1 ≤ money_i ≤ 10,000) that he will need to spend each day over the next N (1 ≤ N ≤ 100,000) days.

FJ wants to create a budget(预算) for a sequential(连续的) set of exactly M (1 ≤ M ≤ N) fiscal(会计的) periods called "fajomonths". Each of these fajomonths contains a set of 1 or moreconsecutive(连贯的) days. Every day is contained in exactly one fajomonth.

FJ's goal is to arrange the fajomonths so as to minimize(使减到最少) the expenses of the fajomonth with the highest spending and thus determine his monthly spending limit.

Input

Line 1: Two space-separated integers(整数): N and M
Lines 2..N+1: Line i+1 contains the number of dollars Farmer John spends on the ith day

Output

Line 1: The smallest possible monthly limit Farmer John can afford to live with.

Sample Input

Sample Output

Hint

If Farmer John schedules(时间表) the months so that the first two days are a month, the third and fourth are a month, and the last three are their own months, he spends at most $500 in any month. Any other method of scheduling gives a larger minimum(最小的) monthly limit.

#include<stdio.h>
int a[511000];
int main()
{
    int m,n;
    int i,j;

    while(~scanf("%d%d",&n,&m))
    {
        int low = 0;
        int high = 0;
        int mid;
        int ans;
        for(i=0;i<n;i++)
        {
            scanf("%d",&a[i]);
            high+=a[i];
            if(low<a[i])
                low=a[i];
        }

        while(low<=high)
        {
            int money = 0;
            int num = 1;
            mid=(low+high)/2;
            for(i=0;i<n;i++)
            {
                if(money+a[i]<=mid)
                     money+=a[i];
                else
                    {
                       num++;
                       money=a[i];
                    }

            }
            if(num>m) low=mid+1;
            else
            {
                ans=mid;
                high = mid-1;


            }
        }
        printf("%d\n",ans);
    }