POJ3273 Monthly Expense —— 二分

题目链接：http://poj.org/problem?id=3273

 

Monthly Expense

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 29231		Accepted: 11104

Description

Farmer John is an astounding accounting wizard and has realized he might run out of money to run the farm. He has already calculated and recorded the exact amount 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 for a sequential set of exactly M (1 ≤ M ≤ N) fiscal periods called "fajomonths". Each of these fajomonths contains a set of 1 or more consecutive days. Every day is contained in exactly one fajomonth.

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

Input

Line 1: Two space-separated integers: 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

7 5
100
400
300
100
500
101
400

Sample Output

500

Hint

If Farmer John schedules 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 monthly limit.

Source

USACO 2007 March Silver

 

 

 

题解：

1.二分答案，即每月的限制。

 2.枚举每一天，然后根据每月的限制，把每一天都分到一个特定的月中。如果所需的月份数小于等于M，则缩小范围，否则扩大范围。

 

 

代码如下：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <string>
#include <set>
#define ms(a,b) memset((a),(b),sizeof((a)))
using namespace std;
typedef long long LL;
const double EPS = 1e-8;
const int INF = 2e9;
const LL LNF = 2e18;
const int MAXN = 1e5+10;

int n, m;
int a[MAXN];

bool test(int mid)
{
    int cnt = 0, sum;
    for(int i = 1; i<=n; i++)
    {
        if(a[i]>mid) return false;  //单独作为一个月都超出限定， 直接退出

        if(i==1 || sum+a[i]>mid)    // 重新开一个月
            cnt++, sum = a[i];
        else                        
            sum += a[i];
    }
    return cnt<=m;
}

int main()
{
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        for(int i = 1; i<=n; i++)
            scanf("%d", &a[i]);

        int l = 0, r = INF;
        while(l<=r)
        {
            int mid = (l+r)>>1;
            if(test(mid))
                r = mid - 1;
            else
                l = mid + 1;
        }
        cout<<l<<endl;
    }
}