POJ3273 Monthly Expense（正确的二分法求最小化最大值）

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本文介绍了一个预算规划问题，目标是最小化连续月份内的最高开销。通过分组每天的开销来形成连续的“fajomonth”，使得任意一个fajomonth的总开销最小。使用二分查找算法优化解决方案。

Link：http://poj.org/problem?id=3273

Monthly Expense

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 29745		Accepted: 11285

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

Sample Output

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

AC code：

#include<iostream>
#include<stdio.h>
#include<algorithm>
#include<math.h>
#include<string.h>
#include<map>
#include<set>
#define LL long long
#define INF 0xfffffff

using namespace std;

int a[100010];
int n,m;

int group(int mid)
{
	int sum=0,cnt=1,i;
	for(i=0;i<n;i++)
	{
		sum+=a[i];
		if(sum>mid)
		{
			cnt++;
			sum=a[i];
		}
	}
	return cnt;
}
/* 
int Bsearch(int low,int high)//错误的二分写法！！！ 
{
	int mid=(low+high)/2;
	while(low<=high)
	{	
		if(group(mid)<=m)
		{
			high=mid-1;
		}
		else
		{
			low=mid+1;
		}
		mid=(low+high)/2;
	}
	return mid;
}
*/ 
int Bsearch(int low,int high)//正确的二分写法！！！ 
{
	int mid;
	while(low<=high)
	{
		mid=(low+high)/2;	
		if(group(mid)<=m)
		{
			high=mid-1;
		}
		else
		{
			low=mid+1;
		}
	}
	return mid;
}
 
int main()
{
//	freopen("in.txt","r",stdin);
	int i,low,high,ans;
	while(scanf("%d%d",&n,&m)!=EOF)
	{
		high=0;
		low=0;
		for(i=0;i<n;i++)
		{
			scanf("%d",&a[i]);
			high+=a[i];
			low=max(low,a[i]);
		}
		ans=Bsearch(low,high);
		printf("%d\n",ans);
	}
	return 0;
}