POJ 3273 Monthly Expense(二分答案)

Monthly Expense

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 36628		Accepted: 13620

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

【题意】

给出农夫在n天中每天的花费，要求把这n天分作m组，每组的天数必然是连续的，要求分得各组的花费之和应该尽可能地小，最后输出各组花费之和中的最大值

【分析】

套路性二分

【代码】

Select Code

#include<cstdio>
#include<algorithm>
#include<iostream>
#define debug(x) cerr<<#x<<" "<<x<<'\n';
using namespace std;
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
const int N=1e5+5;
int n,m,d[N];
inline bool check(int now){
	int res=1,sum=0;
	for(int i=1;i<=n;i++){
		if(sum+d[i]<=now){
			sum+=d[i];
		}else{
			sum=d[i];
			res++;
		}
	}
	return res<=m;
}
int main(){
	n=read();m=read();
	int l=0,r=0,mid=0,ans=0;
	for(int i=1;i<=n;i++) d[i]=read(),r+=d[i],l=max(l,d[i]);
	while(l<=r){
		mid=l+r>>1;
		if(check(mid)){
			ans=mid;
			r=mid-1;
		}
		else{
			l=mid+1;
		}
	}
	printf("%d\n",ans);
	return 0;
}