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

Link：http://poj.org/problem?id=3273

Monthly Expense

Time Limit: 2000MS Memory Limit: 65536KTotal 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

7 5100400300100500101400

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

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 0xfffffffusing 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;}