POJ2456(最大化最小值)

Aggressive cows

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 10728		Accepted: 5288

Description

Farmer John has built a new long barn, with N (2 <= N <= 100,000) stalls. The stalls are located along a straight line at positions x1,...,xN (0 <= xi <= 1,000,000,000). 

His C (2 <= C <= N) cows don't like this barn layout and become aggressive towards each other once put into a stall. To prevent the cows from hurting each other, FJ want to assign the cows to the stalls, such that the minimum distance between any two of them is as large as possible. What is the largest minimum distance?

Input

* Line 1: Two space-separated integers: N and C 

* Lines 2..N+1: Line i+1 contains an integer stall location, xi

Output

* Line 1: One integer: the largest minimum distance

Sample Input

5 3
1
2
8
4
9

Sample Output

3
思路：最大化最小值、最小化最大值等问题常用二分搜索解决。

#include <iostream>
#include <algorithm>
using namespace std;
const int MAXN=100005;
int n,m;
int x[MAXN];
bool test(int d)
{
    int cnt=1;
    int last=x[0];
    for(int i=1;i<n;i++)
    {
        while(i<n&&x[i]-last<d)//两牛舍之间的距离均不小最小值d 
        {
            i++;
        }
        if(i==n)    break;
        cnt++;
        last=x[i];
    }    
    return cnt>=m;
}
int main()
{
    while(cin>>n>>m)
    {
        for(int i=0;i<n;i++)
        {
            cin>>x[i];
        }
        sort(x,x+n);
        int l=0;
        int r=0x3f3f3f3f;
        while(r-l>1)
        {
            int mid=(l+r)>>1;
            if(test(mid))    l=mid;
            else r=mid;
        }        
        cout<<l<<endl;
    }
    return 0;
}