bzoj1734 [Usaco2005 feb]Aggressive cows 愤怒的牛

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?

农夫 John 建造了一座很长的畜栏，它包括N (2 <= N <= 100,000)个隔间，这些小隔间依次编号为x1,...,xN (0 <= xi <= 1,000,000,000). 但是，John的C (2 <= C <= N)头牛们并不喜欢这种布局，而且几头牛放在一个隔间里，他们就要发生争斗。为了不让牛互相伤害。John决定自己给牛分配隔间，使任意两头牛之间的最小距离尽可能的大，那么，这个最大的最小距离是什么呢

Input

* Line 1: Two space-separated integers: N and C * Lines 2..N+1: Line i+1 contains an integer stall location, xi

第一行：空格分隔的两个整数N和C

第二行---第N+1行：i+1行指出了xi的位置

Output

* Line 1: One integer: the largest minimum distance

第一行：一个整数，最大的最小值

Sample Input

5 3
1
2
8
4
9

Sample Output

3

把牛放在1，4，8这样最小距离是3

题意是给定数轴上n个点，要取出其中m个点使得相邻的点的最小距离最大。

看到最小值最大……呵呵……果断二分

每次枚举一个最小距离k，然后贪心验证。

首先第一个点是必取的，然后后面的点一旦超过k就取。因为如果超过k还不取就相当于寻找更“不优”的一组可行解，不取白不取

最后判断一下有没有取光m个点就行了

#include<cstdio>
#include<algorithm>
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;
}
int n,m,ans,l,r;
int a[200001];
inline bool jud(int x)
{
	int tot=1,now=1,save=1;
	while (tot<=m)
	{
		while (a[now]-a[save]<x && now<=n) now++;
		if (now>n && tot<m) return 0;
		tot++;save=now;
		if (tot==m) return 1;
	}
	return 1;
}
int main()
{
	n=read();
	m=read();
	for (int i=1;i<=n;i++) a[i]=read();
	sort(a+1,a+n+1);
	l=1;r=1000000000;
	while (l<=r)
	{
		int mid=(l+r)>>1;
		if (jud(mid)){ans=mid;l=mid+1;}
		else r=mid-1;
	}
	printf("%d",ans);
}