River Hopscotch POJ

Every year the cows hold an event featuring a peculiar version of hopscotch that involves carefully jumping from rock to rock in a river. The excitement takes place on a long, straight river with a rock at the start and another rock at the end, L units away from the start (1 ≤ L≤ 1,000,000,000). Along the river between the starting and ending rocks, N (0 ≤ N ≤ 50,000) more rocks appear, each at an integral distanceD_i from the start (0 < D_i < L).

To play the game, each cow in turn starts at the starting rock and tries to reach the finish at the ending rock, jumping only from rock to rock. Of course, less agile cows never make it to the final rock, ending up instead in the river.

Farmer John is proud of his cows and watches this event each year. But as time goes by, he tires of watching the timid cows of the other farmers limp across the short distances between rocks placed too closely together. He plans to remove several rocks in order to increase the shortest distance a cow will have to jump to reach the end. He knows he cannot remove the starting and ending rocks, but he calculates that he has enough resources to remove up to M rocks (0 ≤ M ≤ N).

FJ wants to know exactly how much he can increase the shortest distance *before* he starts removing the rocks. Help Farmer John determine the greatest possible shortest distance a cow has to jump after removing the optimal set of M rocks.

Input

Line 1: Three space-separated integers: L, N, andM 
Lines 2.. N+1: Each line contains a single integer indicating how far some rock is away from the starting rock. No two rocks share the same position.

Output

Line 1: A single integer that is the maximum of the shortest distance a cow has to jump after removing M rocks

Sample Input

25 5 2
2
14
11
21
17

Sample Output

4

Hint

Before removing any rocks, the shortest jump was a jump of 2 from 0 (the start) to 2. After removing the rocks at 2 and 14, the shortest required jump is a jump of 4 (from 17 to 21 or from 21 to 25).

 

 

典型的二分 求最小值的最大值。

注意一个小细节  a[0]=0 ,a[n+1]=L;

在与河岸垂直的一条线上，河中有N块石头，给定河岸宽度L，以及每一块石头离起点所在河岸的距离，

现在去掉M块石头，要求去掉M块石头后，剩下的石头之间以及石头与河岸的最小距离的最大值。

 

 

#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<queue>
using namespace std;
long long L,n,m,a[50010];
int check(long long x)
{
    int temp=0,k=0;
    for (int i=1 ;i<=n+1 ;i++){
        if (a[i]-a[temp]<x) {
            k++;
            if (k>m) return 0;
        }else temp=i;
    }
    return 1;
}
int main() {
    while(scanf("%lld%lld%lld",&L,&n,&m)!=EOF){
        for (int i=1 ;i<=n ;i++){
            scanf("%d",&a[i]);
        }
        a[0]=0,a[n+1]=L;
        sort(a,a+n+2);
        long long l=0,r=L,mid;
        while(l<=r){
            mid=(l+r)/2;
            if (check(mid)) l=mid+1;
            else r=mid-1;
        }
        printf("%lld
",r);
    }
    return 0;
}