POJ 3258 River Hopscotch（牛过河问题，二分）

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River Hopscotch（查看题目）

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 11391		Accepted: 4890

Description

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 distance D_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 Mrocks (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 ofM rocks.

Input

Line 1: Three space-separated integers: L, N, and M
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

Sample Output

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).

题意理解：

就是一头牛过长度为 l 的河，去掉 n 块石头后问过河距离经过石头之间距离的最大化

代码：

#include<stdio.h>
#include<algorithm>
#define MYDD 11030using namespace std;int l,n,m;
int num[MYDD*50];bool judge(int middle) {int last=0;//记录上一次的位置int sum=0;//记录石头个数for(int j=0; j<n; j++) {if(num[j]-last<middle) {continue;} else {if(l-num[j]<middle)break;last=num[j];sum++;}}return sum>=n-m;
} int main() {scanf("%d%d%d",&l,&n,&m);for(int j=0; j<n; j++) {scanf("%d",&num[j]);}sort(num,num+n);int left=0,right=l,ans=0;while(left<=right) {int middle=(left+right)/2;if(judge(middle)) {ans=middle;left=middle+1;} elseright=middle-1;}printf("%d\n",ans);return 0;
}

参考：学长__ryc

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