poj-3258-River Hopscotch

深藏阁楼爱情的钟 2022-05-20 06:53 175阅读 0赞

River Hopscotch

<table> 
 <tbody> 
  <tr> 
   <td><strong>Time Limit:</strong>&nbsp;2000MS</td> 
   <td>&nbsp;</td> 
   <td><strong>Memory Limit:</strong>&nbsp;65536K</td> 
  </tr> 
  <tr> 
   <td><strong>Total Submissions:</strong>&nbsp;18575</td> 
   <td>&nbsp;</td> 
   <td><strong>Accepted:</strong>&nbsp;7744</td> 
  </tr> 
 </tbody> 
</table>

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 *Di* from the start (0 < *Di* < *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*, 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

25 5 2
    2
    14
    11
    21
    17

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).

Source

[USACO 2006 December Silver][]

题目大意：给出一条河道的长度l和河中石头n现在有头牛可以跳，让你移走m块石头，求移走m块石头后牛的最小跳远距离的最大值

思路：二分查找，右边的最大距离一定要大于河道长度，因为可能把石头全部移走

代码：

#include<map>
    #include<stack>
    #include<cmath>
    #include<string>
    #include<cstdio>
    #include<cstring>
    #include<cstdlib>
    #include<iostream>
    #include<algorithm>
    using namespace std;
    #define maxn 51100
    #define ll long long
    int a[maxn];
    int l,m,n;
    int f(int mid)
    {
        int i,j,before=0,ans=0;
        for(i=1;i<=n+1;i++)
        {
            if(a[i]-a[before]>=mid)
            {
                before=i;
            }
            else
            {
                ans++;
            }
        }
        if(ans<=m)
            return 1;
        else
            return 0;
    }
    int main()
    {
        while(scanf("%d%d%d",&l,&n,&m)!=EOF)
        {
            int i,j,k,ans=0,ans1=0;
            a[0]=0;
            a[n+1]=l;
            for(i=1;i<=n;i++)
            {
                scanf("%d",&a[i]);
            }
            sort(a+1,a+n+1);
            int l1=0,r=l*2,mid=0;
            while(r-l1>1)
            {
                mid=(l1+r)/2;
                if(f(mid))
                {
                    l1=mid;
                }
                else
                    r=mid;
            }
            printf("%d\n",l1);
        }
        return 0;
    }

[USACO 2006 December Silver]: http://poj.org/searchproblem?field=source&key=USACO+2006+December+Silver