UOJ #148. 【NOIP2015】跳石头 二分

时间：2024-08-23 15:04:14

#148. 【NOIP2015】跳石头

Time Limit: 20 Sec

Memory Limit: 256 MB

题目连接

http://uoj.ac/problem/148

Description

一年一度的“跳石头”比赛又要开始了！

这项比赛将在一条笔直的河道中进行，河道中分布着一些巨大岩石。组委会已经选择好了两块岩石作为比赛起点和终点。在起点和终点之间，有 N 块岩石（不含起点和终点的岩石）。在比赛过程中，选手们将从起点出发，每一步跳向相邻的岩石，直至到达终点。

为了提高比赛难度，组委会计划移走一些岩石，使得选手们在比赛过程中的最短跳跃距离尽可能长。由于预算限制，组委会至多从起点和终点之间移走 M 块岩石（不能移走起点和终点的岩石）。

Under two situations the player could score one point.

⋅1. If you touch a buoy before your opponent, you will get one point. For example if your opponent touch the buoy #2 before you after start, he will score one point. So when you touch the buoy #2, you won't get any point. Meanwhile, you cannot touch buoy #3 or any other buoys before touching the buoy #2.

⋅2. Ignoring the buoys and relying on dogfighting to get point.
If you and your opponent meet in the same position, you can try to
fight with your opponent to score one point. For the proposal of game
balance, two players are not allowed to fight before buoy #2 is touched by anybody.

There are three types of players.

Speeder:
As a player specializing in high speed movement, he/she tries to avoid
dogfighting while attempting to gain points by touching buoys.
Fighter:
As a player specializing in dogfighting, he/she always tries to fight
with the opponent to score points. Since a fighter is slower than a
speeder, it's difficult for him/her to score points by touching buoys
when the opponent is a speeder.
All-Rounder: A balanced player between Fighter and Speeder.

There will be a training match between Asuka (All-Rounder) and Shion (Speeder).
Since the match is only a training match, the rules are simplified: the game will end after the buoy #1 is touched by anybody. Shion is a speed lover, and his strategy is very simple: touch buoy #2,#3,#4,#1 along the shortest path.

Asuka is good at dogfighting, so she will always score one point by dogfighting with Shion, and the opponent will be stunned for T seconds after dogfighting.
Since Asuka is slower than Shion, she decides to fight with Shion for
only one time during the match. It is also assumed that if Asuka and
Shion touch the buoy in the same time, the point will be given to Asuka
and Asuka could also fight with Shion at the buoy. We assume that in
such scenario, the dogfighting must happen after the buoy is touched by
Asuka or Shion.

The speed of Asuka is V1 m/s. The speed of Shion is V2 m/s. Is there any possibility for Asuka to win the match (to have higher score)?

Input

输入文件第一行包含三个整数 L,N,M，分别表示起点到终点的距离，起点和终点之间的岩石数，以及组委会至多移走的岩石数。保证 L≥1 且 N≥M≥0。

接下来 N 行，每行一个整数，第 i 行的整数 Di（0<Di<L）， 表示第 i 块岩石与起点的距离。这些岩石按与起点距离从小到大的顺序给出，且不会有两个岩石出现在同一个位置。

Output

输出文件只包含一个整数，即最短跳跃距离的最大值。

Sample Input

25 5 2
2
11
14
17
21

Sample Output

4

HINT

题意

题解：

二分答案，然后check就好了

代码

#include<stdio.h>

#include<iostream>

using namespace std;

int l,n,m;

int a[];

int L;

int check(int x)

{

    int last = ;

    int ans = ;

    for(int i=;i<=n;i++)

    {

        if(a[i]-last<x)

            ans++;

        else

            last = a[i];

    }

    if(ans>m)return ;

    return ;

}

int main()

{

    scanf("%d%d%d",&L,&n,&m);

    for(int i=;i<=n;i++)

        scanf("%d",&a[i]);

    a[n+]=L;n++;

    int l = ,r = L;

    while(l<=r)

    {

        int mid = (l+r)/;

        if(check(mid))l=mid+;

        else r=mid-;

    }

    printf("%d\n",l-);

}

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