codeforces 570B Simple Game

最新推荐文章于 2024-08-31 10:23:18 发布

原创最新推荐文章于 2024-08-31 10:23:18 发布 · 198 阅读

0 ·

CC 4.0 BY-SA版权

文章标签：

#codeforces

ACM算法_思维题专栏收录该内容

14 篇文章

订阅专栏

本文介绍了一个简单的游戏策略问题，玩家需要选择一个整数并利用随机数确定胜者。文章提供了代码实现，帮助读者理解如何计算最优策略下获胜的概率。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

点击打开链接

One day Misha and Andrew were playing a very simple game. First, each player chooses an integer in the range from 1 to n. Let's assume that Misha chose number m, and Andrew chose number a.

Then, by using a random generator they choose a random integer c in the range between 1 and n (any integer from 1 to n is chosen with the same probability), after which the winner is the player, whose number was closer to c. The boys agreed that if m and a are located on the same distance from c, Misha wins.

Andrew wants to win very much, so he asks you to help him. You know the number selected by Misha, and number n. You need to determine which value of a Andrew must choose, so that the probability of his victory is the highest possible.

More formally, you need to find such integer a (1 ≤ a ≤ n), that the probability that $\text{[math]}$ is maximal, where c is the equiprobably chosen integer from 1 to n (inclusive).

Input

The first line contains two integers n and m (1 ≤ m ≤ n ≤ 109) — the range of numbers in the game, and the number selected by Misha respectively.

Output

Print a single number — such value a, that probability that Andrew wins is the highest. If there are multiple such values, print the minimum of them.

   Examples
 
     input 
    
      Copy
    
3 1

     output 
    
      Copy
    
2

     input 
    
      Copy
    
4 3

     output 
    
      Copy
    
2

Note

In the first sample test: Andrew wins if c is equal to 2 or 3. The probability that Andrew wins is 2 / 3. If Andrew chooses a = 3, the probability of winning will be 1 / 3. If a = 1, the probability of winning is 0.

In the second sample test: Andrew wins if c is equal to 1 and 2. The probability that Andrew wins is 1 / 2. For other choices of a the probability of winning is less.

这个题不难理解，但是就是做不出来，都要百度看别人的代码了，他们给的分类是思维题，然后就没看，我想自己做。

注意几组数据

5 5

输出 4

1 1

输出

#include<bits/stdc++.h>  
using namespace std;  
typedef long long ll;  
const int inf = 0x3f3f3f3f;  
int main()   
{  
    // freopen("shuju.txt","r",stdin);
    int n,m;
    cin>>n>>m;
    int dis1=m,dis2=n-m+1;
    if(n==1&&m==1)
        cout<<"1"<<endl;
    else if(n==m)
        cout<<n-1<<endl;
    else
    {
        if(dis1<dis2)
            cout<<m+1<<endl;
        else
            cout<<m-1<<endl;
    }
    return 0;  
}