[思维]Colorful Hats

题目描述

There are N cats. We number them from 1 through N.

Each of the cats wears a hat. Cat i says: "there are exactly ai different colors among the N−1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints
2≤N≤105
1≤ai≤N−1

输入

Input is given from Standard Input in the following format:

N
a1 a2 … aN

输出

Print Yes if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print No otherwise.

样例输入

复制样例数据

3
1 2 2

样例输出

Yes

提示

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

假设共有m种颜色，当猫的颜色是独一无二时，它能看到其他m-1种颜色；否则，能看到所有m种颜色；

当a[1]=a[2]=..=a[n]=m时，若m==n-1，输出Yes；若m<n-1，当2*m<=n时输出Yes，否则输出No

当a[1],a[2],..,a[n]不全相等时，若最大与最小相差超过1，输出No；否则m=max{a[i]}，m种颜色中独一无二的有s=cnt{a[i]==m-1}，当s<=m&&2*(m-s)<=n-s时输出Yes，否则输出No

#include <iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
 
int n,a[100005];
 
int check(){
  for(int i=2;i<=n;i++){
    if(a[i]!=a[1]) return -1;
  }
  return a[1];
}
 
int main()
{
    scanf("%d",&n);
    int m=0,mi=n;
    for(int i=1;i<=n;i++) scanf("%d",&a[i]),m=max(m,a[i]),mi=min(mi,a[i]);
    if(m-mi>=2) return puts("No")*0;
    int tmp=check();
    if(tmp!=-1){
        if(tmp==n-1) return puts("Yes")*0;
        else if(2*tmp<=n) return puts("Yes")*0;
        else return puts("No")*0;
    }
    int s=0;
    for(int i=1;i<=n;i++) if(a[i]==m-1) s++;
    if(s<m&&2*(m-s)<=n-s) return puts("Yes")*0;
    return puts("No")*0;
}