AtCoder Grand Contest 016 B - Colorful Hats

题目传送门:https://agc016.contest.atcoder.jp/tasks/agc016_b

题目大意:

\(N\)只猫,每只猫头上带着一个帽子,帽子有颜色,现在告诉你每只猫能看到的其他猫的帽子颜色种数\(a_i\),问是否可能

又是一个结论题……我们设\(Max=\max\limits_{i=1}^n\{a_i\},Min=\min\limits_{i=1}^n\{a_i\}\),若\(Max-Min>1\),则不可能,然后我们分两种情况讨论:

  • \(Max=Min\),那么若\(Max\in(\lfloor\dfrac{n}{2}\rfloor,n-1)\bigcup[n,\infty)\),则不可能,否则可能(要么都独一无二,要么一种颜色至少出现两次)
  • \(Max=Min+1\),那么对于\(i\in[1,n],a_i=Min\),它们的帽子颜色都独一无二的,因为不可能使得所有帽子颜色都独一无二,所以令\(Max'=Max-Min,n'=n-Min\),若\(Max'\in(-\infty,0]\bigcup(\lfloor\dfrac{n'}{2}\rfloor,\infty)\),则不可能,否则可能
/*program from Wolfycz*/
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define inf 0x7f7f7f7f
using namespace std;
typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
inline char gc(){
    static char buf[1000000],*p1=buf,*p2=buf;
    return p1==p2&&(p2=(p1=buf)+fread(buf,1,1000000,stdin),p1==p2)?EOF:*p1++;
}
inline int frd(){
    int x=0,f=1; char ch=gc();
    for (;ch<'0'||ch>'9';ch=gc())   if (ch=='-')    f=-1;
    for (;ch>='0'&&ch<='9';ch=gc()) x=(x<<3)+(x<<1)+ch-'0';
    return x*f;
}
inline int read(){
    int x=0,f=1; char ch=getchar();
    for (;ch<'0'||ch>'9';ch=getchar())  if (ch=='-')    f=-1;
    for (;ch>='0'&&ch<='9';ch=getchar())    x=(x<<3)+(x<<1)+ch-'0';
    return x*f;
}
inline void print(int x){
    if (x<0)    putchar('-'),x=-x;
    if (x>9)    print(x/10);
    putchar(x%10+'0');
}
const int N=1e5;
int v[N+10];
int main(){
    int n=read(),Max=-inf,Min=inf;
    for (int i=1;i<=n;i++){
        v[i]=read();
        Max=max(Max,v[i]);
        Min=min(Min,v[i]);
    }
    if (Max-Min>1)  printf("No\n");
    if (Max==Min)   printf(Max==n-1||Max<=n>>1?"Yes\n":"No\n");
    if (Max==Min+1){
        int cnt=0;
        for (int i=1;i<=n;i++)  if (v[i]==Min)  cnt++;
        n-=cnt,Max-=cnt;
        printf(Max>0&&Max<=n>>1?"Yes\n":"No\n");
    }
    return 0;
}

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转载自www.cnblogs.com/Wolfycz/p/10119569.html