AtCoder - 2061 Tree Restoring

Problem Statement

Aoki loves numerical sequences and trees.

One day, Takahashi gave him an integer sequence of length N, a₁,a₂,…,a_N, which made him want to construct a tree.

Aoki wants to construct a tree with N vertices numbered 1 through N, such that for each i=1,2,…,N, the distance between vertex i and the farthest vertex from it is a_i, assuming that the length of each edge is 1.

Determine whether such a tree exists.

Constraints

• 2≦N≦100
• 1≦a_i≦N−1

Input

The input is given from Standard Input in the following format:

N
a1 a2 … aN

Output

If there exists a tree that satisfies the condition, print Possible. Otherwise, print Impossible.

Sample Input 1

5
3 2 2 3 3

Sample Output 1

Possible

The diagram above shows an example of a tree that satisfies the conditions. The red arrows show paths from each vertex to the farthest vertex from it.

Sample Input 2

3
1 1 2

Sample Output 2

Impossible

Sample Input 3

10
1 2 2 2 2 2 2 2 2 2

Sample Output 3

Possible

Sample Input 4

10
1 1 2 2 2 2 2 2 2 2

Sample Output 4

Impossible

Sample Input 5

6
1 1 1 1 1 5

Sample Output 5

Impossible

Sample Input 6

5
4 3 2 3 4

Sample Output 6

Possible

    把直径构造出来，然后讨论讨论就好了

#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int maxn=205;

int cnt[maxn],n,now,M;

int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&now);
		M=max(M,now);
		cnt[now]++;
	}

	for(int i=M;i>M-i;i--)
	    if(cnt[i]<2){ puts("Impossible"); return 0;}

	if(!(M&1)&&cnt[M>>1]!=1){ puts("Impossible"); return 0;}
	if((M&1)&&cnt[M-(M>>1)]!=2){ puts("Impossible"); return 0;}

	puts("Possible");
	return 0;
}