题目描述
SH likes traveling around the world. When he arrives at a city, he will ask the staff about the number of cities that connected with this city directly. After traveling around a mainland, SH will collate data and judge whether the data is correct.
A group of data is correct when it can constitute an undirected graph.
输入
There are multiple test cases. The first line of each test case is a positive integer N (1<=N<=10000) standing for the number of cities in a mainland. The second line has N positive integers a1, a2, ...,an. ai stands for the number of cities that connected directly with the ith city. Input will be ended by the END OF FILE.
输出
If a group of data is correct, output "YES" in one line, otherwise, output "NO".
样例输入
8 7 7 4 3 3 3 2 1 10 5 4 3 3 2 2 2 1 1 1 样例输出
NO YES 1 /***********************************************************
2 * OS : Win7
3 * Complier : GCC(G++)
4 * All Rights Reserved by GingerZeng.
5 **********************************************************/
6 #include<cstdio>
7 #include<cstring>
8 #include<algorithm>
9 #include<cmath>
10 #include<cstdlib>
11 #include<iostream>
12 using namespace std;
13 typedef long long LL;
14 const int inf=1e6+10;
15 int a[inf];
16 LL s[inf];
17 int cmp(int a,int b)
18 {
19 return a>b;
20 }
21 int main()
22 {
23 int n;
24 while(~scanf("%d",&n))
25 {
26 LL sum=0;
27 for(int i=1;i<=n;i++){scanf("%d",&a[i]);}
28 sort(a+1,a+1+n,cmp);
29 for(int i=1;i<=n;i++){sum+=a[i];s[i]=sum;}
30 if(sum%2==0)
31 {
32 int flag=0;
33 for(int k=1;k<=n;k++)
34 {
35 LL all=0;
36 LL ans=0;
37 if(k<n)
38 {
39 if(k>a[k+1])
40 ans=s[n]-s[k];
41 else
42 {
43 int l=k;int r=n;int mid;
44 while(r-l>1)
45 {
46 mid=(l+r)/2;
47 if(a[mid]>=k)l=mid;
48 else r=mid;
49
50 }
51 ans=s[n]-s[r-1]+(r-1-k)*k;
52 }
53 }
54 all+=ans;
55 LL temp=all+k*(k-1);
56 if(s[k]>temp){cout<<"NO"<<endl;flag=1;break;}
57 }
58 if(!flag)cout<<"YES"<<endl;
59 }
60 else
61 {
62 cout<<"NO"<<endl;
63 }
64
65 }
66 return 0;
67 }