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  1. import math
  2. def find(u, par):
  3.  
  4.     if par[u] != u:
  5.         par[u] = find(par[u], par)
  6.     return par[u]
  7.  
  8. def union(u, v, par, size):
  9.     u_root = find(u, par)
  10.     v_root = find(v, par)
  11.  
  12.     if u_root == v_root:
  13.         return 
  14.  
  15.  
  16.     if size[u_root] < size[v_root]:
  17.         par[u_root] = v_root
  18.         size[v_root] += size[u_root]
  19.     else:
  20.         par[v_root] = u_root
  21.         size[u_root] += size[v_root]
  22.  
  23. def ip():
  24.     return map(int,input().split())
  25.  
  26.  
  27.  
  28.  
  29. T=1
  30. T=int(input())
  31. for __ in range(T):
  32.     n=int(input())
  33.     lst=list(ip())
  34.  
  35.     if n==1:
  36.         print("yes")
  37.         continue
  38.  
  39.     if (n*(lst[1]-lst[0])+lst[0]) %(n+1)!=0:
  40.         print("no")
  41.         continue
  42.  
  43.     k1=(n*(lst[1]-lst[0])+lst[0])//(n+1)
  44.  
  45.     if (2*lst[0]-lst[1])%(n+1)!=0:
  46.         print("no")
  47.         continue
  48.  
  49.     k2=(2*lst[0]-lst[1])//(n+1)
  50.  
  51.     if k1<0 or k2<0:
  52.         print("no")
  53.         continue
  54.     fg=True
  55.     for i in range(2,n):
  56.         if k1*(i+1)+k2*(n-(i+1)+1)!=lst[i]:
  57.             fg=False
  58.             break
  59.  
  60.     if fg:
  61.         print("yes")
  62.         continue
  63.     print("no")
Success #stdin #stdout 0.08s 14152KB
comments (?)
stdin
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6
4
3 6 6 3
5
21 18 15 12 9
10
2 6 10 2 5 5 1 2 4 10
7
10 2 16 12 8 20 4
2
52 101
2
10 2
stdout
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no
yes
no
no
yes
no
https://ideone.com/ZGblKL
language:
Python 3 (python  3.12)
created:
3 days ago
visibility:
public

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