hud6216 A Cubic number and A Cubic Number O(1)时间复杂度

A Cubic number and A Cubic Number

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 963    Accepted Submission(s): 468

Problem Description

A cubic number is the result of using a whole number in a multiplication three times. For example,3×3×3=27 so 27 is a cubic number. The first few cubic numbers are 1,8,27,64 and 125. Given an prime number p. Check that if p is a difference of two cubic numbers.

 

Input

The first of input contains an integer T (1≤T≤100) which is the total number of test cases.
For each test case, a line contains a prime number p (2≤p≤1012).

 

Output

For each test case, output 'YES' if given p is a difference of two cubic numbers, or 'NO' if not.

 

Sample Input

102357111317192329

 

Sample Output

NONONOYESNONONOYESNONO

 

p = a^3 - b^3;

 p = (a-b)(a^2 + ab + b^2)

又因为p为素数，我们可以跟定a-b = 1;    所以p = 3b(b+1) + 1；

如果(p-1)%3!=0,也就不存在b(b+1),直接输出no。

p = (p-1)/3;

b = (int)sqrt(p)；

这是p应该等于b(b+1).

AC代码。

#includeusing namespace std;#define ll long longint main(){int tc;ll n;cin>>tc;while(tc--){cin>>n;n-=1;if(n%3){cout<<"NO"<