HDU6216

A Cubic number and A Cubic Number

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 313    Accepted Submission(s): 184

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

10
2
3
5
7
11
13
17
19
23
29

 

Sample Output

NO
NO
NO
YES
NO
NO
NO
YES
NO
NO

 

Source

2017 ACM/ICPC Asia Regional Qingdao Online

 

a^3-b^3 == p，p为质数，所以a-b=1

 //2017-09-17
 #include <cstdio>
 #include <cstring>
 #include <iostream>
 #include <algorithm>
 #define ll long long

 using namespace std;

 const int N = ;

 ll cubic[N+];
 ll diff[N+];

 bool check(ll p){
     int pos = lower_bound(diff+, diff+N, p) - diff;
     if(diff[pos] == p)
       return true;
     return false;
 }

 int main()
 {
     int T;
     scanf("%d", &T);
     ll p;
     for(ll i = ; i <= N; i++)
         cubic[i] = i*i*i;
     for(int i = ; i <= N; i++)
         diff[i] = cubic[i+]-cubic[i];
     while(T--){
         scanf("%lld", &p);
         if(check(p))
           printf("YES\n");
         else printf("NO\n");
     }

     return ;
 }