hdu 6216 A Cubic number and A Cubic Number (2017 ACM/ICPC Asia Regional Qingdao Online)

A Cubic number and A Cubic Number

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 101    Accepted Submission(s): 58

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

 

Source

2017 ACM/ICPC Asia Regional Qingdao Online

 

题意：

给出一个素数n,判断能否表示为a*a*a-b*b*b的形式。

思路：

考虑立方差公式

• 

n=a^3-b^3=(a-b)(a^2+ab+b^2)=素数，

则a-b=1;

设b=t,a=t+1,则  n= 3*t^2+3*t+1;

数据量不大 ，直接暴力考虑有没有解即可。

代码：

#include <iostream>#include <algorithm>#include <cstdio>#include <cstring>using namespace std;int main(){    int T;    scanf("%d",&T);    while(T--){        long long n;        scanf("%lld",&n);        long long  i,flag=0,t=1;        while(3*t*t+3*t+1<=n){            if(3*t*t+3*t+1==n){                printf("YES\n");                flag=1;            }            t++;        }        if(!flag)            printf("NO\n");    }    return 0;}

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