HDU-6216 A Cubic number and A Cubic Number (数学)

题面

思路:

1.p=x^3-y^3 

2.p=(x-y)(x^2+xy+y^2) 

3.p是素数,因子只有1和自身,而(x^2+xy+y^2)>1

4.(x-y)==1 , x=y+1

5. p=3*y*y+3*y+1

6.计算i~1e6 之间 A[i]=3*i*i+3*i+1

7.二分查找

代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<map>
using namespace std;
const int N=1e6+5;
typedef long long ll;
ll x[N];
void solve()
{
    for(ll i=0;i<N;i+=1)
    {
        x[i]=3*i*i+3*i+1;
    }
}
bool Binary(ll p)
{
    int L=1;
    int R=N-1;
    while(L<=R)
    {
        int M=(L+R)>>1;
        if(x[M]==p)
            return true;
        else if(x[M]<p)
            L=M+1;
        else
            R=M-1;
    }
    return false;
}
int main()
{
    int T;
    scanf("%d",&T);
    solve();
    while(T--)
    {
        ll p;
        scanf("%lld",&p);
        if(Binary(p))
            printf("YES\n");
        else
            printf("NO\n");
    }
    return 0;
}