hdu-5750 Dertouzos(数论)

题目链接：

Dertouzos

Time Limit: 7000/3500 MS (Java/Others)    

Memory Limit: 131072/131072 K (Java/Others)

Problem Description

A positive proper divisor is a positive divisor of a number n, excluding n itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not.

Peter has two positive integers n and d. He would like to know the number of integers below n whose maximum positive proper divisor is d.

 

Input

There are multiple test cases. The first line of input contains an integer T (1≤T≤106), indicating the number of test cases. For each test case:

The first line contains two integers n and d (2≤n,d≤109).

 

Output

For each test case, output an integer denoting the answer.

 

Sample Input

9

10 2

10 3

10 4

10 5

10 6

10 7

10 8

10 9

100 13

 

Sample Output

1

2

1

0

0

0

0

0

4

 

题意：

 

就是给一个n和一个d,问有多少个小于n的数的最大因子是d;

 

思路：

 

个数为min((n-1)/d,d')d'为d的最小质因子;

素数筛,然后枚举最小质因子,当时忘加一个条件最后测的时候t了;

 

AC代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
//#include <bits/stdc++.h>
#include <stack>

using namespace std;

#define For(i,j,n) for(int i=j;i<=n;i++)
#define mst(ss,b) memset(ss,b,sizeof(ss));

typedef  long long LL;

template<class T> void read(T&num) {
    char CH; bool F=false;
    for(CH=getchar();CH<'0'||CH>'9';F= CH=='-',CH=getchar());
    for(num=0;CH>='0'&&CH<='9';num=num*10+CH-'0',CH=getchar());
    F && (num=-num);
}
int stk[70], tp;
template<class T> inline void print(T p) {
    if(!p) { puts("0"); return; }
    while(p) stk[++ tp] = p%10, p/=10;
    while(tp) putchar(stk[tp--] + '0');
    putchar('\n');
}

const LL mod=1e9+7;
const double PI=acos(-1.0);
const int inf=1e9;
const int N=1e5+10;
const int maxn=500+10;
const double eps=1e-8;

int prime[N],sum[N],a[N],cnt=0,n,d;
void Init()
{
        sum[1]=0;
        For(i,2,N-maxn)
        {
            if(!prime[i])
            {
                for(int j=2*i;j<N-maxn;j+=i)
                {
                    prime[j]=1;
                }
                sum[i]=sum[i-1]+1;
            }
            else sum[i]=sum[i-1];
        }
        For(i,2,N-maxn)
        {
            if(!prime[i])a[++cnt]=i;
        }
}

inline int check(int x)
{
    for(int i=1;i<=cnt;i++)
    {
        if(x%a[i]==0)return a[i];
        if((LL)a[i]*a[i]>x||a[i]>n/d)break;
    }
    return x;
}
int main()
{
        int t;
        read(t);
        Init();
        while(t--)
        {
            read(n);read(d);
            n--;
            int le=min(check(d),n/d);
            printf("%d\n",sum[le]);
        }

        return 0;
}