Problem Description

There are many trees forming a m * n grid, the grid starts from (1,1). Farmer Sherlock is standing at (0,0) point. He wonders how many trees he can see.

If two trees and Sherlock are in one line, Farmer Sherlock can only see the tree nearest to him.

樣例

解題報告

設：

該問題就是求:

程式碼如下:

//求區間x[1,n],y[1,m],gcd(x,y)==1的數量
#include<stdio.h>
#define MAX_C 32
 

typedef long long LL;
int cs[MAX_C],u;

int slove(int m,int n){
    u=0;
    for(int i=2;i*i<=n;i++)
        if(n%i==0){
            cs[u++]=i;
            while(n%i==0) n/=i;
        }
    if(n>1) cs[u++]=n;

    int ans=0;
    for(int i=1;i<(1<<u);i++){
        int cnt=0,res=1;
        for
 
(int k=0;k<u;k++)
            if(i>>k&1){
                res*=cs[k];
                cnt++;
            }
        ans+=cnt&1?m/res:-m/res;
    }
    return m-ans;
}

int main()
{
    int T,a,b;
    scanf("%d",&T);
    while(T--){
        scanf("%d%d",&a,&b);
        LL ans=0; //一組不超int 但是1e5組可能超
        for(int i=1;i<=a;i++)
            ans+=slove(b,i);
        printf("%lld\n",ans);
    }
    return 0;
}