随笔 - 531 文章 - 0 评论 - 3 阅读 - 10215

Divisors UVA - 294

求区间[L,R]的整数中哪一个的正约数最多。

一个数因数分解后，它的约数Cnt = (a[j]+1) 的乘积，j是每个因数的个数

#include <iostream>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std ; 
  const int M=1e5+30;
 #define int long long
 int b[M],prime[M],tot,n;
  
 void init(int top){
     memset(b,1,sizeof b);
     b[1]=0;
      
     int i,j;
     for(i=2;i<=top;i++){
         if(b[i]) prime[++tot]=i;
          
        for(j=1;j<=tot&&i*prime[j]<=top;j++){
             b[i*prime[j]]=0;
             if(i%prime[j]==0) break;
        } 
     }
 }
 int Count(int x){
     
    int i,s=1,cnt;
    for(i=1;prime[i]*prime[i]<=x;i++){
        cnt=1;
        if(x%prime[i]==0){
            while(x%prime[i]==0) x/=prime[i],cnt++;
            s*=cnt;
        }
    }
    if(x>1) s*=2;
    return s; 
 }
 signed main(){
    int tes,L,R;
     
    init(1e5);
    cin>>tes;
    while(tes--){
        cin>>L>>R; 
         
        int ans=0,id=0;
        for(int i=L;i<=R;i++){
            int x =Count(i);
            if(x>ans) ans=x,id=i;
        }
        printf("Between %d and %d, %d has a maximum of %d divisors."
        ,L,R,id,ans);
        puts("");
    }
 }