[LightOJ 1341] Aladdin and the Flying Carpet (算数基本定理(唯一分解定理))

题目链接: https://vjudge.net/problem/LightOJ-1341

题目描述:

问有几种边长为整数的矩形面积等于a，且矩形的短边不小于b

算数基本定理的知识点:https://baike.baidu.com/item/%E7%AE%97%E6%9C%AF%E5%9F%BA%E6%9C%AC%E5%AE%9A%E7%90%86/10920095?fr=aladdin

#include<cstdio>
#include<vector>
#include<cstring>
#include <cmath>

using namespace std;

typedef long long ll;

const int maxn = 1e6+10;

bool vis[maxn];
vector<ll> v;
ll a,b;

//素数打表
void init_prime()
{
    memset(vis,1,sizeof(vis));
    for(ll i = 2;i < maxn;i++)
    {
        for(ll j = i * i;j < maxn;j += i)
        {
            vis[j] = 0;
        }
    }
    for(ll i = 2;i < maxn;i++)
    {
        if(vis[i] == 1)
            v.push_back(i);
    }
}

ll a_count(ll a);

int main()
{
    int t,flag = 1;
    init_prime();
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lld%lld",&a,&b);
        if(b >= sqrt(a))
        {
            printf("Case %d: %d
",flag++,0);
            continue;
        }
        else
        {
            ll cnt = 0;
            for(ll i = 1;i < b;i++)
            {
                if(a % i == 0)
                    cnt++;
            }
            ll sum = a_count(a)/2;
            sum -= cnt;
            printf("Case %d: %lld
",flag++,sum);
        }
    }
    return 0;
}


ll a_count(ll a)
{
    if(a == 0)
        return 0;
    ll num,sum = 1,i = 0;
    while(v[i] < a && i < v.size())
    {
        if(a % v[i] == 0)
        {
            num = 0;
            while(a % v[i] == 0)
            {
                a /= v[i];
                num++;
            }
            sum *= (1+num);
        }
        i++;
    }
    if(a>1)
        sum *= 1+1;
    return sum;
}