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

Posted 2021-02-03 youpeng

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

 1 #include<cstdio>
 2 #include<vector>
 3 #include<cstring>
 4 #include <cmath>
 5 
 6 using namespace std;
 7 
 8 typedef long long ll;
 9 
10 const int maxn = 1e6+10;
11 
12 bool vis[maxn];
13 vector<ll> v;
14 ll a,b;
15 
16 //素数打表
17 void init_prime()
18 {
19     memset(vis,1,sizeof(vis));
20     for(ll i = 2;i < maxn;i++)
21     {
22         for(ll j = i * i;j < maxn;j += i)
23         {
24             vis[j] = 0;
25         }
26     }
27     for(ll i = 2;i < maxn;i++)
28     {
29         if(vis[i] == 1)
30             v.push_back(i);
31     }
32 }
33 
34 ll a_count(ll a);
35 
36 int main()
37 {
38     int t,flag = 1;
39     init_prime();
40     scanf("%d",&t);
41     while(t--)
42     {
43         scanf("%lld%lld",&a,&b);
44         if(b >= sqrt(a))
45         {
46             printf("Case %d: %d
",flag++,0);
47             continue;
48         }
49         else
50         {
51             ll cnt = 0;
52             for(ll i = 1;i < b;i++)
53             {
54                 if(a % i == 0)
55                     cnt++;
56             }
57             ll sum = a_count(a)/2;
58             sum -= cnt;
59             printf("Case %d: %lld
",flag++,sum);
60         }
61     }
62     return 0;
63 }
64 
65 
66 ll a_count(ll a)
67 {
68     if(a == 0)
69         return 0;
70     ll num,sum = 1,i = 0;
71     while(v[i] < a && i < v.size())
72     {
73         if(a % v[i] == 0)
74         {
75             num = 0;
76             while(a % v[i] == 0)
77             {
78                 a /= v[i];
79                 num++;
80             }
81             sum *= (1+num);
82         }
83         i++;
84     }
85     if(a>1)
86         sum *= 1+1;
87     return sum;
88 }