Gym 100917C Constant Ratio 数论+暴力

Posted 2020-08-12 声声醉如兰

Sn=a1*(1-q^n)/(1-q),枚举q的值，判断a1是否为整数，比较暴力

题目：

Description

standard input/output
Statements

Given an integer n, find out number of ways to represent it as the sum of two or more integers a_i with the next property: ratio a_i / a_i - 1is the same positive integer for all possible i > 1.

Input

Input consists of one integer n (1 ≤ n ≤ 10⁵).

Output

Print one integer — number of representations.

Sample Input

Input

1

Output

0

Input

5

Output

2

Input

567

Output

21

Hint

In the first sample no such representation exists.

In the second sample there exist two representations:

• 1 1 1 1 1, then q = 1.
• 1 4, then q = 4.

题目大意：给出一个等比数列（至少连个元素）的和n，要求公比q为整数，求满足要求的等比数列的个数。

题目思路：Sn=a1*(1-q^n)/(1-q),枚举q的值，判断a1是否为整数，比较暴力……

 1 #include<iostream>
 2 #include<algorithm>
 3 #include<cstring>
 4 #include<vector>
 5 #include<stdio.h>
 6 #include<stdlib.h>
 7 #include<queue>
 8 #include<math.h>
 9 #define INF 0x3f3f3f3f
10 #define MAX 1000005
11 #define Temp 1000000000
12 
13 using namespace std;
14 
15 int check(long long q,long long n)
16 {
17     long long a=q;
18     int ans=0;
19     while(n*(q-1)/(a-1) >= 1)
20     {
21         if(n*(q-1)%(a-1)==0 && n*(q-1)/(a-1)>=1 && n*(q-1)/(a-1)<n)//判断a1是否为整数，且满足要求
22             ans++;
23         a*=q;
24     }
25     return ans;
26 }
27 
28 int main()
29 {
30     int n,sum;
31     sum=0;
32     scanf("%d",&n);
33     for(int i=1; i<n; i++)
34     {
35         if(n%i==0 && n/i>1)
36             sum++;
37     }
38     for(int i=2; i<n; i++)//枚举公比的值
39     {
40         sum+=check(i,n);
41     }
42     printf("%d\\n",sum);
43     return 0;
44 }

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