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 ai with the next property: ratio ai / ai - 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 }
时间： 2024-08-02 06:54:09