CDUESTC 2016 假期赛1 D题

D - An easy problem

Time Limit:3000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u

Description

When Teddy was a child , he was always thinking about some simple math problems ,such as “What it’s 1 cup of water plus 1 pile of dough ..” , “100 yuan buy 100 pig” .etc.. 

One day Teddy met a old man in his dream , in that dream the man whose name was“RuLai” gave Teddy a problem : 

Given an N , can you calculate how many ways to write N as i * j + i + j (0 < i <= j) ? 

Teddy found the answer when N was less than 10…but if N get bigger , he found it was too difficult for him to solve. 
Well , you clever ACMers ,could you help little Teddy to solve this problem and let him have a good dream ? 

Input

The first line contain a T(T <= 2000) . followed by T lines ,each line contain an integer N (0<=N <= 10 ¹⁰).

Output

For each case, output the number of ways in one line.

Sample Input

213 

Sample Output

0

此题是一个数学规律题，（其实我一开始也是想暴力的，TLE了两次，WA了一次，发现必须得用数学公式），不难发现(i+1)*(j+1)=m+1，所以题目变成了求m+1的因数的对数个数

#include <stdio.h>  #include <math.h>  int main()  {      int n;    __int64 m,i,j;      scanf("%d",&n);      while(n--)      {          scanf("%I64d",&m);          m++;          int count = 0;          j = sqrt(m);        for(i = 2;i<=j ; i++)// (i+1)*(j+1) = m+1          {              if(m % i == 0)              count++;          }          printf("%d\n",count);      }     return 0; }