HDU 2601 An easy problem(数学转换)
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An easy problem
Time Limit: 6000/3000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 9162 Accepted Submission(s): 2254
Problem 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 ?
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 <= 1010).
Output
For each case, output the number of ways in one line.
Sample Input
213
Sample Output
01
题如其名,真的是一道easy problem。
要注意的是N的数据范围很大,因此需要用long long这种类型定义N;
下面说数学转换:
N=i*j+i+j=(i+1)*(j+1)-1
让i=i+1;j=j+1;
那么N+1=i*j(i<=j<=2);
根据这个算是可以得到
i<=sqrt(N+1);
那么题目就可以得到解决了,
下面的代码采用cin,运行时间2.9s,题目要求时间是3s,所以水水的过了。
用scanf的话会稍微快一点。
下面是AC代码:
#include<iostream>
#include<string.h>
#include<string>
#include<stack>
#include<cmath>
#include<queue>
#include<vector>
#include<algorithm>
using namespace std;
const int inf=0x7FFFFFFF;
const int M=1000+10;
int dp[M];
int v,t,val[M],vo[M];
long long n;
int main()
{
cin>>t;
while(t--)
{
cin>>n;
long long cnt=0;
n++;
for(int i=2;i<=sqrt(n);i++)
{
if(n%i==0) cnt++;
}
cout<<cnt<<endl;
}
return 0;
}
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