Counting Triangles(hd1396)

Counting Triangles

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2506    Accepted Submission(s): 1184

Problem Description

Given an equilateral triangle with n the length of its side, program to count how many triangles in it.

Input

The length n (n <= 500) of the equilateral triangle's side, one per line.

process to the end of the file

 

Output

The number of triangles in the equilateral triangle, one per line.

 

Sample Input

1

2

3

 

Sample Output

1

5

13

　　分正三角形和倒三角形，

　　当长度为n时，在最低边上长度为x的正三角形，个数为n-x+1，所以总的个数为(n-x+1+1)*(n-x+1)/2

　　　　　　　　  在最低边上长度为x的倒三角形，个数为n-x*2+1(2*x<=n),所以总的个数为(n-2*x+1+1)*(n-2*x+1)/2;

#include <iostream>
using namespace std;
int main()
{
    int n,i,j;
    long long a[501]={0};
    for(i=1;i<501;i++)
    {
        for(j=1;j<=i;j++)
        {
            a[i]+=(i-j+1+1)*(i-j+1)/2;
            if(j*2<=i)
                a[i]+=(i-2*j+1+1)*(i-2*j+1)/2;
        }
    }
    while(cin>>n)
        cout<<a[n]<<endl;
}