hdu 1396 Counting Triangles (递推)

Counting Triangles

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2012    Accepted Submission(s): 966

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

 

 

Author

JIANG, Jiefeng

 

 

Source

ZOJ Monthly, June 2003

 

 

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 推了一段时间没推出来= =！

//15MS    232K    347 B    C++
/*

递推:
     a[n] = a[n-1] + n * (n + 1) / 2; 

还有一种情况是最底下一行顶角朝下的三角形： 
观察规律得:left = (n-1) + (n-1)-2 + (n-1)-4... + last(n为奇数, last为2, 反之为1)
    
    a[n] = a[n] + left;
     

*/
#include<stdio.h>
int main(void)
{
    __int64 ans[505]={0,1};
    for(int i=2;i<=500;i++){
        ans[i]=ans[i-1]+i*(i+1)/2;
        int k=i-1;
        while(k>0){
            ans[i]+=k;
            k-=2;
        }
    }
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        printf("%I64d\n",ans[n]);
    }
    return 0;
}