ZOJ Problem Set - 2773 Triangular Sums【公式】

ZOJ Problem Set - 2773

Triangular Sums

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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The nth Triangular number, T(n) = 1 + ... + n, is the sum of the first n integers. It is the number of points in a triangular array with n points on side.

For example T(4):

   X  X X X X XX X X X

Write a program to compute the weighted sum of triangular numbers:

W(n) = SUM[k = 1..n; k*T(k+1)]

Input

The first line of input contains a single integer N, (1 <= N <= 1000) which is the number of datasets that follow.

Each dataset consists of a single line of input containing a single integer n, (1 <= n <= 300), which is the number of points on a side of the triangle.

Output

For each dataset, output on a single line the dataset number, (1 through N), a blank, the value of n for the dataset, a blank, and the weighted sum , W(n), of triangular numbers for n.

Sample Input

4
3
4
5
10

Sample Output

1 3 45
2 4 105
3 5 210
4 10 2145

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Source: Greater New York Regional 2006

解题思路：

两个公式的递推。

#include<stdio.h>#include<string.h>#include<algorithm>using namespace std;double oo(int i){return (i*i*i+3*i*i+2*i)/2;}int main(){int T;int y=1;scanf("%d",&T);while(T--){int n;scanf("%d",&n);printf("%d %d ",y++,n);int i,j;double ans=0;for(i=1;i<=n;i++){ans+=oo(i);}printf("%.0lf\n",ans);}return 0;}