joj 1026: The Staircases

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本文介绍了一个关于使用砖块构建不同楼梯组合的问题，并提供了一段C++代码实现。任务目标是从给定数量的砖块中计算出可以构建的不同楼梯组合的数量。楼梯必须至少包含两个台阶，每个台阶至少包含一块砖且大小递减。输入为一系列砖块数量，输出为相应的楼梯组合数。

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1026: The Staircases

Status	In/Out	TIME Limit	MEMORY Limit	Submit Times	Solved Users	JUDGE TYPE
	stdin/stdout	3s	8192K	1415	454	Standard

One curious child has a set of N little bricks. From these bricks he builds different staircases. Staircase consists of steps of different sizes in a strictly descending order. It is not allowed for staircase to have steps equal sizes. Every staircase consists of at least two steps and each step contains at least one brick. Picture gives examples of staircase for N=11 and N=5:

Your task is to write a program that reads from input numbers N and writes to output numbers Q - amount of different staircases that can be built from exactly N bricks.

Input

Numbers N, one on each line. You can assume N is between 3 and 500, both inclusive. A number 0 indicates the end of input.

Output

Numbers Q, one on each line.

Sample Input

3
5
0

Sample Output

1
2

#include <cstdio>
#include <string>

double a[505][505];

int main()
{
    int i, k, n;
    memset(a, 0, sizeof(a));
    a[0][0] = 1;
    for(i = 0; i < 505; i ++)
    {
        for(k = 1; k <= i; k ++)
            a[i][k] = a[i - k][k - 1] + a[i][k - 1];
        for(k = i + 1; k < 505; k ++)
            a[i][k] = a[i][i];
    }
    while(scanf("%d", &n) && n)
    {
        printf("%0.0f/n", a[n][n] - 1);
    }
    return 0;
}