Ural 1017. Staircases

1017. Staircases

Time limit: 1.0 second
Memory limit: 64 MB

One curious child has a set of N little bricks (5 ≤ N ≤ 500). 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 andN=5:

Your task is to write a program that reads the number N and writes the only number Q — amount of different staircases that can be built from exactly N bricks.

Input

Number N

Output

Number Q

Sample

inputoutput

212

995645335

Problem Source: Ural State University Internal Contest '99 #2 

一个好奇的小孩子有N个小砖块(5<=N<=500).用这些砖块，他搭建了一些不同的楼梯。楼梯由严格递减的梯子序列组成，楼梯不允许有相同的两梯。每个楼梯至少有2格，每格至少有一个砖块。读入N,输出唯一的数Q--能用N块砖搭建的不同梯子的总数。

类似背包思想，其实是递推

#include <iostream>using namespace std;long long arr[505];int main(){    int n,i,j;    arr[0]=1;    cin>>n;    for(i=1; i<=n; i++)        for(j=n; j>=i; j--)            arr[j]=arr[j]+arr[j-i];    cout<<arr[n]-1<<endl;    return 0;}