ural 1017. Staircases

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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 

用n个砖块搭建楼梯，要求楼梯数的砖块数是递增的，求一共有多少种方案。

dp[i][j]表示当前楼梯共用了i块砖，且最后一格共j个砖的方案数，则：
dp[0][0]=1
dp[i][j]=sum{ dp[i-j][k],0<=k<j }

//0.0622 190 KB#include<stdio.h>#define ll long longll dp[507][507];int main(){    dp[0][0]=1;    for(int i=1;i<=500;i++)        for(int j=1;j<=i;j++)            for(int k=0;k<j;k++)                dp[i][j]+=dp[i-j][k];    int n;    while(scanf("%d",&n)!=EOF)    {        ll ans=0;        for(int i=1;i<n;i++)            ans+=dp[n][i];        printf("%lld\n",ans);    }    return 0;}