UVA11137 Ingenuous Cubrency

题意

PDF

分析

考虑dp.

用\(d(i,j)\)表示用不超过i的立方凑成j的方案数。

\(d(i,j)=d(i-1,j)+d(i,j-i^3)\)

时间复杂度\(O(IN+T)\)

代码

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<set>
#include<map>
#include<queue>
#include<stack>
#include<algorithm>
#include<bitset>
#include<cassert>
#include<ctime>
#include<cstring>
#define rg register
#define il inline
#define co const
template<class T>il T read()
{
    rg T data=0;
    rg int w=1;
    rg char ch=getchar();
    while(!isdigit(ch))
    {
        if(ch=='-')
            w=-1;
        ch=getchar();
    }
    while(isdigit(ch))
    {
        data=data*10+ch-'0';
        ch=getchar();
    }
    return data*w;
}
template<class T>T read(T&x)
{
    return x=read<T>();
}
using namespace std;
typedef long long ll;

co int I=21,N=1e4;
ll d[I+1][N+1];

int main()
{
//  freopen(".in","r",stdin);
//  freopen(".out","w",stdout);
    d[0][0]=1;
    for(int i=1;i<=I;++i)
        for(int j=0;j<=N;++j)
        {
            d[i][j]=d[i-1][j];
            if(i*i*i<=j)
                d[i][j]+=d[i][j-i*i*i];
        }
    int n;
    while(~scanf("%d",&n))
        printf("%lld\n",d[I][n]);
    return 0;
}