hdoj--2709--Sumsets(数位dp)

Sumsets

Time Limit: 6000/2000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 1996    Accepted Submission(s): 786

Problem Description

Farmer John commanded his cows to search for different sets of numbers that sum to a given number. The cows use only numbers that are an integer power of 2. Here are the possible sets of numbers that sum to 7:



1) 1+1+1+1+1+1+1

2) 1+1+1+1+1+2

3) 1+1+1+2+2

4) 1+1+1+4

5) 1+2+2+2

6) 1+2+4



Help FJ count all possible representations for a given integer N (1 <= N <= 1,000,000).

 

Input

A single line with a single integer, N.

 

Output

The number of ways to represent N as the indicated sum. Due to the potential huge size of this number, print only last 9 digits (in base 10 representation).

 

Sample Input

7

 

Sample Output

6

 

Source

USACO 2005 January Silver

 

/*
题意:给出一个整数n,求解该整数n有多少种由2的幂次之和组成的方案.
解题思路：
1.可以将n用二进制表示.
n=1,只有1种表示方法。
n=2，10(2)，二进制表示下，可以分拆成{1,1}，{10}有两种表示方法
n=3, 11(2),可以分拆成{1,1,1},{10,1}.
n=4, 100(2),{1,1,1,1},{10,1,1},{10,10},{100}.
总结：如果所求的n为奇数，那么所求的分解结果中必含有1，
因此，直接将n-1的分拆结果中添加一个1即可 为s[n-1]
如果所求的n为偶数，那么n的分解结果分两种情况
1.含有1 这种情况可以直接在n-1的分解结果中添加一个1即可 s[n-1]
2.不含有1 那么，分解因子的都是偶数，将每个分解的因子都除以2，
刚好是n/2的分解结果，并且可以与之一一对应，这种情况有 s[n/2]

*/
/*#include<stdio.h>
#include<string.h>
int a[1000010];
int main()
{
    a[1]=1;
    a[2]=2;
    int n,i=3;
    while(i<=1000000)
	{
            a[i++]=a[i-1];
            a[i++]=(a[i-1]+a[i>>1])%1000000000;
    }
    while(scanf("%d",&n)!=EOF)
	{
        printf("%d\n",a[n]);
    }
    return 0;
}*/
#include<stdio.h>
#include<string.h>
int f[1000010];
int main()
{
	int n;
	while(scanf("%d",&n)!=EOF)
	{
		memset(f,0,sizeof(f));
		f[1]=1;
		for(int i=2;i<=n;i++)
		{
			if(i&1)
			f[i]=f[i-1];
			else
			f[i]=(f[i-1]+f[i>>1])%1000000000;
		}
		printf("%d\n",f[n]);
	}
	return 0;
}