poj 2229 Sumsets 【動态規劃】

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Sumsets

Time Limit: 2000MS

Memory Limit: 200000K

Total Submissions: 13291

Accepted: 5324

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 &lt;= N &lt;= 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

Sample Output

題目翻譯：給出一個數字n，給出一個集合{1,2,4,8,16,32,64。。。。}，求n有多少種不同的由集合内的數字的加和情況。

解題思路：本以為是母函數，但是在網上搜了一下結果發現是遞推，可以有前面推出後面的結果，原因是和2的指數關系有關。