Sumsets
| Time Limit: 2000MS |
|
Memory Limit: 200000K |
| Total Submissions: 14968 |
|
Accepted: 5978 |
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
题意：给定一个N，只允许使用2的幂次数，问有多少种不同的方案组成N。
首先这道题有一个很好想的思路：裸完全背包
最多20个物品，价值分别为2^0, 2^1, ..., 2^19。
这样直接跑一次完全背包打好表就可以了。 G++可以过，C++过不了。。。
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另外一种思路：
两种dp状态推导dp[]。
一、dp[i] = dp[i-1];
二、dp[i] = dp[i-1] + dp[i>>1]。
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