POJ 2229 HDU 2709 Sumsets

  • 2018-07-16
  • 14
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题目:

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

题目链接

这道题目用母函数超时,所以采用递推法。

dp[i]记录i可以被组成的种类数。

当i为奇数时:i可以被分为一个1和一个偶数,所以dp[i]=d[i-1]

当i为偶数时有两种情况:

  1. 有两个1,dp[i-2]
  2. 全是偶数,显然等于dp[i/2]

所以dp[i]=dp[i-2]+dp[i/2]

AC代码:

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