3382. 整数拆分

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3382. 整数拆分

• 题意

  一个整数总可以拆分为 2的幂的和
  用 f(n)表示 n的不同拆分的种数，例如 f(7)=6
  要求编写程序，读入 n，输出 f(n)mod109

• 思路

  完全背包问题 求方案数
  

• 代码

  '''
  Author: NEFU AB-IN
  Date: 2023-03-23 16:16:15
  FilePath: \Acwing\3382\3382.py
  LastEditTime: 2023-03-23 19:43:52
  '''
  read = lambda: map(int, input().split())
  from collections import Counter, deque
  from heapq import heappop, heappush
  from itertools import permutations
  
  N = int(1e6 + 10)
  INF = int(2e9)
  MOD = int(1e9)
  dp = [0] * N
  
  n = int(input())
  dp[0] = 1
  
  i = 1
  while i <= n:
      for j in range(i, n + 1):
          dp[j] = (dp[j] + dp[j - i]) % MOD
      i *= 2
  
  print(dp[n])