[BZOJ1677] [Usaco2005 Jan]Sumsets 求和

[Usaco2005 Jan]Sumsets 求和

Time Limit: 5 Sec Memory Limit: 64 MB

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).

给出一个N(1≤N≤10^6)，使用一些2的若干次幂的数相加来求之．问有多少种方法

Input

一个整数N.

Output

方法数．这个数可能很大，请输出其在十进制下的最后9位．

Sample Input

7

Sample Output

6

有以下六种方式

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

题解

• 完全背包

var
 dp:array[0..1000000]of longint;
 x:array[0..30]of longint;
 i,j,k:longint;
 n,m,a:longint;
begin
 readln(m);
 a:=1;
 while a<=m do
  begin
   inc(x[0]); x[x[0]]:=a;
   a:=a*2;
  end;
 dp[0]:=1;
 for i:=1 to x[0] do
  for j:=x[i] to m do
   dp[j]:=(dp[j]+dp[j-x[i]])mod 1000000000;
 writeln(dp[m]);
end.