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+4Help 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
代码
#include<iostream>
#include<string.h>
int dp[1000003];
using namespace std;
int main()
{
int n;
cin>>n;
int q=n,t=1,i;
memset(dp,0,sizeof(dp));
dp[0]=1;
while(1)
{
if(!q)
break;
q=q/2;
for(i=t;i<=n;i++)
dp[i]=(dp[i]+dp[i-t])%1000000000;
t=t*2;
}
cout<<dp[n]<<endl;
return 0;
}
//状态转移
//d [ n ] = d [ n ] + d [ n - t ] ;