## 1677: [Usaco2005 Jan]Sumsets 求和

Time Limit: 5 Sec  Memory Limit: 64 MB
Submit: 696  Solved: 387
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## 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).

一个整数N.

7

6

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

## Source

Silver

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#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
int a[100];
int f[1000005];
int main(){
int n;
scanf("%d",&n);
for(int i=1;i<=n;i*=2)
a[++a[0]]=i;
int len=a[0];
f[0]=1;
for(int i=1;i<=len;i++){
for(int j=a[i];j<=n;j++){
f[j]+=f[j-a[i]];
f[j]%=1000000000;
}
}
printf("%d\n",f[n]);
return 0;
}

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