USACO 2.2 Subset Sums (subset)

//Main Idea
//Dynamic Programming.This problem is variant of 0-1 knapsack problem.
// ans[i][j] means the subset number whose sum is j for the set {1,2,..,i};

/*
ID: haolink1
PROG: subset
LANG: C++
*/

//#include <iostream>
#include <fstream>

using namespace std;

int max_num = 0;
unsigned long ans[40][40*(40+1)/2];

int main(){
ifstream fin("subset.in");
fin >> max_num;
int sum = max_num*(max_num+1)/2;
ofstream fout("subset.out");
//The sum of set must be exactly divided by 2 if the sums of both subsets are identical;
if(sum % 2 != 0){
fout<<0<<endl;
return 0;
}
int half_sum = sum/2;
ans[1][1] = 1;
for(int i = 2; i <= max_num; i++){
for(int j = 1; j <= half_sum; j++){
if(j < i) ans[i][j] = ans[i-1][j];
if(j == i) ans[i][j] = ans[i-1][j]+1;
if(j > i) ans[i][j] = ans[i-1][j]+ans[i-1][j-i];
}
}
fout<<ans[max_num][half_sum]/2<<endl;
return 0;
}