USACO 3.2 Stringsorbits

#include <algorithm>
#include <vector>
#include <iostream>
#include <fstream>
#include <utility>
#include <cmath>
#include <string>
#include <map>
#include <unordered_map>
#include <climits>
#include <sstream>

using namespace std;

int N/* length of string*/, L/* max number of bits per string */;
long long I /* the order */;
int dp[32][32];

int compute(int i, int j){
  if(dp[i][j] != 0)
    return dp[i][j];
  else{
    dp[i][j] = compute(i - 1, j) + compute(i - 1, j - 1);
    return dp[i][j];
  }
}

int main(){
  ifstream fin("kimbits.in");
  ofstream fout("kimbits.out");
  
  fin >> N >> L >> I;
  for(int i = 0; i <= N; i++){
    dp[i][0] = 1;
  }
  
  for(int j = 1; j <= L; j++){
    dp[0][j] = 1;
  }
  
  for(int k = N - 1; k >= 0; k--){
    if(compute(k, L) < I){
      cout << 1;
      fout << 1;
      I -= compute(k,L);
      L--;
    }else{
      cout << 0;
      fout << 0;
    }
  }
  
  cout << endl;
  fout << endl;