HackerEarth Binary numbers problem solution

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <chrono>
#include <random>
#include <queue>
#include <bitset>
#include <iomanip>
#include <fstream>
#include <stack>

using namespace std;
 
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> PII;
typedef pair<ll , ll> PLL;
typedef long double ld;
 
#define pb push_back
#define all(c) c.begin(),c.end()
#define allr(c) c.rbegin(),c.rend()
int mod = 1000000007;
const int inf = 1034567891;
const ll LL_INF = 1234567890123456789ll;
#define PI 3.14159265
#define endl 'n'
#define F first
#define S second
#define debug(x) cout << #x << " = " << x << endl;
#define TRACE
 
#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
  cout << name << " : " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
  const char* comma = strchr(names + 1, ',');cout.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}
#else
#define trace(...)
#endif
 
#define out(container) for (auto it : container) cout << it << " "; cout << endl;
 
 
template < typename T > T GCD(T a, T b)            { ll t; while(a) { t = a; a = b % a; b = t; } return b; }
template < typename T > string toString(T a)       { return to_string(a); }
template < typename T > void toInt(string s, T &x) { stringstream str(s); str >> x;}
inline int add(int x, int y){ x += y; if(x >= mod) x -= mod; return x;}
inline int sub(int x, int y){ x -= y; if(x < 0) x += mod; return x;}
inline int mul(int x, int y){ return (x * 1ll * y) % mod;}
inline int powr(int a, ll b){
  int x = 1 % mod;
  while(b){
    if(b & 1) x = mul(x, a);
    a = mul(a, a);
    b >>= 1;
  }
  return x;
}
inline int inv(int a){ return powr(a, mod - 2);}

vector<int> num;

long long dp[60][2][2][2];

long long fun(int ind, int f, int prev, int sub) {
  if (sub)
    return 0;
  if (ind == num.size()) {
    return 1;
  }
  if (~dp[ind][f][prev][sub]) return dp[ind][f][prev][sub];
  int can = (f == 1 ? 1 : num[ind]);
  long long ans = 0;
  for (int i = 0; i <= can; i++) {
    int nf = f, nsub = sub;
    if (!nf && i < num[ind])
      nf = true;
    if (prev == 1 && i == 1)
      nsub = 1;
    ans += fun(ind + 1, nf, i, nsub);
  }
  return dp[ind][f][prev][sub] = ans;
}

map<long long, int> mp;

long long solve(long long n) {
  if (mp.find(n) != mp.end())
    return mp[n];
  num.clear();
  int tn = n;
  while (n) {
    num.push_back(n % 2);
    n /= 2;
  }
  reverse(all(num));
  memset(dp, -1, sizeof(dp));
  long long ans = fun(0, 0, 0, 0);
  mp[tn] = ans - 1;
  return ans - 1;
}

long long get(long long k) {
  long long low = 1, high = 1e12, mid, ans = -1;
  while (low <= high) {
    mid = low + (high - low) / 2;
    if (solve(mid) >= k) {
      ans = mid;
      high = mid - 1;
    } else {
      low = mid + 1;
    }
  }
  assert(ans != -1);
  return ans;
}

long long fib[50];

void pre() {
  fib[0] = 1;
  fib[1] = 2;
  for (int i = 2; i < 50; i++) {
    fib[i] = fib[i - 1] + fib[i - 2]; 
  }
}

long long get1(long long k) {
  long long ans = 0;
  for (int i = 49; i >= 0; i--) {
    if (k >= fib[i]) {
      ans += (1ll << i);
      k -= fib[i];
    }
  }
  return ans;
}

int main()
{
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  
  pre();
  int test;
  cin >> test;
  assert(test >= 1 && test <= 1e5);
  while (test--) {
    int k;
    cin >> k;
    assert(k >= 1 && k <= 1e8);
    long long ans = get1(k);
    vector<int> vec;
    while (ans) {
      vec.push_back(ans % 2);
      ans /= 2;
    }
    reverse(all(vec));
    for (auto it : vec)
      cout << it;
    cout << endl;
  }

  return 0;
}