Bittijono

#include <iostream>
using namespace std;

const int inf = 1e9;
int solve(int a, int b, int p) {
	int res = 0;
	while(a != b) {
		int div = a / (b+1); // how many times we reduce b+1 from a
		if (p) {
			for (int j = 0; j < div; ++j) cout << (p == 1 ? 1 : 0);
			p = -p;
		} else {
			res += div;
		}
		int tmp = a - div * (b + 1);
		a = b;
		b = tmp;
	}
	if (b > 0) return inf;
	return res + a;
}

int main() {
	std::ios_base::sync_with_stdio(false);
	std::cin.tie(0);

	int n;
	cin >> n;

	int best = 0;
	int steps = inf;
	
	for (int i = 0; i <= n - i; ++i) {
		int j = n-i;
		int val = solve(j,i,0);
		if (val < steps) {
			steps = val;
			best = i;
		}
	}
	
	solve(n-best, best, 1); cout << '\n';
}

Test 1

Group: 1

Verdict: ACCEPTED

Test 2

Group: 1

Verdict: ACCEPTED

Test 3

Group: 1

Verdict: ACCEPTED

Test 4

Group: 1

Verdict: ACCEPTED

Test 5

Group: 1

Verdict: ACCEPTED

Test 6

Group: 1

Verdict: ACCEPTED

Test 7

Group: 1

Verdict: ACCEPTED

Test 8

Group: 1

Verdict: ACCEPTED

Test 9

Group: 1

Verdict: ACCEPTED

Test 10

Group: 1

Verdict: ACCEPTED

Test 11

Group: 2

Verdict: ACCEPTED

Test 12

Group: 2

Verdict: ACCEPTED

Test 13

Group: 2

Verdict: ACCEPTED

Test 14

Group: 2

Verdict: ACCEPTED

Test 15

Group: 2

Verdict: ACCEPTED

Test 16

Group: 2

Verdict: ACCEPTED

Test 17

Group: 2

Verdict: ACCEPTED

Test 18

Group: 2

Verdict: ACCEPTED

Test 19

Group: 2

Verdict: ACCEPTED

Test 20

Group: 2

Verdict: ACCEPTED

Test 21

Group: 3

Verdict: ACCEPTED

Test 22

Group: 3

Verdict: ACCEPTED

Test 23

Group: 3

Verdict: ACCEPTED

Test 24

Group: 3

Verdict: ACCEPTED

Test 25

Group: 3

Verdict: ACCEPTED

Test 26

Group: 3

Verdict: ACCEPTED

Test 27

Group: 3

Verdict: ACCEPTED

Test 28

Group: 3

Verdict: ACCEPTED

Test 29

Group: 3

Verdict: ACCEPTED

Test 30

Group: 3

Verdict: ACCEPTED

Test 31

Group: 4

Verdict: ACCEPTED

Test 32

Group: 4

Verdict: ACCEPTED

Test 33

Group: 4

Verdict: ACCEPTED

Test 34

Group: 4

Verdict: ACCEPTED

Test 35

Group: 4

Verdict: ACCEPTED

Test 36

Group: 4

Verdict: ACCEPTED

Test 37

Group: 4

Verdict: ACCEPTED

Test 38

Group: 4

Verdict: ACCEPTED

Test 39

Group: 4

Verdict: ACCEPTED

Test 40

Group: 4

Verdict: ACCEPTED