Bittijono

input/code.cpp: In function 'int main()':
input/code.cpp:181:25: warning: statement has no effect [-Wunused-value]
     if (res == "fail") 0;//cout << "Length of " << j << " failed!\n";
                         ^
input/code.cpp:163:6: warning: unused variable 'high' [-Wunused-variable]
  int high = len + 2;
      ^

/*
	Written by, Tuukka Yildirim.
	
	input: n.
	
	I blindly followed a false idea that I came up with, which prolonged the
	solving of this problem. Always doubt your ideas that aren't deeply thought ;-)
	
	A binary string of length <s> will have the most unique substrings when filled with
	consecutive ones and zeros. For example, "10101" is the max for <s> = 5.
	Based on this fact, I thought that the shortest binary string <b> with exactly <n> unique
	substrings, will not be found on a region, that has higher amount of maximum unique substrings.
	For example, "10101" contains 19 unique substrings, the highest for <s> = 5. I thought that if
	I were to find the shortest binary string containing 5 unique substrings, it couldn't possibly
	be at <s> = 4 or over, when in fact it could be found at <s> = a high number (in this example,
	it's actually not true, but generally it is).
	
	When I dumped the idea, I constructed a Monte Carlo algorithm to solve the problem.
	Let's call the solution <b>, that is the shortest binary string containing exactly
	<n> unique substrings. NOTE! <b> is not a constant string, but instead many strings
	at the same time (for most of the time).
	
	First, I try to find the solution from the lowest length, from which <b> can be found.
	I do this up to a length of 32 inclusive.
	
	I have a string array <chains> that contain templates to be tested, before shuffling.
	For every length, I take a string <s>, that is one of the strings in <chains> on the
	first 8 iterations, and otherwise a shuffled string based on the modifications done to it.
	I take <s> and start flipping every bit starting from the second bit. At each individual
	flip, I calculate the fitness of <s> with the following formula: abs(distinctSubstrings(s) - n)
	The fitness yields how close it is to the binary string <b>; 0 meaning it's <b>.
	
	After testing, I flip the bit that led to the best fitness (lowest value). I do this, as long as
	the fitness keeps getting better, or the solution gets found. If I encounter a string, that doesn't
	yield any improvement, I shuffle the string with C++'s  std::random_shuffle, that can
	be found at <algorithm>s. I do this almost 21000 times, which seems to be enough.
	NOTE! I never shuffle the first index, nor do I flip it, since it doesn't matter whether the first
	bit is 0 or 1. They are basically the same thing, when you think about it.
	
	A deterministic algorithm I thought about concerned inverting the function that calculates the amount
	of unique substrings a binary string has. However, this seemed easier. Gratz to everyone who solved
	this with a fast and deterministic algorithm! :)
	
	
*/
 
 
 
#include <iostream>
#include <string>
#include <algorithm>
 
#define T 8
 
using namespace std;
int n;
string chains[T] = {"101010101010101010101010101010101010101010101",
				   "110100100100010011010010010010010010010010010",
				   "111111111111111111111111111111111111111111111",
				   "100000100001000100100001000010000100001000010",
				   "100010001001011100111110111111011001111101111",
				   "100101000111010010110101001010010100011101001",
				   "110110101100101010101010010111011010110010101",
				   "101011010110100110010011010011010110101101001"};
 
int bounds[27] = {1, 3, 6, 11, 19, 32, 53, 87, 142, 231, 375, 608, 985, 1595, 2582, 4179,
              6763, 10944, 17709, 28655, 46366, 75023, 121391, 196416, 317809, 514227, 832038};
 
int numberOfDistinct(const string& str)
{
	int ones = 0;
	int zeros = 0;
	int distinct = 0;
	
	for (size_t i = 0; i < str.length(); i++)
	{
		char bit = str[i];
		bool isOne = bit == '1';
		
		int newSum = 1 + distinct;
		distinct = distinct - (isOne ? ones : zeros) + newSum;
		if (isOne) ones = newSum;
		else zeros = newSum;
	}
	
	return distinct;
}
 
int binSizeLowerBound(int n)
{
	for (int i = 26; i != 0; i--)
	{
		int bound = bounds[i];
		if (bound < n)
		{
			return i + 1;
		}
	}
	return 1;
}
 
 
string findBitstring(string b, int tries)
{
	size_t len = b.size();
	for (int test = 0; test < tries; test++)
	{
		int maxFitness = 123456879, fitIndex = -1;
		while (true)
		{
			bool foundImprovement = false;
			for (size_t i = 1; i < len; i++)
			{
				char bit = b[i];
				char rev = (bit == '1') ? '0' : '1';
				b[i] = rev;
				
				int distinctSubs = numberOfDistinct(b);
				//cout << b << " : " << distinctSubs << "\n";
				
				int fitness = abs(distinctSubs - n);
				if (fitness == 0)
				{
					// Solution found.
					return b;
				}
				if (fitness < maxFitness)
				{
					maxFitness = fitness;
					fitIndex = (int)i;
					foundImprovement = true;
				}
				
				b[i] = bit;
			}
			
			if (foundImprovement) b[fitIndex] = (b[fitIndex] == '1') ? '0' : '1';
			else
			{
				//cout << "No improvement found :-( shuffling\n";
				if (test < T) b = chains[test].substr(0, len);
				else random_shuffle(b.begin() + 1, b.end());
				break;
			}
		}
	}
	return "fail";
}
 
 
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	
	cin >> n;
	bool found = false;
	string s = "10101010101010101010101010101010101010101010";
	
	
	int len = binSizeLowerBound(n);
	int low = len + 1;
	int high = len + 2;
	
	for (int i = 0; i < 27; i++)
		if (bounds[i] == n) found = true;
	
	bool foundAns = false;
	if (n == 1) cout << "1";
	else if (found) cout << s.substr(0, low);
	else
	{
		for (int i = 0; i < 1; i++)
		{
			string chain = s;
			
			for (int j = low; j < 33; j++)
			{
				string sub = chain.substr(0, j);
				string res = findBitstring(sub, 21000);
				if (res == "fail") 0;//cout << "Length of " << j << " failed!\n";
				else
				{
					// Found an answer....
					cout << res << "\n";
					foundAns = true;
					break;
				}
			}
			
			if (foundAns) break;
		}
	}
	
	return 0;
}

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