EqualsONES.cpp

// Zero Ones Equal One Zeros Problem Code: ZOOZSolvedSubmit
// Kulyash believes in equality.
// Given an integer N, output a binary string of length N such that:

// The count of 01 subsequences in the string is equal to the count of 10 subsequences;
// The string has at least one occurrence of 0 as well as 1.
// If multiple such strings exist, print any. Also, it is guaranteed that corresponding to the given input, an answer always exists.

// Input Format
// First line will contain T, number of test cases. Then the test cases follow.
// Each test case contains of a single line of input, an integer N - the length of the binary string.
// Output Format
// For each test case, output any binary string of length N satisfying the given conditions.
// Constraints
// 1≤T≤100
// 3≤N≤1000
// Subtasks
// Sample Input 1 
// 2
// 4
// 3
// Sample Output 1 
// 1001
// 010
// Explanation
// Test case 1: A binary string satisfying both the conditions is 1001. The count of 01 as well as 10 subsequences in the string is 2.

// Test case 2: A binary string satisfying both the conditions is 010. The count of 01 as well as 10 subsequences in the string is 1.


#include <iostream>
using namespace std;

int main() 
{
    int test;
    cin>>test;
    
    while(test--)
    {
        int num;
        cin>>num;
    
        for(int j=0;j<num;j++)
        {
            if(num%4==0)
            {
                if((j%4==0)||(j+1)%4==0)
                {
                    cout<<"1";
                    
                }
                else
                {
                    cout<<"0";
                }
                
            }
            else
            {
                if(j==0 || j==num-1)
                {
                    cout<<"0";
                }
                else
                {
                    cout<<"1";
                }
            }
            
        }
        cout<<endl;
        
       
        
        
        
    }
	// your code goes here
	return 0;
}