Print N-bit binary numbers having more 1’s than 0’s in all prefixes

Given a positive integer n, print all n-bit binary numbers having more 1’s than 0’s for any prefix of the number.

Examples: 

Input : n = 2
Output : 11 10

Input : n = 4
Output : 1111 1110 1101 1100 1011 1010

A simple but not efficient solution will be to generate all N-bit binary numbers and print those numbers that satisfy the conditions. The time complexity of this solution is exponential. 

An efficient solution is to generate only those N-bit numbers that satisfy the given conditions. We use recursion, At each point in the recursion, we append 0 and 1 to the partially formed number and recur with one less digit. 

Implementation:

1111 1110 1101 1100 1011 1010 

Time Complexity: O(n)
Auxiliary Space: O(n)

A non-recursive solution also exists, the idea is to directly generate the numbers in the range of 2^N to 2^(N-1) then require, only these which satisfies the condition:

Implementation:

1111 1110 1101 1100 1011 1010 

Time Complexity: O(m*n)
Auxiliary Space: O(n)