Find all even length binary sequences with same sum of first and second half bits - GeeksforGeeks

Find all even length binary sequences with same sum of first and second half bits - GeeksforGeeks

Given a number n, find all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.

Examples:

Input:  N = 2  Output:   0101 1111 1001 0110 0000 1010     Input:  N = 3  Output:    011011 001001 011101 010001 101011 111111  110011 101101 100001 110101 001010 011110   010010 001100 000000 010100 101110 100010   110110 100100   

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The idea is to fix first and last bits and then recur for remaining 2*(n-1) bits. There are four possibilities when we fix first and last bits –

1. First and last bits are 1, remaining n – 1 bits on both sides should also have the same sum.
2. First and last bits are 0, remaining n – 1 bits on both sides should also have the same sum.
3. First bit is 1 and last bit is 0, sum of remaining n – 1 bits on left side should be 1 less than the sum n-1 bits on right side.
4. First bit is 0 and last bit is 1, sum of remaining n – 1 bits on left side should be 1 more than the sum n-1 bits on right side.

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