Apply Bitwise Operations to Make Strings Equal

Apply Bitwise Operations to Make Strings Equal

What is this problem about?

The "Apply Bitwise Operations to Make Strings Equal interview question" is a binary string logic problem. You are given two binary strings, s and target. You can perform a specific bitwise operation: choose two indices $i$ and $j$, and replace s[i] with (s[i] OR s[j]) and s[j] with (s[i] XOR s[j]). You need to determine if it's possible to transform s into target using any number of these operations.

Why is this asked in interviews?

Sprinklr uses the "Apply Bitwise Operations to Make Strings Equal coding problem" to test a candidate's ability to find invariants in a system. Rather than trying to simulate the operations (which would be nearly impossible), you must observe the fundamental behavior of the bits under these rules. It's a test of "Bit Manipulation interview pattern" and logical deduction.

Algorithmic pattern used

This problem relies on Invariance Analysis. Let's look at what the operations do to a pair $(s[i], s[j])$:

• (0, 0) becomes (0 OR 0, 0 XOR 0) = (0, 0).
• (0, 1) becomes (0 OR 1, 0 XOR 1) = (1, 1).
• (1, 0) becomes (1 OR 0, 1 XOR 0) = (1, 1).
• (1, 1) becomes (1 OR 1, 1 XOR 1) = (1, 0). Crucial Observation: You can only create or destroy 1s if there is at least one 1 already present in the string. A string of all 0s can never change. A string with at least one 1 can transform into any other string that also has at least one 1.

Example explanation

$s = "1010"$, $target = "0000"$

• We have 1s in $s$. Can we make it all 0s? No, because to change the last 1, we need another 1 to operate with, but the operation always leaves at least one 1 (unless we start with all 0s). $s = "11"$, $target = "01"$
• We have at least one 1 in $s$ and at least one 1 in $target$. Transition is possible.

Common mistakes candidates make

• Attempting Simulation: Trying to use BFS or backtracking to find a sequence of operations. The state space is far too large.
• Ignoring the all-zero case: Forgetting that if both strings are all 0s, they are already equal and "reachable."
• Over-complicating the logic: Not realizing the simple condition that both strings must either both have at least one 1, or both be all 0s.

Interview preparation tip

When given strange operations in a bitwise problem, write out the truth table for all inputs (0,0), (0,1), (1,0), (1,1). Look for what cannot change. Finding these invariants is the key to solving "Hard" brain-teaser style questions.