LeetCode #2546 — MEDIUM

Apply Bitwise Operations to Make Strings Equal

Move from brute-force thinking to an efficient approach using bit manipulation strategy.

Solve on LeetCode
The Problem

Problem Statement

You are given two 0-indexed binary strings s and target of the same length n. You can do the following operation on s any number of times:

  • Choose two different indices i and j where 0 <= i, j < n.
  • Simultaneously, replace s[i] with (s[i] OR s[j]) and s[j] with (s[i] XOR s[j]).

For example, if s = "0110", you can choose i = 0 and j = 2, then simultaneously replace s[0] with (s[0] OR s[2] = 0 OR 1 = 1), and s[2] with (s[0] XOR s[2] = 0 XOR 1 = 1), so we will have s = "1110".

Return true if you can make the string s equal to target, or false otherwise.

Example 1:

Input: s = "1010", target = "0110"
Output: true
Explanation: We can do the following operations:
- Choose i = 2 and j = 0. We have now s = "0010".
- Choose i = 2 and j = 1. We have now s = "0110".
Since we can make s equal to target, we return true.

Example 2:

Input: s = "11", target = "00"
Output: false
Explanation: It is not possible to make s equal to target with any number of operations.

Constraints:

  • n == s.length == target.length
  • 2 <= n <= 105
  • s and target consist of only the digits 0 and 1.
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: You are given two 0-indexed binary strings s and target of the same length n. You can do the following operation on s any number of times: Choose two different indices i and j where 0 <= i, j < n. Simultaneously, replace s[i] with (s[i] OR s[j]) and s[j] with (s[i] XOR s[j]). For example, if s = "0110", you can choose i = 0 and j = 2, then simultaneously replace s[0] with (s[0] OR s[2] = 0 OR 1 = 1), and s[2] with (s[0] XOR s[2] = 0 XOR 1 = 1), so we will have s = "1110". Return true if you can make the string s equal to target, or false otherwise.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Bit Manipulation

Example 1

"1010"
"0110"

Example 2

"11"
"00"

Related Problems

  • Minimum One Bit Operations to Make Integers Zero (minimum-one-bit-operations-to-make-integers-zero)
Step 02

Core Insight

What unlocks the optimal approach

  • Think of when it is impossible to convert the string to the target.
  • If exactly one of the strings is having all 0’s, then it is impossible. And it is possible in all other cases. Why is that true?
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2546: Apply Bitwise Operations to Make Strings Equal
class Solution {
    public boolean makeStringsEqual(String s, String target) {
        return s.contains("1") == target.contains("1");
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n)
Space
O(1)

Approach Breakdown

SORT + SCAN
O(n log n) time
O(n) space

Sort the array in O(n log n), then scan for the missing or unique element by comparing adjacent pairs. Sorting requires O(n) auxiliary space (or O(1) with in-place sort but O(n log n) time remains). The sort step dominates.

BIT MANIPULATION
O(n) time
O(1) space

Bitwise operations (AND, OR, XOR, shifts) are O(1) per operation on fixed-width integers. A single pass through the input with bit operations gives O(n) time. The key insight: XOR of a number with itself is 0, which eliminates duplicates without extra space.

Shortcut: Bit operations are O(1). XOR cancels duplicates. Single pass → O(n) time, O(1) space.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.