What is the time and space complexity of Gray Code?

Time complexity: O(2^n). Space complexity: O(2^n).

Gray Code

Med

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Solution Guide: Gray Code

Approach

Generate 2^n Gray codes using the formula gray(i) = i ^ (i >> 1). Iterate from 0 to 2^n - 1 and apply the formula to each index. Adjacent values in the sequence differ by exactly one bit.

Complexity Analysis

Time: O(2^n)
Space: O(2^n)

Pattern

Bit Shifting

Why It Works

XOR-ing a number with its right-shifted self flips at most one bit between consecutive integers, which is exactly the Gray code property.

Updated Feb 2026