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$ curl repovive.com/roadmaps/fundamental-algorithms/bit-manipulation/single-number-ii

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Single Number II - Bit Manipulation | Fundamental Algorithms | Repovive

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Fundamental Algorithms8 sections · 294 units2h total

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Single Number II

Find the unique element when others appear three times.

Problem: Every element appears three times except one. Find it.

Approach: Count bits. For each bit position, sum the bits across all numbers. If divisible by $3$ , the unique element has $0$ there. Otherwise, it has $1$ .

function singleNumber(nums):
    result = 0
    for i from 0 to 31:
        bitSum = 0
        for num in nums:
            bitSum = bitSum + ((num >> i) & 1)
        if bitSum mod 3 != 0:
            result = result | (1 << i)
    return result

Time: $O(32n) = O(n)$ .

Space: $O(1)$ (excluding input array).

Alternative: Use two variables to simulate a base- $3$ counter per bit.