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array plus bit manipulation Pattern

Pattern hubs are for building transferable solving frames. Learn the recognition signals first, then drill state definition, update rules, and edge explanation until the pattern feels stable.

database24 problemstune8/14/2 difficulty mixcategory6 linked topics

Pattern brief

Recognize first

The candidate shows an understanding of bitwise operations, especially XOR, and how it can be used to efficiently solve problems with unique constraints.

Solve rhythm

State the active state and invariant first, explain how each update preserves them, then pressure-test with counterexamples.

Most common miss

A common mistake is to use extra space for storing values or counting occurrences (e.g., using a hash map or sorting), which violates the constant space constraint.

Recognition signals

The candidate shows an understanding of bitwise operations, especially XOR, and how it can be used to efficiently solve problems with unique constraints.
The candidate provides an optimal solution that minimizes both time complexity and space usage, which is crucial for scalability in large datasets.
Look for an efficient solution using bit manipulation techniques to handle large arrays within time and space constraints.

Solve flow

1. Define the active state/window.
2. Update state while preserving invariants.
3. Validate with edge-heavy examples.

Common misses

A common mistake is to use extra space for storing values or counting occurrences (e.g., using a hash map or sorting), which violates the constant space constraint.
Relying on hashmaps or arrays, which violate the constant space requirement.
Attempting to use a hash map violates constant space requirement.

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Showing 24 / 24 problems

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Single Number

Solve the Single Number problem using an efficient approach with constant space and linear time complexity.

Single Number II

Find the single element in an array where every other element appears three times, using bit manipulation and constant s…

Single Number III

Find the two unique numbers in an array where all other numbers appear exactly twice using bit manipulation efficiently.

UTF-8 Validation

Determine if an integer array represents valid UTF-8 encoding based on its byte sequences using bit manipulation.

Binary Prefix Divisible By 5

Determine which binary prefixes of a given array are divisible by 5 using bit manipulation for efficient checks.

Sort Integers by The Number of 1 Bits

Sort an array of integers by the number of 1's in their binary representation and then by their value in case of ties.

Maximum XOR With an Element From Array

Solve the Maximum XOR With an Element From Array problem by efficiently finding the maximum XOR for each query using bit…

Decode XORed Array

Recover the original integer array from its XOR-encoded version using direct bitwise manipulation and sequential reconst…

Decode XORed Permutation

Decode XORed Permutation uses prefix reconstruction with global XOR to recover the hidden odd-length permutation in line…

Count Pairs With XOR in a Range

Count all pairs in an array whose XOR falls within a given range using efficient bit manipulation techniques and a trie …

Longest Subarray With Maximum Bitwise AND

Find the length of the longest subarray whose bitwise AND reaches the array's maximum value, combining array scanning wi…

Bitwise XOR of All Pairings

Compute the overall bitwise XOR from all pairings between two arrays using efficient array and bit manipulation techniqu…

Find The Original Array of Prefix Xor

Find the original array from a given prefix XOR array using bitwise manipulation techniques.

Minimum Impossible OR

Find the smallest positive integer that cannot be formed from any subsequence OR combination in the array.

Neighboring Bitwise XOR

Determine if a binary array original exists that produces the given derived array using neighboring bitwise XOR logic.

Sum of Values at Indices With K Set Bits

Sum values in an array where the indices have exactly k set bits in binary representation.

Find the K-or of an Array

Given an integer array nums and an integer k, find the K-or of nums where bits qualify based on the occurrence of 1s.

Check if Bitwise OR Has Trailing Zeros

Check if a bitwise OR of two or more numbers has trailing zeros in its binary representation.

Minimum Number of Operations to Make Array XOR Equal to K

Find the minimum number of operations to make the XOR of an array equal to a given value k by modifying array elements.

Find if Array Can Be Sorted

Determine if a given array can be sorted using adjacent swaps restricted by equal set bits in binary representation.

Maximum Possible Number by Binary Concatenation

Determine the largest number achievable by reordering three integers and concatenating their binary forms efficiently.

Construct the Minimum Bitwise Array I

Learn how to construct an array minimizing each element while matching given primes using bitwise operations efficiently…

Construct the Minimum Bitwise Array II

Learn to build the minimum array matching a bitwise OR pattern for each prime in nums, focusing on binary optimization.

Partition Array into Two Equal Product Subsets

Determine if you can partition an array into two subsets with equal product using recursion and bit manipulation.

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Array plus Bit Manipulation LeetCode Pattern: 24 Solutions