array plus bit manipulation Pattern
24 problems
Pattern pages help build reusable solving frames. Identify signals first, then explain state, transition, and edge handling.
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.
Recommended Ladder
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.