What is the time complexity of Longest Strictly Increasing Subsequence With Non-Zero Bitwise AND?

The optimal solution for Longest Strictly Increasing Subsequence With Non-Zero Bitwise AND runs in O(n log n) time and uses O(n) space. The complexity is driven by filtering and applying binary search for LIS, making it efficient for large inputs.

What is the brute force solution for Longest Strictly Increasing Subsequence With Non-Zero Bitwise AND?

The brute force approach for Longest Strictly Increasing Subsequence With Non-Zero Bitwise AND is Brute Force, with O(n²) time complexity and O(1) space complexity. Generate all possible subsequences and check if they are strictly increasing and have a non-zero bitwise AND. This approach is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Longest Strictly Increasing Subsequence With Non-Zero Bitwise AND?

Longest Strictly Increasing Subsequence With Non-Zero Bitwise AND uses the following concepts: Array, Binary Search, Bit Manipulation, Enumeration. The recommended patterns to study are: Binary Search, Dynamic Programming.

What are the interview tips for Longest Strictly Increasing Subsequence With Non-Zero Bitwise AND?

Clarify the constraints and edge cases. Discuss your thought process and approach before coding. Test your solution with various inputs after coding.

What are common mistakes when solving Longest Strictly Increasing Subsequence With Non-Zero Bitwise AND?

Overlooking the bitwise AND condition. Not maintaining the order of elements in subsequences.

#3825

Longest Strictly Increasing Subsequence With Non-Zero Bitwise AND

Medium

ArrayBinary SearchBit ManipulationEnumerationBinary SearchDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

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Intuition

Time O(n log n)Space O(n)

Utilize bit manipulation to filter elements based on their bits, then apply a modified LIS algorithm to find the longest increasing subsequence for each bit position.

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Algorithm

3 steps

1Step 1: Iterate through each bit position from 0 to 30.
2Step 2: Filter nums to keep only elements with the current bit set, maintaining their order.
3Step 3: Apply a dynamic programming approach to find the longest increasing subsequence for the filtered array.

solution.py13 lines

1def longestIncreasingSubseq(nums):
2    max_length = 0
3    for b in range(31):
4        filtered = [x for x in nums if x & (1 << b)]
5        lis = []
6        for num in filtered:
7            pos = bisect.bisect_left(lis, num)
8            if pos == len(lis):
9                lis.append(num)
10            else:
11                lis[pos] = num
12        max_length = max(max_length, len(lis))
13    return max_length

ℹ

Complexity note: The complexity is driven by filtering and applying binary search for LIS, making it efficient for large inputs.

1Bitwise operations can significantly reduce the problem size.
2Dynamic programming is effective for finding increasing subsequences.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.