How do you solve Bitwise AND of Numbers Range on LeetCode?

Bitwise AND of Numbers Range (LeetCode #201) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(log(max)) time complexity and O(1) space complexity. Key insight: The bitwise AND operation only retains bits that are set in all numbers.

What is the brute force solution for Bitwise AND of Numbers Range?

The brute force approach for Bitwise AND of Numbers Range is Brute Force, with O(n) time complexity and O(1) space complexity. The brute-force approach involves calculating the bitwise AND of all numbers in the range [left, right] by iterating through each number and applying the AND operation. This is straightforward but inefficient for large ranges. The optimal Optimal Solution approach improves this to O(log(max)).

What algorithm or data structure is used to solve Bitwise AND of Numbers Range?

Bitwise AND of Numbers Range uses the following concepts: Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Binary Representation.

What are the interview tips for Bitwise AND of Numbers Range?

Always discuss your thought process and approach before jumping into coding. Consider edge cases, such as when left equals right or when the range is very large. Practice explaining your code and logic clearly, as communication is key in interviews.

What are common mistakes when solving Bitwise AND of Numbers Range?

Failing to recognize that the AND operation can result in zero for large ranges. Not considering the efficiency of the brute-force approach for larger inputs.

#201

Bitwise AND of Numbers Range

Medium

Bit ManipulationBit ManipulationBinary Representation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(log(max))Space O(1)

The optimal solution leverages the properties of binary numbers. The bitwise AND of a range will only preserve bits that are the same for all numbers in that range. We can find the common prefix of 'left' and 'right' to determine the result efficiently.

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Algorithm

3 steps

1Step 1: Initialize a variable 'shift' to 0.
2Step 2: While 'left' is not equal to 'right', shift both left and right to the right by 1 bit and increment 'shift'.
3Step 3: After the loop, shift 'left' back to the left by 'shift' bits to get the final result.

solution.py9 lines

1# Full working Python code
2
3def rangeBitwiseAnd(left, right):
4    shift = 0
5    while left < right:
6        left >>= 1
7        right >>= 1
8        shift += 1
9    return left << shift

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Complexity note: The time complexity is O(log(max)) because we are shifting bits, which takes logarithmic time relative to the size of the numbers. The space complexity is O(1) since we only use a constant amount of space.

1The bitwise AND operation only retains bits that are set in all numbers.
2The common prefix of the binary representations of 'left' and 'right' determines the result.

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