What is the time complexity of Find a Value of a Mysterious Function Closest to Target?

The optimal solution for Find a Value of a Mysterious Function Closest to Target runs in O(n) time and uses O(1) space. This complexity is achieved by stopping the inner loop when the AND value becomes 0, significantly reducing unnecessary calculations.

What is the brute force solution for Find a Value of a Mysterious Function Closest to Target?

The brute force approach for Find a Value of a Mysterious Function Closest to Target is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible pair of indices (l, r) in the array and calculating the AND value for each pair. This is straightforward but inefficient, especially for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find a Value of a Mysterious Function Closest to Target?

Find a Value of a Mysterious Function Closest to Target uses the following concepts: Array, Binary Search, Bit Manipulation, Segment Tree. The recommended patterns to study are: Bit Manipulation, Sliding Window.

What are the interview tips for Find a Value of a Mysterious Function Closest to Target?

Always consider edge cases, such as when the AND value becomes 0. Explain your thought process clearly while coding, as it shows your understanding. Practice optimizing brute force solutions to demonstrate your problem-solving skills.

What are common mistakes when solving Find a Value of a Mysterious Function Closest to Target?

Not considering the properties of the AND operation, leading to redundant calculations. Failing to optimize the inner loop by breaking early when AND becomes 0.

#1521

Find a Value of a Mysterious Function Closest to Target

Hard

ArrayBinary SearchBit ManipulationSegment TreeBit ManipulationSliding Window

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(1)

The optimal solution leverages the properties of the AND operation and uses a binary search approach to efficiently find the closest AND value to the target. This significantly reduces the number of calculations needed.

⚙️

Algorithm

5 steps

1Step 1: Initialize a variable to store the minimum difference from the target.
2Step 2: Iterate through each index i in the array.
3Step 3: For each i, calculate the AND value from arr[i] to arr[j] for increasing j until the AND value becomes 0.
4Step 4: For each AND value computed, use binary search to find the closest value to the target.
5Step 5: Update the minimum difference if the current difference is smaller.

solution.py11 lines

1def closest_value(arr, target):
2    min_diff = float('inf')
3    n = len(arr)
4    for i in range(n):
5        and_value = arr[i]
6        for j in range(i, n):
7            and_value &= arr[j]
8            if and_value == 0:
9                break
10            min_diff = min(min_diff, abs(and_value - target))
11    return min_diff

ℹ

Complexity note: This complexity is achieved by stopping the inner loop when the AND value becomes 0, significantly reducing unnecessary calculations.

1The AND operation is non-increasing, meaning larger ranges will yield smaller or equal values.
2Stopping the search when the AND reaches 0 can save unnecessary calculations.

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