How do you solve Maximum of Absolute Value Expression on LeetCode?

Maximum of Absolute Value Expression (LeetCode #1131) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding how to manipulate absolute values can simplify complex expressions.

What is the brute force solution for Maximum of Absolute Value Expression?

The brute force approach for Maximum of Absolute Value Expression is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks every possible pair of indices (i, j) to calculate the expression. This is straightforward but inefficient as it examines all combinations. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum of Absolute Value Expression?

Maximum of Absolute Value Expression uses the following concepts: Array, Math. The recommended patterns to study are: Mathematical Manipulation, Array Traversal.

What are the interview tips for Maximum of Absolute Value Expression?

Always start with a brute force solution to understand the problem better. Look for patterns in the problem that can help reduce complexity. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Maximum of Absolute Value Expression?

Forgetting to consider all combinations of signs when dealing with absolute values. Not optimizing the brute force solution when a clearer pattern emerges.

#1131

Maximum of Absolute Value Expression

Medium

ArrayMathMathematical ManipulationArray Traversal

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(1)

By breaking down the absolute value expression into four cases, we can simplify the calculation and avoid nested loops. This allows us to compute the maximum value in linear time.

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Algorithm

3 steps

1Step 1: Initialize a variable to track the maximum value.
2Step 2: Iterate through the array and calculate the expression for all four combinations derived from the absolute value properties.
3Step 3: For each combination, calculate the maximum value and update the result.

solution.py7 lines

1def maxAbsValExpr(arr1, arr2):
2    max_value = 0
3    n = len(arr1)
4    for sign1 in [1, -1]:
5        for sign2 in [1, -1]:
6            max_value = max(max_value, max(sign1 * arr1[i] + sign2 * arr2[i] + i for i in range(n)) - min(sign1 * arr1[i] + sign2 * arr2[i] + i for i in range(n)))
7    return max_value

ℹ

Complexity note: The time complexity is O(n) because we only iterate through the arrays a constant number of times. The space complexity is O(1) as we are using a fixed amount of space.

1Understanding how to manipulate absolute values can simplify complex expressions.
2Identifying patterns in index differences can lead to more efficient solutions.

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