How do you solve Maximize Expression of Three Elements on LeetCode?

Maximize Expression of Three Elements (LeetCode #3745) 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: Select the two largest values for a and b.

What is the time complexity of Maximize Expression of Three Elements?

The optimal solution for Maximize Expression of Three Elements runs in O(n) time and uses O(1) space. We traverse the array once to find the required values, resulting in linear time complexity.

What is the brute force solution for Maximize Expression of Three Elements?

The brute force approach for Maximize Expression of Three Elements is Brute Force, with O(n²) time complexity and O(1) space complexity. We can check every combination of three distinct indices in the array to find the maximum value of the expression a + b - c. This guarantees we explore all possibilities. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximize Expression of Three Elements?

Maximize Expression of Three Elements uses the following concepts: Array, Greedy, Sorting, Enumeration. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Maximize Expression of Three Elements?

Explain your thought process clearly. Consider edge cases like duplicates or negative values. Optimize your solution after the brute force explanation.

What are common mistakes when solving Maximize Expression of Three Elements?

Forgetting to check distinct indices. Not handling negative numbers correctly.

#3745

Maximize Expression of Three Elements

Easy

ArrayGreedySortingEnumerationGreedySorting

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)

To maximize a + b - c, we should select the two largest numbers for a and b, and the smallest number for c. This reduces the problem to finding these three numbers efficiently.

⚙️

Algorithm

3 steps

1Step 1: Find the two largest numbers in the array.
2Step 2: Find the smallest number in the array.
3Step 3: Calculate the expression using the two largest and the smallest number.

solution.py12 lines

1def maxExpression(nums):
2    largest1 = largest2 = float('-inf')
3    smallest = float('inf')
4    for num in nums:
5        if num > largest1:
6            largest2 = largest1
7            largest1 = num
8        elif num > largest2:
9            largest2 = num
10        if num < smallest:
11            smallest = num
12    return largest1 + largest2 - smallest

ℹ

Complexity note: We traverse the array once to find the required values, resulting in linear time complexity.

1Select the two largest values for a and b.
2Select the smallest value for c.

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