How do you solve Maximum Product Difference Between Two Pairs on LeetCode?

Maximum Product Difference Between Two Pairs (LeetCode #1913) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: The maximum product difference can be achieved by focusing on the largest and smallest numbers.

What is the time complexity of Maximum Product Difference Between Two Pairs?

The optimal solution for Maximum Product Difference Between Two Pairs runs in O(n log n) time and uses O(1) space. The time complexity is O(n log n) due to the sorting step. The space complexity is O(1) since we are only using a constant amount of space for calculations.

What is the brute force solution for Maximum Product Difference Between Two Pairs?

The brute force approach for Maximum Product Difference Between Two Pairs is Brute Force, with O(n²) time complexity and O(1) space complexity. We can check all possible pairs of indices to find the maximum product difference. This involves calculating the product for every combination of two pairs from the array. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Product Difference Between Two Pairs?

Maximum Product Difference Between Two Pairs uses the following concepts: Array, Sorting. The recommended patterns to study are: Sorting, Array.

What are the interview tips for Maximum Product Difference Between Two Pairs?

Always think about edge cases, such as arrays with duplicate values. Explain your thought process clearly while coding; it shows your understanding. Practice both brute force and optimal solutions to demonstrate problem-solving skills.

What are common mistakes when solving Maximum Product Difference Between Two Pairs?

Not considering that only four distinct indices are needed. Overlooking the importance of sorting to easily find the largest and smallest products.

#1913

Maximum Product Difference Between Two Pairs

Easy

ArraySortingSortingArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n log n)Space O(1)

To maximize the product difference, we only need the two largest and two smallest numbers from the array. This is because the maximum product will come from the largest numbers and the minimum product from the smallest numbers.

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Algorithm

4 steps

1Step 1: Sort the array.
2Step 2: Calculate the product of the two largest numbers (last two elements in sorted array).
3Step 3: Calculate the product of the two smallest numbers (first two elements in sorted array).
4Step 4: Return the difference between the two products.

solution.py5 lines

1# Full working Python code
2
3def maxProductDifference(nums):
4    nums.sort()
5    return (nums[-1] * nums[-2]) - (nums[0] * nums[1])

ℹ

Complexity note: The time complexity is O(n log n) due to the sorting step. The space complexity is O(1) since we are only using a constant amount of space for calculations.

1The maximum product difference can be achieved by focusing on the largest and smallest numbers.
2Sorting the array simplifies the problem by allowing easy access to the required numbers.

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