LeetCode #1913 — EASY

Maximum Product Difference Between Two Pairs

Build confidence with an intuition-first walkthrough focused on array fundamentals.

The Problem

Problem Statement

The product difference between two pairs (a, b) and (c, d) is defined as (a * b) - (c * d).

For example, the product difference between (5, 6) and (2, 7) is (5 * 6) - (2 * 7) = 16.

Given an integer array nums, choose four distinct indices w, x, y, and z such that the product difference between pairs (nums[w], nums[x]) and (nums[y], nums[z]) is maximized.

Return the maximum such product difference.

Example 1:

Input: nums = [5,6,2,7,4]
Output: 34
Explanation: We can choose indices 1 and 3 for the first pair (6, 7) and indices 2 and 4 for the second pair (2, 4).
The product difference is (6 * 7) - (2 * 4) = 34.

Example 2:

Input: nums = [4,2,5,9,7,4,8]
Output: 64
Explanation: We can choose indices 3 and 6 for the first pair (9, 8) and indices 1 and 5 for the second pair (2, 4).
The product difference is (9 * 8) - (2 * 4) = 64.

Constraints:

4 <= nums.length <= 10⁴
1 <= nums[i] <= 10⁴

Step 01

Brute Force Baseline

Problem summary: The product difference between two pairs (a, b) and (c, d) is defined as (a * b) - (c * d). For example, the product difference between (5, 6) and (2, 7) is (5 * 6) - (2 * 7) = 16. Given an integer array nums, choose four distinct indices w, x, y, and z such that the product difference between pairs (nums[w], nums[x]) and (nums[y], nums[z]) is maximized. Return the maximum such product difference.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array

Example 1

[5,6,2,7,4]

Example 2

[4,2,5,9,7,4,8]

Step 02

Core Insight

What unlocks the optimal approach

If you only had to find the maximum product of 2 numbers in an array, which 2 numbers should you choose?
We only need to worry about 4 numbers in the array.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1913: Maximum Product Difference Between Two Pairs
class Solution {
    public int maxProductDifference(int[] nums) {
        Arrays.sort(nums);
        int n = nums.length;
        return nums[n - 1] * nums[n - 2] - nums[0] * nums[1];
    }
}

// Accepted solution for LeetCode #1913: Maximum Product Difference Between Two Pairs
func maxProductDifference(nums []int) int {
	sort.Ints(nums)
	n := len(nums)
	return nums[n-1]*nums[n-2] - nums[0]*nums[1]
}

# Accepted solution for LeetCode #1913: Maximum Product Difference Between Two Pairs
class Solution:
    def maxProductDifference(self, nums: List[int]) -> int:
        nums.sort()
        return nums[-1] * nums[-2] - nums[0] * nums[1]

// Accepted solution for LeetCode #1913: Maximum Product Difference Between Two Pairs
struct Solution;

impl Solution {
    fn max_product_difference(mut nums: Vec<i32>) -> i32 {
        let n = nums.len();
        nums.sort_unstable();
        nums[n - 1] * nums[n - 2] - nums[0] * nums[1]
    }
}

#[test]
fn test() {
    let nums = vec![5, 6, 2, 7, 4];
    let res = 34;
    assert_eq!(Solution::max_product_difference(nums), res);
    let nums = vec![4, 2, 5, 9, 7, 4, 8];
    let res = 64;
    assert_eq!(Solution::max_product_difference(nums), res);
}

// Accepted solution for LeetCode #1913: Maximum Product Difference Between Two Pairs
// Auto-generated TypeScript example from java.
function exampleSolution(): void {
}
// Reference (java):
// // Accepted solution for LeetCode #1913: Maximum Product Difference Between Two Pairs
// class Solution {
//     public int maxProductDifference(int[] nums) {
//         Arrays.sort(nums);
//         int n = nums.length;
//         return nums[n - 1] * nums[n - 2] - nums[0] * nums[1];
//     }
// }

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n)

Space

O(1)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.