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Maximum Product of Three Numbers

LeetCode 628 | Difficulty: Easy​

Easy

Problem Description​

Given an integer array nums, find three numbers whose product is maximum and return the maximum product.

Example 1:

Input: nums = [1,2,3]
Output: 6

Example 2:

Input: nums = [1,2,3,4]
Output: 24

Example 3:

Input: nums = [-1,-2,-3]
Output: -6

Constraints:

- `3 <= nums.length <= 10^4`

- `-1000 <= nums[i] <= 1000`

Topics: Array, Math, Sorting

Approach​

Mathematical​

Look for mathematical patterns or formulas. Consider: modular arithmetic, GCD/LCM, prime factorization, combinatorics, or geometric properties.

When to use

Problems with clear mathematical structure, counting, number properties.

Sorting​

Sort the input to bring related elements together or enable binary search. Consider: does sorting preserve the answer? What property does sorting give us?

When to use

Grouping, finding closest pairs, interval problems, enabling two-pointer or binary search.

Solutions​

Solution 1: C# (Best: 200 ms)​

MetricValue
Runtime200 ms
MemoryN/A
Date2018-04-13
Solution
public class Solution {
    public int MaximumProduct(int[] nums) {
        Array.Sort(nums);
        int n = nums.Length;
        return Math.Max(nums[n-1]*nums[n-2]*nums[n-3],nums[0]*nums[1]*nums[n-1]);
    }
}

Complexity Analysis​

ApproachTimeSpace
Sort + Process$O(n log n)$$O(1) to O(n)$

Interview Tips​

Key Points
  • Start by clarifying edge cases: empty input, single element, all duplicates.