Max Product of Three Numbers - Amazon Top Interview Questions


Problem Statement :


Given a list of integers nums, find the largest product of three distinct elements.

Constraints

3 ≤ n ≤ 100,000 where n is the length of nums


Example 1

Input
nums = [5, 4, 1, 3, -2, -2]


Output
60


Explanation
We can multiply 5 * 4 * 3




Example 2

Input
nums = [-3, 1, 1, 0]


Output
0


Explanation
We can multiply 1 * 1 * 0



Solution :



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                        Solution in C++ :

int solve(vector<int>& nums) {
    sort(begin(nums), end(nums));
    int ans = max(nums[0] * nums[1] * nums[nums.size() - 1],
                  nums[nums.size() - 1] * nums[nums.size() - 2] * nums[nums.size() - 3]);
    return ans;
}
                    


                        Solution in Java :

import java.util.*;

class Solution {
    public int solve(int[] nums) {
        int max1 = Integer.MIN_VALUE, max2 = max1, max3 = max1;
        int min1 = Integer.MAX_VALUE, min2 = min1;

        for (int num : nums) {
            // Find 3 max nums
            if (num > max1) {
                max3 = max2;
                max2 = max1;
                max1 = num;
            } else if (num > max2) {
                max3 = max2;
                max2 = num;
            } else if (num > max3)
                max3 = num;

            // Find 2 min nums
            if (num < min1) {
                min2 = min1;
                min1 = num;
            } else if (num < min2)
                min2 = num;
        }

        return Math.max(max1 * max2 * max3, max1 * min1 * min2);
    }
}
                    


                        Solution in Python : 
                            
class Solution:
    def solve(self, l):
        l = sorted(l)
        return max(l[-1] * l[-2] * l[-3], l[0] * l[1] * l[-1])
                    


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