### Max Product Of Three

January 27, 2020

A non-empty array A consisting of N integers is given. The product of triplet (P, Q, R) equates to A[P] * A[Q] * A[R] (0 ≤ P < Q < R < N).

For example, array A such that:

A[0] = -3

A[1] = 1

A[2] = 2

A[3] = -2

A[4] = 5

A[5] = 6

contains the following example triplets:

• (0, 1, 2), product is −3 * 1 * 2 = −6

• (1, 2, 4), product is 1 * 2 * 5 = 10

• (2, 4, 5), product is 2 * 5 * 6 = 60

Your goal is to find the **maximal product** of any triplet.

**Write a function:**

function solution(A);

that, given a non-empty array A, returns the value of the maximal product of any triplet.

For example, given array A such that:

A[0] = -3

A[1] = 1

A[2] = 2

A[3] = -2

A[4] = 5

A[5] = 6

the function should return 60, as the product of triplet (2, 4, 5) is maximal.

Write an efficient algorithm for the following assumptions:

• N is an integer within the range [3..100,000];

• each element of array A is an integer within the range [−1,000..1,000].

```
function solution(A) {
// write your code in JavaScript (Node.js 8.9.4)
A.sort((a,b)=>a-b)
//console.log("sorted: ",A)
const L = A.length
//possible max products:
//1.first two negative numbers * the last positive number
//or 2.last three positive numbers
const max = Math.max(A[0]*A[1]*A[L-1], A[L-3]*A[L-2]*A[L-1])
return max
}
```