### Problem

Given an **n-length** Array of integers ranging from -1000 to 1000 find the largest product of three numbers in **A** that you can get.

#### Example

[-3,2,6,4,8] => 192

### My Solution

There are three basic scenarios that can produce the largest product:

- The largest three positive numbers
- The largest positive number and the smallest two negative numbers
- The largest three negative numbers

The first task is to sort the array, that means that the largest numbers are at the right and the smallest area on the left.

a | b | c | … | … | … | x | y | z |

Something like this, with **a**, **b **and **c** being the smallest values and **x**, **y**, and **z** being the largest values.

The first scenario happens when `x*y`

is greater than `a*b`

. Consequently, the second scenario only occurs when `a*b`

is greater than `x*y`

. We will always use **z** in these two scenarios because it is the largest positive number and two negatives will always give a positive.

The third scenario only occurs when z is less than 0. In this case, we now want the **smallest absolute value** which happens to be the largest number.

#### Examples

##### Scenario 1

[-4, -5, 1, 2, 7, 9, 10]`x * y = 7 * 9 = 63`

which is greater than`a * b = -5 * -4 = 20`

##### Scenario 2

[-9, -8, -7, 1, 2, 3]`x * y = 2`

which is less than`a * b = 72`

##### Scenario 3

[-5, -4, -3, -2, -1] z is negative,

This leads to the following code

```
function solution(A) {
A.sort((a,b) => a-b)
const n = A.length
const positiveProduct = A[n-2] * A[n-3]
const negativeProduct = A[0] * A[1]
if (positiveProduct > negativeProduct || A[n -1] < 0){
return A[n-1] * positiveProduct
}
return A[n-1] * negativeProduct
}
```

Code language: JavaScript (javascript)

**Notes**:

- You shouldn’t do operations on A because that mutates the A outside the function. So here normally we’d have created a copy
**const**aCopy = [...A]; - The
`positiveProduct`

and`negativeProduct`

could be named better.

And that’s that.

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