Max Profit Algorithm - php

Question

I came across this question on one of my interviews, can't remember the company.
A product marketer has several suppliers of a product.
The stock is represented by an array of quantities for each supplier.
As items are purchased, the supplier raises the price by 1 unit per item purchased, reducing the marketer's profit per unit.
Assume the marketer's profit on any one item is the same as the number of those items the supplier has.
For example, the supplier has 4 units, the marketer's profit on the first unit sold is 4, then 3, then 2, and the last one the profit is 1.
Given the array of quantities at suppliers and the number of items ordered, determine the highest profit that can be generated.
Example
inventory = [3, 5]
order = 6
Two suppliers have inventory = [3, 5] units to sell, and 6 items
were ordered.
The maximum profit is made by selling 1 for 5, 1 for 4, and 2 at 3 and 2 at 2 units profit. The two suppliers are
left with a unit of product each.
The maximum profit generated is 5 + 4 + 2 * 3 + 2 * 2 = 19
Complete the function maxProfit with the following parameter(s);
int inventory[n]: an array of integers representing units available in the stock per supplier
int order: a long integer, the number of items ordered
Returns:
long int: the maximum profit achievable
Constraints
1 ≤ n ≤ 10
1 ≤ inventory[i] ≤ 10^5, where 0 ≤ i < n
1 ≤ order ≤ sum(inventory)
My answer was like this
function maximumProfit($inventory, $order) {
// Write your code here
$profit = 0;
for ($i=0; $i<$order; $i++) {
$inventory = sortInventoryMax($inventory);
$profit += $inventory[0];
$inventory[0]--;
}
return $profit;
}
function sortInventoryMax($inventory) {
usort($inventory, function($a, $b) {
return $b - $a;
});
return $inventory;
}
it fails on the cases when it took more than 9 seconds time execution.

Answer 1

You need to use a max heap to keep track of running maximum in your array as sorting at every iteration is time consuming. PHP has the max heap class SplMaxHeap to do the job for you.
We put all the elements in the max heap. Now, for every order, extract the top value from the heap, add it to the profit, and insert a new unit reduced price in to the heap again.
Snippet:
<?php
function maximumProfit($inventory, $order) {
$profit = 0;
$max_heap = new SplMaxHeap();
foreach($inventory as $inv){
$max_heap->insert($inv);
}
while($order-- > 0){
$curr = $max_heap->extract();
$profit += $curr;
if($curr > 1) $max_heap->insert($curr - 1);
}
return $profit;
}
echo maximumProfit([3,5], 6);
Online Demo