![image.png](https://prod-files-secure.s3.us-west-2.amazonaws.com/c26cbd8c-4ae9-4ab6-b595-99bb653f9d83/30435da7-c384-4fb8-8a17-21e44dac718a/image.png)

Q- bahii 3ana problem esmo “Maximum Units on a Truck” 

---

—> bahiii el role mt3ik el lyom enik we put some amount of boxes onto one track . 

You are given a 2d array “boxTypes” , wherre 

boxTypes[i] = [numberOfBoxesi , numberOfUnitsPerBoxi] 

- bahiiii honii numberOfBoxesi : hiya el number of boxes of type i
- numerOfUnitsPerBoxi : is the number of units in each box of the type i

bahhii honii you are also given an integer “truckSize” , which is the maximum number of boxes that cann be put on the truck , You can choose any boxes to put on the truck as long as the  number of boxes doest not execde the truckSize

—> bahii honii chnowa howa el objetive okii that can be put on the truck 

![image.png](https://prod-files-secure.s3.us-west-2.amazonaws.com/c26cbd8c-4ae9-4ab6-b595-99bb653f9d83/7043671c-233d-4dab-af48-ce6edbf76bca/image.png)

Q- what is the input & output format ? 

input : List[List[int]] , truckSize = 4 

output : x : int 

Q- can you go through an exmple ? 

boxTypes = [[1,3],[2,2] ,[3,1]] , truckSize = 4 okiii 

bahii honiii at index i 

we have 1 box with size of 3 unites have 

at idex 2 

we have 2 boxs each on of size of 3 unites okii 

at index 3 

we have 3 boxes each one of size of 1 unite okii 

here we can have only 4 boxes and we want maximumse the number of units okii 

so w greedy approch is to choice the box type with the max number of unites and so on 

here for exmple we have only 1 box with the max number of unties so we we add it 

total_unites+=3 okii 

next it remain with 3 boxes left 

we continue the same reasoning 

we add the first track of unit equal = 2 

total_unites +=2 

next we are letft wih 2 boexes 

we add the second box with the units equal t2 

total_unites+=2 

only one left so we add the last one okii 

only one from the 3 remaing of unit number = 1 

total_unites+=1 

Q- as i can see the problem neeed to preporcessing step okii where we need to flatten the input list of list 

for exmple [[1,3],[2,2] ,[3,1]]

become [3,2,2,1,1,1,1] 

the sort them non decresing order (this exmple is already sorted okii ) 

and reutrn the sum of the 

`truckSize` first elements okii 

Q- let’s test it in this exmple? 

![image.png](https://prod-files-secure.s3.us-west-2.amazonaws.com/c26cbd8c-4ae9-4ab6-b595-99bb653f9d83/55c402e5-5814-49b9-b501-7f95eaeee5f6/image.png)

nums = [[5,10] , [2,5] , [4,7] ,[3,9]] 

step one flatten this array 

[10,10,10,10,10,5,5,7,7,7,7,9,9,9] 

next step sort it 

[10,10,10,10,10,9,9,9,7,7,7,7,5,5] 

next get the sum of the first truckSieze elements 

Q- first think without changing my style just translate it in english

Here's the solution translated into English, while keeping your style:

---

We have a problem called "Maximum Units on a Truck."

The goal here is to load a truck with boxes in a way that maximizes the units we can carry, given a 2D list `boxTypes` and an integer `truckSize`.

- `boxTypes[i] = [numberOfBoxesi, numberOfUnitsPerBoxi]`
    - `numberOfBoxesi`: the count of boxes of type `i`
    - `numberOfUnitsPerBoxi`: the number of units inside each box of type `i`

And `truckSize` represents the maximum number of boxes that can fit on the truck.

### Objective

Maximize the number of units we can load onto the truck without exceeding the limit (`truckSize`) of the total number of boxes.

---

### Input and Output Format

- **Input**: `List[List[int]]`, `truckSize = 4`
- **Output**: `x: int` (the maximum units that can be carried)

### Example Walkthrough

Let's go through an example:

Given:

```python
boxTypes = [[1, 3], [2, 2], [3, 1]]
truckSize = 4

```

1. For each index in `boxTypes`:
    - At index 0: We have 1 box with 3 units each.
    - At index 1: We have 2 boxes with 2 units each.
    - At index 2: We have 3 boxes with 1 unit each.
2. Since we can only take 4 boxes, we should prioritize boxes with the maximum number of units per box.
3. Using a greedy approach, we pick the type with the highest units first:
    - Take 1 box of 3 units: `total_units += 3` (remaining truck capacity = 3 boxes)
    - Take 2 boxes of 2 units each: `total_units += 2 + 2` (remaining truck capacity = 1 box)
    - Take 1 box of 1 unit: `total_units += 1`
    
    Final result: `total_units = 3 + 2 + 2 + 1 = 8`
    

---

### Approach

1. Sort `boxTypes` by `numberOfUnitsPerBox` in descending order.
2. Pick boxes from the sorted list until we reach `truckSize` or exhaust the list.
3. Sum up the units of the chosen boxes.

Q- next think be my coding partener okii and just given me a honst feadback about my reasining process it’s in the right direct yes or non ?

Yes, your reasoning process is in the right direction. You've correctly identified the greedy approach – prioritizing boxes with the highest units per box – and understand the need to sort the box types accordingly. Your example walkthrough demonstrates the logic clearly.  The idea of "flattening" the list isn't strictly necessary, and might actually add complexity.  It's more efficient to work directly with the boxTypes list after sorting.

Here are a few minor points to consider:

- **Clarity on Sorting:** You mentioned sorting, but be explicit about sorting based on numberOfUnitsPerBox in descending order. This is crucial for the greedy approach to work.
- **No Need to Flatten:** As mentioned, flattening and then sorting adds an unnecessary step. You can directly sort boxTypes using a custom sorting key (e.g., lambda x: -x[1] in Python to sort by the second element in descending order).
- **Edge Cases:** While not explicitly mentioned in your reasoning, be mindful of edge cases where truckSize might be larger than the total number of available boxes. Your code should handle this gracefully.

Overall, your approach is sound, and you've grasped the core concepts of the problem.  By incorporating these minor refinements, you'll be well on your way to a correct and efficient solution.

Q- okii we have figure out that the approch here can work so let’s try to generate a solution in the fly okii 

![image.png](https://prod-files-secure.s3.us-west-2.amazonaws.com/c26cbd8c-4ae9-4ab6-b595-99bb653f9d83/216a5b85-9173-4672-8f83-20bf4c572989/image.png)

![image.png](https://prod-files-secure.s3.us-west-2.amazonaws.com/c26cbd8c-4ae9-4ab6-b595-99bb653f9d83/78a797b8-6e5a-4424-a75f-b3a2edd73f50/image.png)

bahii honii first in this exmple we try to sort it based on the second element in each box okii 

[ [5,10] , [2,5] ,[4,7] , [3,9]] 

sort it [ [5,10] , [3,9] , [4,7] , [2,5]]

i=0

total_unites =0 

—> next while truckSize >0: 

current_box_numbers=boxTypes[i][0] 

current_box_numbers=boxTypes[i][1] 

total_unites+=(current_box_numbers*current_box_numbers)

truckSize-=current_box_numbers 

return total_unites 

```
class Solution:
    def maximumUnits(self, boxTypes: List[List[int]], truckSize: int) -> int:
        """ Step we need to sort the boxTypes by unites amount in decreasing order it will help guide the greed search  """
        boxTypes.sort(key=lambda x:x[-1])
        """ compute the length of the boxTypes """
        n=len(boxTypes)
        """ initiate a pointer to traverse the boxtypes  """
        i=0
        """ initiate a variable to truck the number of units we have put  """
        total_units=0
        """ while the we still have space and i does not execde the uppper bound """
        while truckSize > 0 and i < n:
            """ get the number of boxes in the i'th position """
            current_box_numbers=boxTypes[i][0]
            """ get the amount of units in the i'th box """
            current_box_amount=boxTypes[i][1]
            """ pick the min one always  """
            box_numbers=min(current_box_numbers,truckSize)
            """ update the total unites counter """
            total_units+=(current_box_numbers * current_box_amount)
            """ update the new truckSize  """
            truckSize-=box_numbers
            """ update the pointer next """
            i+=1 
        return total_units 
```

Q- create a manula exection of my approch here 

for this exmple 

[ [5,10] , [2,5] ,[4,7] , [3,9]]