How do you solve Maximum Units on a Truck on LeetCode?

Maximum Units on a Truck (LeetCode #1710) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Always prioritize boxes with higher units per box.

What is the time complexity of Maximum Units on a Truck?

The optimal solution for Maximum Units on a Truck runs in O(n log n) time and uses O(1) space. The sorting step dominates the time complexity, making it O(n log n). The subsequent iteration through the box types is O(n).

What is the brute force solution for Maximum Units on a Truck?

The brute force approach for Maximum Units on a Truck is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying every possible combination of boxes to see which combination yields the maximum units. This is straightforward but inefficient as it can take a long time with larger inputs. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Units on a Truck?

Maximum Units on a Truck uses the following concepts: Array, Greedy, Sorting. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Maximum Units on a Truck?

Explain your thought process clearly while coding. Discuss the trade-offs of your approaches. Practice similar greedy problems to build intuition.

What are common mistakes when solving Maximum Units on a Truck?

Not sorting the box types before selection. Failing to check if truckSize is exhausted.

#1710

Maximum Units on a Truck

Easy

ArrayGreedySortingGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

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Intuition

Time O(n log n)Space O(1)

The optimal solution leverages a greedy approach by sorting the box types based on the units per box in descending order. This ensures that we always take the boxes that provide the most units first, maximizing the total units on the truck.

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Algorithm

3 steps

1Step 1: Sort the boxTypes array by numberOfUnitsPerBox in descending order.
2Step 2: Initialize totalUnits to 0 and iterate through the sorted boxTypes.
3Step 3: For each box type, check if the truckSize can accommodate the number of boxes available. If yes, take all boxes; otherwise, take as many as the truck can hold.

solution.py11 lines

1# Full working Python code
2def maxUnits(boxTypes, truckSize):
3    boxTypes.sort(key=lambda x: x[1], reverse=True)
4    total_units = 0
5    for boxes, units in boxTypes:
6        if truckSize <= 0:
7            break
8        boxes_to_take = min(boxes, truckSize)
9        total_units += boxes_to_take * units
10        truckSize -= boxes_to_take
11    return total_units

ℹ

Complexity note: The sorting step dominates the time complexity, making it O(n log n). The subsequent iteration through the box types is O(n).

1Always prioritize boxes with higher units per box.
2Sorting helps in efficiently selecting the best boxes.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.