#3492

Easy

auto_awesomeMath-driven solution strategy

LeetCode Problem Workspace

Maximum Containers on a Ship

Determine the maximum number of containers that can be loaded onto a ship's deck without exceeding weight limits.

Problem Statement

You are tasked with determining how many containers can be loaded onto a ship's cargo deck, represented by an n x n grid. Each cell in the grid holds one container with a specific weight, w. The total weight of the loaded containers must not exceed the ship's maximum weight capacity, maxWeight.

Given the grid dimensions (n x n), calculate how many containers can be loaded such that the total weight does not exceed maxWeight. Return the maximum number of containers that can fit within the weight restriction.

Examples

Example 1

Input: n = 2, w = 3, maxWeight = 15

Output: 4

The deck has 4 cells, and each container weighs 3. The total weight of loading all containers is 12, which does not exceed maxWeight .

Example 2

Input: n = 3, w = 5, maxWeight = 20

Output: 4

The deck has 9 cells, and each container weighs 5. The maximum number of containers that can be loaded without exceeding maxWeight is 4.

Constraints

1 <= n <= 1000
1 <= w <= 1000
1 <= maxWeight <= 109

Solution Approach

Basic Calculation

Start by calculating the maximum number of containers the deck can hold, which is n * n. Then, determine how many containers can be loaded by dividing maxWeight by the weight of one container, w. The smaller of these two values is the answer.

Greedy Strategy

A greedy approach could involve filling the grid with containers up to the weight limit. After calculating how many containers fit within the maxWeight, verify that the deck capacity allows for this number of containers to be loaded.

Optimization Considerations

Consider edge cases like when n is very large or the weight of the container is small. Optimize calculations to avoid unnecessary complexity by using simple arithmetic rather than loops that may increase time complexity.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time and space complexity depend on the approach used. A direct calculation involves constant time O(1), while more complex strategies may introduce higher time complexity depending on optimization techniques applied.

What Interviewers Usually Probe

Understanding of how to calculate the number of containers under constraints
Ability to apply greedy or straightforward math-based approaches
Familiarity with optimizing math-driven solutions for large inputs

Common Pitfalls or Variants

Common pitfalls

Misunderstanding the weight limit and exceeding maxWeight
Not accounting for grid dimensions when calculating maximum capacity
Overcomplicating the solution with unnecessary steps like loops or conditionals

Follow-up variants

What if the number of containers was restricted by a different factor, like deck shape or location?
How would the solution change if container weights varied?
What would the time complexity look like if n were in the order of magnitude of 1000?

FAQ

How do I approach the 'Maximum Containers on a Ship' problem?

Start by calculating the number of containers the deck can hold, then check how many can be loaded without exceeding the maxWeight. Use simple math to find the solution.

What’s the time complexity of solving this problem?

The time complexity is O(1) with a direct calculation, but may vary based on optimization strategies or if complex algorithms are applied.

Can the number of containers exceed the ship's capacity?

No, the solution should ensure that the total weight does not exceed the ship's maxWeight by determining the number of containers that fit within the limit.

What strategy can I use to optimize this problem?

Focus on simple arithmetic to calculate the maximum number of containers that fit within the given weight constraint. Avoid unnecessary loops or iterations.

How does the grid dimension (n x n) affect the solution?

The grid dimension provides the maximum possible number of containers, but the actual number loaded is determined by the weight constraint maxWeight.

terminal

Solution

Solution 1: Mathematics

First, we calculate the maximum weight the boat can carry, which is $n \times n \times w$. Then, we take the minimum of this value and $\text{maxWeight}$, and divide it by $w$.

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class Solution:
    def maxContainers(self, n: int, w: int, maxWeight: int) -> int:
        return min(n * n * w, maxWeight) // w

Continue Practicing

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