We use cookies (including Google cookies) to personalize ads and analyze traffic. By continuing to use our site, you accept our Privacy Policy.

SimplyLeet
TagsDisclaimersPrivacyTermsContactAbout Us

Maximum Containers on a Ship

Difficulty: Easy

Problem Description

You are given a positive integer n representing an n x n cargo deck on a ship. Each cell on the deck can hold one container with a weight of exactly w. However, the total weight of all containers, if loaded onto the deck, must not exceed the ship's maximum weight capacity, maxWeight. Return the maximum number of containers that can be loaded onto the ship.

Key Insights

  • The total number of cells on the deck is n * n.
  • Each container has a fixed weight w.
  • The total weight of k containers is k * w.
  • To determine the maximum number of containers, calculate how many can fit within the maxWeight constraint.
  • The maximum number of containers is limited by both the number of cells and the weight capacity.

Space and Time Complexity

Time Complexity: O(1)
Space Complexity: O(1)

Solution

To solve this problem, we can use a mathematical approach. First, calculate the maximum number of containers that can be loaded without exceeding maxWeight by dividing maxWeight by the weight of each container, w. This gives us the number of containers based on weight. However, since we also have a limit on the number of cells, we take the minimum of the number of cells (n * n) and this calculated number to ensure we do not exceed the available space.

Code Solutions

def maxContainers(n: int, w: int, maxWeight: int) -> int:
    # Calculate the maximum number of containers based on weight
    max_by_weight = maxWeight // w
    # Calculate the total number of cells on the deck
    total_cells = n * n
    # The maximum containers is the minimum of these two values
    return min(max_by_weight, total_cells)
← Back to All Questions