3492. Maximum Containers on a Ship

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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.

 

Example 1:

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

Output: 4

Explanation:

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

Explanation:

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

Solutions

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 $w$.

The time complexity is $O(1)$, and the space complexity is $O(1)$.

Python3

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

Java

class Solution {
    public int maxContainers(int n, int w, int maxWeight) {
        return Math.min(n * n * w, maxWeight) / w;
    }
}

C++

class Solution {
public:
    int maxContainers(int n, int w, int maxWeight) {
        return min(n * n * w, maxWeight) / w;
    }
};

Go

func maxContainers(n int, w int, maxWeight int) int {
	return min(n*n*w, maxWeight) / w
}

TypeScript

function maxContainers(n: number, w: number, maxWeight: number): number {
    return (Math.min(n * n * w, maxWeight) / w) | 0;
}