Maximum Containers on a Ship

Maximum Containers on a Ship - Problem

Math Easy

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.

Input & Output

Example 1 — Weight Limited

$ Input: n = 3, w = 10, maxWeight = 50

› Output: 5

💡 Note: Deck can hold 3×3 = 9 containers, but weight limit allows only 50÷10 = 5 containers. Take minimum: 5.

Example 2 — Deck Limited

$ Input: n = 2, w = 5, maxWeight = 100

› Output: 4

💡 Note: Deck can hold 2×2 = 4 containers, weight limit allows 100÷5 = 20 containers. Take minimum: 4.

Example 3 — Equal Constraints

$ Input: n = 4, w = 8, maxWeight = 128

› Output: 16

💡 Note: Deck holds 4×4 = 16 containers, weight allows 128÷8 = 16 containers. Both equal, so 16.

Constraints

1 ≤ n ≤ 10⁵
1 ≤ w ≤ 10⁴
1 ≤ maxWeight ≤ 10⁹

Visualization

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Asked in

a Amazon 25 G Google 20 M Microsoft 15

The key insight is that this is a simple constraint optimization problem. We have two limits: deck space (n²) and weight capacity (maxWeight÷w). The answer is simply the minimum of these two values. Best approach is the mathematical solution with Time: O(1), Space: O(1).

Common Approaches

Approach	Time	Space	Notes
✓ Mathematical Solution	O(1)	O(1)	Use simple division to find maximum containers instantly
Brute Force - Try All Combinations	O(2^(n²))	O(1)	Generate all possible container placements and count valid ones

Mathematical Solution — Algorithm Steps

Calculate deck capacity: n × n
Calculate weight-limited capacity: maxWeight ÷ w
Return minimum of both capacities

Visualization

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Step-by-Step Walkthrough

Deck Limit

Calculate n × n maximum deck capacity

Weight Limit

Calculate maxWeight ÷ w maximum by weight

Minimum

Take smaller of the two limits

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

int solution(int n, int w, int maxWeight) {
    // Deck can hold n*n containers maximum
    int deckCapacity = n * n;
    
    // Weight constraint limits us to maxWeight / w containers
    int weightCapacity = maxWeight / w;
    
    // Take the minimum of both constraints
    return (deckCapacity < weightCapacity) ? deckCapacity : weightCapacity;
}

int main() {
    int n, w, maxWeight;
    scanf("%d %d %d", &n, &w, &maxWeight);
    
    int result = solution(n, w, maxWeight);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Only performs constant-time arithmetic operations

✓ Linear Growth

Space Complexity

O(1)

Uses only a few integer variables

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Mathematical Solution — Algorithm Steps

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Code -

Time & Space Complexity

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