Fitting Shelves Problem in C++

In this article, you will learn about the Fitting Shelves Problem in C++ with their example and applications.

Fitting Shelves problem

In real-world situations like warehouse management or interior design, the Fitting Shelves issue is a well-known optimization issue in computer science. With the least amount of wasted space and ensuring no shelf overlaps, the objective is to effectively arrange shelves of different lengths onto a wall of a particular length.

Dynamic programming is essential for effectively resolving the Fitting Shelves problem. Dynamic programming can help solve tough problems by dividing complicated problems into smaller, more manageable subproblems and addressing each one just once. After that, the solution to each subproblem is stored and reused to solve larger subproblems.

Brute Force Approach

A brute-force approach to the Fitting Shelves Problem is to create every possible arrangement of shelves on the wall and calculate how much space is wasted in each arrangement. After that, the best option is determined by arranging things such that a minimal amount of space is wasted. However, this method can be computationally demanding and ineffective, particularly when dealing with many shelves or a large wall length.

Example:

Let us take an example to illustrate the Fitting Shelves Problem in C++.

#include <iostream>
#include <vector>
using namespace std;
//Function to fit shelves onto the wall
int fitting_Shelves(vector<int>& shelves, int wall_Length) 
{
    int num_Shelves = shelves.size();
    int used_Length = 0; 
    // Total Length of shelves used
    int wasted_Space = 0; 
    // Total wasted space
    // Iterating through each shelf
    for (int i = 0; i < num_Shelves; ++i) 
    {
        // If the current shelf can be placed on the wall
        if (used_Length + shelves[i] <= wall_Length)
        {
            used_Length += shelves[i]; 
            // Updating used Length
        } 
        else
        {
            wasted_Space += wall_Length - used_Length; 
            // Updating wasted space
            used_Length = wall_Length; 
            // No more space available on the wall
            break;
        }
    }
    // If there's still unused space on the wall, update wasted space
    if (used_Length < wall_Length)
    {
        wasted_Space += wall_Length - used_Length;
    }
    return wasted_Space;
}
int main()
{
    vector<int> shelves = {6, 7, 4, 3, 2};
    // Shelves lengths in non-increasing order
    int wall_Length = 10;
    // Call the fitShelves function to fit shelves onto the wall
    int minimum_WastedSpace = fitting_Shelves(shelves, wall_Length);
    cout << "The Length of the wall is: " << wall_Length << endl;
    //Output the minimum wasted space
    cout << "Minimum wasted space: " << minimum_WastedSpace << endl;
    return 0;
}

Output:

The Length of the wall is: 10
Minimum wasted space: 4

Explanation:

A method called fitting_Shelves is implemented in the provided C++ code, and it fits shelves onto a wall of a specified length. It goes through every shelf individually, trying to fit it on the wall without exceeding the allotted space. It determines the wasted space, terminates the loop if a shelf does not fit, and updates the overall used Length. With sample shelf lengths and a wall length of 10, the main Function demonstrates how to use the fitting_Shelves function. The Output shows the wall's Length and the minimal amount of space wasted when the shelves are fitted in. The code effectively calculates the wasted space while arranging shelves on a wall.

Some of the notable applications:

Retail Store Layout Optimization: Retailers frequently need to optimize how their shelves are arranged to make the best use of their floor space and maximize product presentation. They can arrange shelves to reduce wasted space and improve customers' shopping experience by finding a solution to the problem of fitting shelves.
Warehouse Management: Warehouses must practice effective storage management to optimize storage capacity and simplify inventory operations. In order to save wasted space, warehouse managers may use the Fitting Shelves Problem to help them position shelves in storage facilities to fit a range of goods sizes.
Interior Design: When arranging shelves in homes, workplaces, or commercial spaces, interior designers might use the Fitting Shelves Problem as an organizing tool. By organizing shelves, designers may create visually appealing spaces that optimize storage capacity and utility.
Organization of the Library: Libraries frequently need to maximize shelf space to store a large amount of books and ensure users can access them. By resolving the problem of fitting shelves, librarians can optimize shelf layout to save wasted space and enhance effective book retrieval.
Manufacturing and Production Facilities: Efficient material and equipment organization is crucial in manufacturing and production facilities to maximize efficiency and productivity. The design of shelves and storage spaces within these establishments may be planned using the Fitting Shelves Problem to guarantee that resources are conveniently accessible and that available space is used efficiently.

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