The k weakest rows in a matrix problem in c#

Programming C#
1

To find the K weakest rows in a matrix representing soldiers and civilians, we need to identify the rows based on the number of soldiers in each row. Each row consists of binary values where 1 represents a soldier and 0 represents a civilian. The weakness of a row can be defined as the number of soldiers in that row.

Problem Statement

Given a 2D binary matrix where:

  • 1 represents a soldier,
  • 0 represents a civilian,

Find the indices of the K weakest rows in the matrix. If two rows have the same number of soldiers, the row with the lower index should come first.

C# Implementation

Here’s how you can implement this:

using System;
using System.Collections.Generic;
using System.Linq;

public class KWeakestRowsFinder
{
    public static int[] KWeakestRows(int[][] matrix, int k)
    {
        // Create a list of tuples to store row index and count of soldiers
        List<(int index, int soldierCount)> rows = new List<(int, int)>();

        // Count soldiers in each row
        for (int i = 0; i < matrix.Length; i++)
        {
            int soldierCount = matrix[i].Count(cell => cell == 1);
            rows.Add((i, soldierCount));
        }

        // Sort rows first by soldier count, then by index
        var sortedRows = rows.OrderBy(r => r.soldierCount).ThenBy(r => r.index).ToArray();

        // Extract the indices of the K weakest rows
        return sortedRows.Take(k).Select(r => r.index).ToArray();
    }

    public static void Main(string[] args)
    {
        int[][] matrix = new int[][]
        {
            new int[] { 1, 1, 0, 0 },
            new int[] { 1, 0, 0, 0 },
            new int[] { 1, 1, 1, 1 },
            new int[] { 0, 0, 0, 0 }
        };

        int k = 2;
        int[] weakestRows = KWeakestRows(matrix, k);
        
        Console.WriteLine($"The indices of the {k} weakest rows are: {string.Join(", ", weakestRows)}");
    }
}

Explanation

  1. Data Structure:

    • The matrix is represented as a jagged array (int[][]), where each inner array corresponds to a row of soldiers and civilians.

  2. KWeakestRows Method:

    • This method takes the matrix and an integer k as input and returns an array of indices of the K weakest rows.

  3. Counting Soldiers:

    • We iterate over each row of the matrix and count the number of soldiers (1s) using the Count method with a condition.

  4. Storing Results:

    • Each row’s index and soldier count are stored as tuples in a list: List<(int index, int soldierCount)>.

  5. Sorting Rows:

    • We sort the list of tuples first by the number of soldiers and then by the row index. This is done using LINQ’s OrderBy and ThenBy methods.

  6. Selecting Weakest Rows:

    • After sorting, we take the first k elements from the sorted list and extract their indices using Select.

  7. Return Value:

    • The method returns an array containing the indices of the K weakest rows.

  8. Main Method:

    • In the Main method, a sample matrix and a value for k are defined. The KWeakestRows method is called, and the result is printed.

Complexity Analysis

  • Time Complexity: (O(m \cdot n + m \log m)), where (m) is the number of rows and (n) is the number of columns. The (O(m \cdot n)) is for counting soldiers in each row, and (O(m \log m)) is for sorting the rows.
  • Space Complexity: (O(m)) for storing the tuples in the list.

Usage

You can modify the matrix and k values in the Main method to test different scenarios. This implementation efficiently finds the K weakest rows based on the number of soldiers present in a binary matrix.