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
-
Data Structure:
- The matrix is represented as a jagged array (
int[][]
), where each inner array corresponds to a row of soldiers and civilians.
- The matrix is represented as a jagged array (
-
KWeakestRows Method:
- This method takes the matrix and an integer
k
as input and returns an array of indices of the K weakest rows.
- This method takes the matrix and an integer
-
Counting Soldiers:
- We iterate over each row of the matrix and count the number of soldiers (
1
s) using theCount
method with a condition.
- We iterate over each row of the matrix and count the number of soldiers (
-
Storing Results:
- Each row’s index and soldier count are stored as tuples in a list:
List<(int index, int soldierCount)>
.
- Each row’s index and soldier count are stored as tuples in a list:
-
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
andThenBy
methods.
- We sort the list of tuples first by the number of soldiers and then by the row index. This is done using LINQ’s
-
Selecting Weakest Rows:
- After sorting, we take the first
k
elements from the sorted list and extract their indices usingSelect
.
- After sorting, we take the first
-
Return Value:
- The method returns an array containing the indices of the K weakest rows.
-
Main Method:
- In the
Main
method, a sample matrix and a value fork
are defined. TheKWeakestRows
method is called, and the result is printed.
- In the
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.