Search in 2D Matrix in DSA C# - Build from Scratch

Search in 2D Matrix

📖 Scenario: You are working on a simple inventory system for a small store. The store's products are arranged in a 2D grid where each row represents a category and each column represents a shelf position. You want to find if a specific product ID exists in the store's inventory.

🎯 Goal: Build a program that searches for a given product ID in a 2D matrix and tells if it is found or not.

📋 What You'll Learn

Create a 2D integer array called inventory with exact values

Create an integer variable called targetProduct to hold the product ID to search

Use nested for loops with variables row and col to search the matrix

Print "Found" if the product is in the matrix, otherwise print "Not Found"

💡 Why This Matters

🌍 Real World

Searching in a 2D matrix is common in inventory systems, image processing, and game boards where data is arranged in grids.

💼 Career

Understanding how to traverse and search 2D arrays is essential for software developers working with matrices, tables, or grid-based data.

1

Create the 2D matrix

Create a 2D integer array called inventory with these exact values: {{101, 102, 103}, {201, 202, 203}, {301, 302, 303}}

DSA C#

// Your code here

Hint

Use int[,] to declare a 2D array and initialize it with the given values.

2

Set the target product ID

Create an integer variable called targetProduct and set it to 202

DSA C#

int[,] inventory = new int[,] { {101, 102, 103}, {201, 202, 203}, {301, 302, 303} };
// Your code here

Hint

Declare an integer variable and assign the value 202 to it.

3

Search the matrix for the target product

Use nested for loops with variables row and col to iterate over inventory. Inside the loops, check if inventory[row, col] equals targetProduct. If found, set a boolean variable found to true and break out of the loops.

DSA C#

int[,] inventory = new int[,] { {101, 102, 103}, {201, 202, 203}, {301, 302, 303} };
int targetProduct = 202;

// Your code here

Hint

Use inventory.GetLength(0) for rows and inventory.GetLength(1) for columns. Use a boolean found to track if the product is found.

4

Print the search result

Print "Found" if found is true, otherwise print "Not Found"

DSA C#

int[,] inventory = new int[,] { {101, 102, 103}, {201, 202, 203}, {301, 302, 303} };
int targetProduct = 202;

bool found = false;
for (int row = 0; row < inventory.GetLength(0); row++)
{
    for (int col = 0; col < inventory.GetLength(1); col++)
    {
        if (inventory[row, col] == targetProduct)
        {
            found = true;
            break;
        }
    }
    if (found) break;
}

// Your code here

Hint

Use System.Console.WriteLine to print the result based on the found variable.

Practice

1. What is the main idea behind searching in a 2D matrix where each row and column is sorted in ascending order?

easy

A. Start from the top-right corner and move left or down based on comparison

B. Start from the bottom-left corner and move right or up based on comparison

C. Search each row completely using linear search

D. Use binary search on each column independently

Solution

1. Step 1: Understand matrix sorting property

   Each row and column is sorted ascending, so top-right is smallest in column and largest in row.

2. Step 2: Use top-right start to decide movement

   If target is less than current, move left; if greater, move down to find target efficiently.

3. Final Answer:

   Start from the top-right corner and move left or down based on comparison -> Option A

4. Quick Check:

   Top-right corner search = Start from the top-right corner and move left or down based on comparison [OK]

Hint: Start search at top-right corner for sorted 2D matrix [OK]

Common Mistakes:

• Starting from bottom-left corner without reason
• Searching each row fully ignoring sorting
• Applying binary search on columns only

2. Which of the following is the correct C# syntax to declare a 2D integer array named matrix with 3 rows and 4 columns?

easy

A. int matrix = new int[3,4];

B. int[,] matrix = new int[3,4];

C. int matrix[3,4];

D. int[][] matrix = new int[3][4];

Solution

1. Step 1: Understand C# 2D array declaration

   In C#, multidimensional arrays use comma inside brackets: int[,] for 2D arrays.

2. Step 2: Check syntax correctness

   int[,] matrix = new int[3,4]; uses correct syntax. Options A, B, C are invalid syntax.

3. Final Answer:

   int[,] matrix = new int[3,4]; -> Option B

4. Quick Check:

   Correct 2D array syntax = int[,] matrix = new int[3,4]; [OK]

Hint: Use int[,] for 2D arrays in C# [OK]

Common Mistakes:

• Using jagged array syntax with wrong initialization
• Trying to declare array without new keyword
• Using incorrect brackets or missing commas

3. What will be the output of the following C# code snippet?

int[,] matrix = {
  {1, 3, 5},
  {7, 9, 11},
  {13, 15, 17}
};
int target = 9;
bool found = false;
int row = 0, col = 2;
while (row < 3 && col >= 0) {
  if (matrix[row, col] == target) {
    found = true;
    break;
  } else if (matrix[row, col] > target) {
    col--;
  } else {
    row++;
  }
}
Console.WriteLine(found);

medium

A. false

B. Runtime exception

C. Compilation error

D. true

Solution

1. Step 1: Trace the search starting at (0,2)

   Start at matrix[0,2] = 5. 5 < 9, so move down (row++).

2. Step 2: Move to (1,2) and compare

   matrix[1,2] = 11. 11 > 9, so move left (col--).

3. Step 3: Move to (1,1) and compare

   matrix[1,1] = 9 equals target, set found = true and break loop.

4. Final Answer:

   true -> Option D

5. Quick Check:

   Target found = true [OK]

Hint: Start top-right, move left/down comparing target [OK]

Common Mistakes:

• Confusing row and column indices
• Not updating row or col correctly
• Assuming linear search instead of optimized

4. Identify the error in the following C# code that searches for a target in a sorted 2D matrix:

int[,] matrix = {
  {1, 4, 7},
  {2, 5, 8},
  {3, 6, 9}
};
int target = 5;
int row = 0, col = 0;
bool found = false;
while (row < 3 && col < 3) {
  if (matrix[row, col] == target) {
    found = true;
    break;
  } else if (matrix[row, col] < target) {
    col++;
  } else {
    row++;
  }
}
Console.WriteLine(found);

medium

A. Starting point should be top-right, not top-left

B. Loop condition should use OR instead of AND

C. Should increment row when element is less than target

D. No error, code works correctly

Solution

1. Step 1: Check starting point for search

   Code starts at top-left (0,0), but matrix sorted rows and columns require top-right start for correct search.

2. Step 2: Understand movement logic

   Moving right or down from top-left does not guarantee finding target efficiently or correctly.

3. Final Answer:

   Starting point should be top-right, not top-left -> Option A

4. Quick Check:

   Correct start point = top-right [OK]

Hint: Start search at top-right corner, not top-left [OK]

Common Mistakes:

• Starting search at wrong corner
• Using wrong loop conditions
• Incorrect movement directions

5. Given a 2D matrix where each row and column is sorted ascending, write a method to count how many times a target number appears. Which approach is most efficient?

hard

A. Traverse entire matrix and count matches (O(m*n))

B. Use binary search on each row separately (O(m*log n))

C. Start from top-right and move left/down counting matches (O(m+n))

D. Use hash map to store counts before searching (O(m*n))

Solution

1. Step 1: Analyze brute force approach

   Traversing entire matrix is simple but slow (O(m*n)).

2. Step 2: Consider optimized search from top-right

   Starting at top-right, move left/down to find all occurrences efficiently in O(m+n) time.

3. Step 3: Compare with binary search per row

   Binary search per row is better than brute force but slower than top-right approach.

4. Final Answer:

   Start from top-right and move left/down counting matches (O(m+n)) -> Option C

5. Quick Check:

   Efficient count = top-right search O(m+n) [OK]

Hint: Count matches by top-right search moving left/down [OK]

Common Mistakes:

• Using full matrix traversal ignoring sorting
• Applying binary search without combining results
• Using extra space unnecessarily