Search in 2D Matrix in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to check if the matrix is empty.

DSA C#

if (matrix == null || matrix.Length == 0 || matrix[0].Length [1] 0) {
    return false;
}

Drag options to blanks, or click blank then click option'

A!=

B==

C>

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' or '<' instead of '==' causes wrong condition checks.

Using '!=' will not correctly detect empty matrix.

We check if the first row length is equal to zero to confirm the matrix has no columns.

2fill in blank

medium

Complete the code to initialize the number of rows in the matrix.

DSA C#

int rows = matrix.[1];

Drag options to blanks, or click blank then click option'

ALength

BCount

CSize

DGetLength

Attempts:

3 left

💡 Hint

Common Mistakes

Using Count causes compile error because arrays do not have Count property.

Using GetLength without parameters is incorrect.

In C#, arrays use Length property to get the number of elements in the first dimension.

3fill in blank

hard

Fix the error in the binary search loop condition to avoid infinite loop.

DSA C#

while (left [1] right) {
    int mid = left + (right - left) / 2;
    int midValue = matrix[mid / cols][mid % cols];
    if (midValue == target) return true;
    else if (midValue < target) left = mid + 1;
    else right = mid - 1;
}

Drag options to blanks, or click blank then click option'

A>=

B<

C>

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' causes missing the last element check.

Using '>' or '>=' reverses the logic and causes infinite loop.

The binary search loop should run while left is less than or equal to right to cover all elements.

4fill in blank

hard

Fill both blanks to correctly calculate the middle element's row and column indices.

DSA C#

int midRow = mid [1] cols;
int midCol = mid [2] cols;

Drag options to blanks, or click blank then click option'

A/

B%

C*

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication or subtraction instead of division/modulo.

Swapping division and modulo operators.

Row index is mid divided by number of columns; column index is mid modulo number of columns.

5fill in blank

hard

Fill all three blanks to complete the binary search in the 2D matrix.

DSA C#

int left = 0, right = rows [1] cols [2] 1;
while (left [3] right) {
    int mid = left + (right - left) / 2;
    int midValue = matrix[mid / cols][mid % cols];
    if (midValue == target) return true;
    else if (midValue < target) left = mid + 1;
    else right = mid - 1;
}
return false;

Drag options to blanks, or click blank then click option'

A*

B-

C<=

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using '+' instead of '-' for right boundary causes index out of range.

Using '<' instead of '<=' misses last element check.

The right boundary is rows * cols - 1; the loop runs while left <= right.

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