Search in 2D Matrix in DSA Typescript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of the search function?

Given the matrix and the target, what will the search function return?

DSA Typescript

function searchMatrix(matrix: number[][], target: number): boolean {
  let row = 0;
  let col = matrix[0].length - 1;
  while (row < matrix.length && col >= 0) {
    if (matrix[row][col] === target) {
      return true;
    } else if (matrix[row][col] > target) {
      col--;
    } else {
      row++;
    }
  }
  return false;
}

const matrix = [
  [1, 4, 7, 11],
  [2, 5, 8, 12],
  [3, 6, 9, 16],
  [10, 13, 14, 17]
];
const target = 5;
console.log(searchMatrix(matrix, target));

A true

B false

C undefined

D TypeError

💡 Hint

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

The function starts at top-right (11), since 11 > 5, it moves left to 7, then 4, then moves down to 5 which matches the target, so returns true.

❓ Predict Output

intermediate

What is the output of the search for a missing target?

What will the function return when searching for a target not in the matrix?

DSA Typescript

function searchMatrix(matrix: number[][], target: number): boolean {
  let row = 0;
  let col = matrix[0].length - 1;
  while (row < matrix.length && col >= 0) {
    if (matrix[row][col] === target) {
      return true;
    } else if (matrix[row][col] > target) {
      col--;
    } else {
      row++;
    }
  }
  return false;
}

const matrix = [
  [1, 4, 7, 11],
  [2, 5, 8, 12],
  [3, 6, 9, 16],
  [10, 13, 14, 17]
];
const target = 15;
console.log(searchMatrix(matrix, target));

A undefined

B RangeError

C false

D true

💡 Hint

If the target is not found, the function returns false.

The function moves through the matrix but never finds 15, so it returns false.

🧠 Conceptual

advanced

Why does the search start from the top-right corner?

Why is the top-right corner chosen as the starting point for searching in a sorted 2D matrix?

A Because top-right corner is always the smallest element in the matrix.

B Because it is easier to implement recursion from top-right corner.

C Because starting from top-right allows binary search on rows only.

D Because from top-right, we can move left to smaller numbers and down to larger numbers, narrowing search efficiently.

💡 Hint

Think about how the matrix is sorted and how moving left or down changes values.

The matrix rows and columns are sorted ascending. From top-right, moving left decreases values, moving down increases values, allowing efficient elimination of rows or columns.

🔧 Debug

advanced

What error does this code produce?

What error will this code produce when run?

DSA Typescript

function searchMatrix(matrix: number[][], target: number): boolean {
  let row = 0;
  let col = matrix[0].length;
  while (row < matrix.length && col >= 0) {
    if (matrix[row][col] === target) {
      return true;
    } else if (matrix[row][col] > target) {
      col--;
    } else {
      row++;
    }
  }
  return false;
}

const matrix = [
  [1, 4, 7, 11],
  [2, 5, 8, 12],
  [3, 6, 9, 16],
  [10, 13, 14, 17]
];
const target = 5;
console.log(searchMatrix(matrix, target));

A IndexError

B RangeError

C TypeError

D undefined behavior

💡 Hint

Check the initial value of col and array indexing.

col is initialized to matrix[0].length which is out of bounds (indexing starts at 0), so accessing matrix[row][col] causes RangeError.

🚀 Application

expert

How many elements are checked in worst case?

Given an n x n matrix sorted as described, what is the maximum number of elements the search function checks in the worst case?

A 2n

B log n

C n^2

D n

💡 Hint

Consider the path the search pointer takes from top-right to bottom-left.

The search moves at most n steps down and n steps left, so maximum 2n elements are checked.

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 bottom-left corner and move right or up based on comparison

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

C. Search each element row by row until the target is found

D. Use binary search on each row independently

Solution

1. Step 1: Understand matrix properties

   Since each row and column is sorted ascending, the top-right element is the largest in its row and smallest in its column.

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

   If the target is less than the current element, move left; if greater, move down. This efficiently narrows search space.

3. Final Answer:

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

4. Quick Check:

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

Hint: Start at top-right, move left if bigger, down if smaller [OK]

Common Mistakes:

• Starting from bottom-left without adjusting moves correctly
• Searching row by row wastes time
• Using binary search on rows ignores column sorting

2. Which of the following TypeScript code snippets correctly initializes a 2D matrix of numbers?

easy

A. const matrix: number[][] = [[1,2,3],[4,5],[6,7,8,9]];

B. const matrix: number[] = [1,2,3,4,5,6,7,8,9];

C. const matrix: number[][] = [[1,2,3],[4,5,6],[7,8,9]];

D. const matrix: number[][] = [1,2,3,4,5,6,7,8,9];

Solution

1. Step 1: Check matrix type declaration

   TypeScript 2D array is declared as number[][]. const matrix: number[][] = [[1,2,3],[4,5,6],[7,8,9]];.

2. Step 2: Validate matrix structure

   const matrix: number[][] = [[1,2,3],[4,5,6],[7,8,9]]; has uniform rows with 3 elements each, valid for a matrix. const matrix: number[][] = [[1,2,3],[4,5],[6,7,8,9]]; has rows of different lengths, which is allowed but less common for matrices.

3. Final Answer:

   const matrix: number[][] = [[1,2,3],[4,5,6],[7,8,9]]; -> Option C

4. Quick Check:

   Proper 2D array syntax = const matrix: number[][] = [[1,2,3],[4,5,6],[7,8,9]]; [OK]

Hint: Use number[][] with nested arrays for 2D matrix [OK]

Common Mistakes:

• Using single array for 2D matrix
• Incorrect type declaration like number[] for 2D
• Mixing array elements without nested arrays

3. What will be the output of the following TypeScript code?

const matrix = [
  [1, 4, 7, 11],
  [2, 5, 8, 12],
  [3, 6, 9, 16],
  [10, 13, 14, 17]
];

function searchMatrix(matrix: number[][], target: number): boolean {
  let row = 0;
  let col = matrix[0].length - 1;
  while (row < matrix.length && col >= 0) {
    if (matrix[row][col] === target) return true;
    else if (matrix[row][col] > target) col--;
    else row++;
  }
  return false;
}

console.log(searchMatrix(matrix, 5));

medium

A. Runtime error

B. false

C. undefined

D. true

Solution

1. Step 1: Start search from top-right corner

   Initial position is row=0, col=3 (value 11). Since 11 > 5, move left to col=2 (value 7).

2. Step 2: Compare and move accordingly

   7 > 5, move left to col=1 (value 4). 4 < 5, move down to row=1, col=1 (value 5). Found target 5, return true.

3. Final Answer:

   true -> Option D

4. Quick Check:

   Search finds 5 = true [OK]

Hint: Start top-right, move left if bigger, down if smaller [OK]

Common Mistakes:

• Not updating row and col correctly
• Returning false too early
• Confusing row and column indices

4. Identify the bug in this TypeScript function that searches a target in a sorted 2D matrix:

function searchMatrix(matrix: number[][], target: number): boolean {
  let row = 0;
  let col = matrix.length - 1;
  while (row < matrix.length && col >= 0) {
    if (matrix[row][col] === target) return true;
    else if (matrix[row][col] > target) col--;
    else row++;
  }
  return false;
}

medium

A. col should be initialized to matrix[0].length - 1, not matrix.length - 1

B. row should start from matrix.length - 1

C. The while loop condition should use col < matrix[0].length

D. The function should return true at the end instead of false

Solution

1. Step 1: Check initialization of col variable

   col is set to matrix.length - 1, which is number of rows minus one, but columns count is matrix[0].length.

2. Step 2: Correct col initialization

   col should be matrix[0].length - 1 to point to the last column index in the first row.

3. Final Answer:

   col should be initialized to matrix[0].length - 1, not matrix.length - 1 -> Option A

4. Quick Check:

   col init must match columns count = col should be initialized to matrix[0].length - 1, not matrix.length - 1 [OK]

Hint: col index = last column, use matrix[0].length - 1 [OK]

Common Mistakes:

• Using rows count for column index
• Wrong loop conditions causing out-of-bounds
• Returning true instead of false when not found

5. Given a 2D matrix where each row and column is sorted ascending, how would you modify the search function to return the position [row, col] of the target if found, or [-1, -1] if not found? Choose the correct code snippet.

function searchMatrix(matrix: number[][], target: number): number[] {
  let row = 0;
  let col = matrix[0].length - 1;
  while (row < matrix.length && col >= 0) {
    if (matrix[row][col] === target) {
      // What to return here?
    } else if (matrix[row][col] > target) {
      col--;
    } else {
      row++;
    }
  }
  // What to return if not found?
}

hard

A. Return [row, col] inside if, and [-1, -1] after loop

B. Return [col, row] inside if, and [0, 0] after loop

C. Return true inside if, and false after loop

D. Return matrix[row][col] inside if, and null after loop

Solution

1. Step 1: Return position when target found

   Inside the if condition, return the current indices as [row, col] to indicate target position.

2. Step 2: Return [-1, -1] if target not found

   After the loop ends without finding target, return [-1, -1] to indicate absence.

3. Final Answer:

   Return [row, col] inside if, and [-1, -1] after loop -> Option A

4. Quick Check:

   Return position or [-1, -1] if missing = Return [row, col] inside if, and [-1, -1] after loop [OK]

Hint: Return indices when found, [-1, -1] if not found [OK]

Common Mistakes:

• Swapping row and col in return
• Returning boolean instead of position
• Returning wrong default value when not found