Set Matrix Zeroes In Place in DSA Python - Build from Scratch

Set Matrix Zeroes In Place

📖 Scenario: You are working with a grid of numbers representing a seating chart in a theater. Some seats are broken and marked with zero. You want to mark all seats in the same row and column as broken if any seat in that row or column is broken.

🎯 Goal: Modify the given matrix in place so that if a seat is broken (0), all seats in that seat's row and column become broken (0).

📋 What You'll Learn

Create a 2D list called matrix with the exact values [[1,1,1],[1,0,1],[1,1,1]]

Create two variables called rows and cols to store the number of rows and columns in matrix

Use the first row and first column of matrix as markers to track which rows and columns should be zeroed

Modify matrix in place without using extra space for another matrix

Print the final matrix after modification

💡 Why This Matters

🌍 Real World

This technique is useful in image processing, seating arrangements, and spreadsheet software where marking entire rows and columns based on conditions is needed.

💼 Career

Understanding in-place matrix modification is important for optimizing memory usage in software engineering roles, especially in data processing and algorithm design.

1

Create the initial matrix

Create a 2D list called matrix with these exact values: [[1,1,1],[1,0,1],[1,1,1]]

DSA Python

# Create the matrix variable with the given values
# Your code here

Hint

Use square brackets to create a list of lists exactly as shown.

2

Set up row and column counts

Create two variables called rows and cols to store the number of rows and columns in matrix using len(matrix) and len(matrix[0]) respectively

DSA Python

matrix = [[1,1,1],[1,0,1],[1,1,1]]
# Create rows and cols variables to store matrix dimensions
# Your code here

Hint

Use len() to find the number of rows and columns.

3

Mark rows and columns to be zeroed

Use a for loop with variables r and c to iterate over all cells in matrix. If matrix[r][c] is 0, set matrix[r][0] and matrix[0][c] to 0 to mark the row and column

DSA Python

matrix = [[1,1,1],[1,0,1],[1,1,1]]
rows = len(matrix)
cols = len(matrix[0])
# Use nested for loops to mark rows and columns with zero
# Your code here

Hint

Check each cell and mark the first cell of its row and column if zero.

4

Set zeroes based on markers and print

Use nested for loops with variables r and c starting from 1 to rows and cols. If matrix[r][0] or matrix[0][c] is 0, set matrix[r][c] to 0. Then print the final matrix

DSA Python

matrix = [[1,1,1],[1,0,1],[1,1,1]]
rows = len(matrix)
cols = len(matrix[0])
for r in range(rows):
    for c in range(cols):
        if matrix[r][c] == 0:
            matrix[r][0] = 0
            matrix[0][c] = 0
# Use nested loops from 1 to rows and cols to set zeroes based on markers
# Then print the matrix
# Your code here

Hint

Start loops from 1 to avoid overwriting markers too early. Then print the matrix.

Practice

1. What is the main goal of the Set Matrix Zeroes In Place problem?

easy

A. Find the sum of all elements in the matrix.

B. Modify the matrix so that if an element is 0, its entire row and column become 0.

C. Sort each row of the matrix in ascending order.

D. Transpose the matrix without changing its elements.

Solution

1. Step 1: Understand the problem requirement

   The problem asks to change the matrix so that if any element is zero, all elements in that element's row and column become zero.

2. Step 2: Identify the correct description

   Modify the matrix so that if an element is 0, its entire row and column become 0. exactly describes this transformation, while others describe unrelated operations.

3. Final Answer:

   Modify the matrix so that if an element is 0, its entire row and column become 0. -> Option B

4. Quick Check:

   Set matrix zeroes means zero rows and columns [OK]

Hint: Remember zero means zero entire row and column [OK]

Common Mistakes:

• Confusing with matrix transpose
• Thinking only the zero element changes
• Trying to sum or sort instead

2. Which of the following Python code snippets correctly initializes a 3x3 matrix with all zeros?

easy

A. matrix = [[0]*3]*3

B. matrix = [0,0,0]*3

C. matrix = [0]*3 for _ in range(3)

D. matrix = [[0 for _ in range(3)] for _ in range(3)]

Solution

1. Step 1: Analyze each initialization method

   matrix = [[0]*3]*3 creates shallow copies of the same row, causing changes in one row to affect others. matrix = [[0 for _ in range(3)] for _ in range(3)] creates independent rows correctly. matrix = [0]*3 for _ in range(3) is invalid syntax. matrix = [0,0,0]*3 creates a flat list, not a matrix.

2. Step 2: Choose the correct matrix initialization

   Only matrix = [[0 for _ in range(3)] for _ in range(3)] correctly creates a 3x3 matrix with independent rows filled with zeros.

3. Final Answer:

   matrix = [[0 for _ in range(3)] for _ in range(3)] -> Option D

4. Quick Check:

   Use nested list comprehension for independent rows [OK]

Hint: Use nested list comprehension for 2D matrix [OK]

Common Mistakes:

• Using [[0]*3]*3 causes shared references
• Incorrect syntax in option C
• Flat list instead of 2D matrix

3. What will be the matrix after applying the Set Matrix Zeroes In Place logic on this matrix?

[[1, 2, 3],
 [4, 0, 6],
 [7, 8, 9]]

medium

A. [[1, 0, 3], [0, 0, 0], [7, 0, 9]]

B. [[1, 2, 3], [4, 0, 6], [7, 8, 9]]

C. [[1, 2, 3], [0, 0, 0], [7, 8, 9]]

D. [[0, 0, 0], [0, 0, 0], [0, 0, 0]]

Solution

1. Step 1: Identify zero positions

   The zero is at position (1,1) (second row, second column).

2. Step 2: Set entire row 1 and column 1 to zero

   Row 1 becomes [0,0,0]. Column 1 elements at rows 0 and 2 become zero, changing matrix to [[1,0,3],[0,0,0],[7,0,9]].

3. Final Answer:

   [[1, 0, 3], [0, 0, 0], [7, 0, 9]] -> Option A

4. Quick Check:

   Zero at (1,1) zeroes row 1 and column 1 [OK]

Hint: Zero row and column for each zero element [OK]

Common Mistakes:

• Not zeroing the entire column
• Changing elements not in zero row/column
• Confusing row and column indices

4. Given this code snippet to set matrix zeroes in place, what is the main bug?

def setZeroes(matrix):
    rows = len(matrix)
    cols = len(matrix[0])
    zero_rows = set()
    zero_cols = set()
    for i in range(rows):
        for j in range(cols):
            if matrix[i][j] == 0:
                zero_rows.add(i)
                zero_cols.add(j)
    for i in zero_rows:
        for j in range(cols):
            matrix[i][j] = 0
    for j in zero_cols:
        for i in range(rows):
            matrix[i][j] = 0

medium

A. It misses zeroing the diagonal elements.

B. It modifies the matrix before identifying all zeroes.

C. It uses extra space, not in-place modification.

D. It does not handle empty matrices.

Solution

1. Step 1: Analyze space usage

   The code uses sets zero_rows and zero_cols to store indices, which uses extra space proportional to matrix size.

2. Step 2: Understand in-place requirement

   The problem requires modifying the matrix without extra space (in-place). Using sets violates this.

3. Final Answer:

   It uses extra space, not in-place modification. -> Option C

4. Quick Check:

   Extra sets mean not in-place [OK]

Hint: In-place means no extra sets or arrays [OK]

Common Mistakes:

• Ignoring extra space used by sets
• Thinking diagonal needs special handling
• Assuming empty matrix causes error here

5. How can you modify the matrix [[1,2,3],[4,0,6],[7,8,9]] in place to set zeroes without using extra space for rows and columns? Which approach is correct?

hard

A. Use first row and first column as markers to track zero rows and columns, then update matrix accordingly.

B. Create two separate lists to store zero rows and columns, then update matrix.

C. Copy the matrix, modify the copy, then replace original matrix.

D. Only zero the rows where zero is found, ignore columns.

Solution

1. Step 1: Use first row and column as markers

   Mark zeros in first row and column to remember which rows and columns to zero later, avoiding extra space.

2. Step 2: Update matrix based on markers

   After marking, iterate matrix to set zeros in rows and columns indicated by markers, then handle first row and column separately.

3. Final Answer:

   Use first row and first column as markers to track zero rows and columns, then update matrix accordingly. -> Option A

4. Quick Check:

   First row/column markers enable in-place zeroing [OK]

Hint: Use matrix edges as markers to avoid extra space [OK]

Common Mistakes:

• Using extra lists violates in-place rule
• Copying matrix wastes space
• Ignoring zero columns leads to wrong result