Set Matrix Zeroes In Place in DSA Python - Execution Trace

Concept Flow - Set Matrix Zeroes In Place

Start: Given matrix

↓

Scan matrix for zeros

↓

Mark rows and columns to zero

↓

Update matrix cells to zero

↓

Done: Matrix updated in place

We scan the matrix to find zeros, mark which rows and columns to zero, then update the matrix in place.

Execution Sample

DSA Python

matrix = [
  [1,1,1],
  [1,0,1],
  [1,1,1]
]
# Set zeros in place

This code sets entire row and column to zero if any cell is zero, modifying the matrix directly.

Execution Table

Step	Operation	Nodes in Matrix	Pointer Changes	Visual State
1	Scan matrix for zeros	matrix[1][1] == 0 found	Mark row 1 and column 1 for zeroing	[[1,1,1], [1,0,1], [1,1,1]]
2	Mark rows and columns to zero	Rows to zero: {1}, Columns to zero: {1}	No pointer change	[[1,1,1], [1,0,1], [1,1,1]]
3	Update matrix cells to zero	Set matrix[1][0], matrix[1][1], matrix[1][2] = 0 Set matrix[0][1], matrix[1][1], matrix[2][1] = 0	No pointer change	[[1,0,1], [0,0,0], [1,0,1]]
4	Done	Matrix updated in place	No pointer change	[[1,0,1], [0,0,0], [1,0,1]]

💡 All rows and columns with zeros are updated; matrix is modified in place.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
matrix	[[1,1,1],[1,0,1],[1,1,1]]	[[1,1,1],[1,0,1],[1,1,1]]	[[1,1,1],[1,0,1],[1,1,1]]	[[1,0,1],[0,0,0],[1,0,1]]	[[1,0,1],[0,0,0],[1,0,1]]
rows_to_zero	{}	{1}	{1}	{1}	{1}
cols_to_zero	{}	{1}	{1}	{1}	{1}

Key Moments - 3 Insights

Why do we mark rows and columns first instead of setting zeros immediately?

If we set zeros immediately, new zeros would affect other rows and columns incorrectly. Marking first (see Step 2 in execution_table) ensures only original zeros cause changes.

How do we update the matrix in place without extra space for a copy?

We use sets to remember which rows and columns to zero, then update the matrix directly (Step 3). This avoids making a full copy.

What if the matrix has multiple zeros in different rows and columns?

All rows and columns with zeros are marked (Step 1 and 2). Then all those rows and columns are zeroed together (Step 3), ensuring correctness.

Visual Quiz - 3 Questions

Look at the execution_table at Step 1, which cell is found to be zero?

A matrix[0][0]

B matrix[2][2]

C matrix[1][1]

D matrix[0][2]

💡 Hint

Check the 'Nodes in Matrix' column in Step 1 of execution_table.

At which step does the matrix get updated with zeros?

A Step 3

B Step 2

C Step 1

D Step 4

💡 Hint

Look at the 'Operation' and 'Visual State' columns in execution_table.

If there was a zero at matrix[0][2], which rows and columns would be marked after Step 2?

A Rows {0,1}, Columns {2}

B Rows {0,1}, Columns {1,2}

C Rows {0}, Columns {2}

D Rows {1}, Columns {1}

💡 Hint

Mark rows and columns for all zeros found; see variable_tracker for rows_to_zero and cols_to_zero.

Concept Snapshot

Set Matrix Zeroes In Place:
- Scan matrix to find zeros
- Mark rows and columns to zero
- Update matrix cells in place
- Avoid immediate zeroing to prevent cascading
- Use sets to track rows and columns
- Modify matrix directly without extra matrix copy

Full Transcript

We start with a matrix. We scan it to find cells with zero. When we find a zero, we mark its entire row and column to be zeroed later. We do not change the matrix immediately to avoid affecting other cells incorrectly. After scanning, we update all marked rows and columns by setting their cells to zero. This changes the matrix in place without extra space. The process ensures all rows and columns containing zeros are zeroed correctly.

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