Set Matrix Zeroes In Place in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the problem 'Set Matrix Zeroes In Place' ask you to do?

It asks to modify a given matrix so that if an element is 0, its entire row and column are set to 0, without using extra space for another matrix.

beginner

Why can't we simply create a new matrix to solve 'Set Matrix Zeroes In Place'?

Because the problem requires modifying the matrix in place, meaning no extra matrix or significant extra space should be used.

intermediate

How can the first row and first column be used in the 'Set Matrix Zeroes In Place' solution?

They can be used as markers to indicate which rows and columns should be zeroed, avoiding extra space usage.

intermediate

What is the main challenge when using the first row and column as markers in 'Set Matrix Zeroes In Place'?

The first row and column themselves might need to be zeroed, so we must track separately if they originally contained zeros.

intermediate

What is the time and space complexity of the optimal 'Set Matrix Zeroes In Place' solution?

Time complexity is O(m*n) where m and n are matrix dimensions; space complexity is O(1) because no extra space is used except variables.

What does 'in place' mean in the context of the 'Set Matrix Zeroes In Place' problem?

A Return a new matrix with zeros set

B Create a new matrix to store results

C Use extra arrays to track zeros

D Modify the input matrix without using extra space

In place means changing the original matrix directly without extra space.

Which part of the matrix is commonly used as a marker to avoid extra space in 'Set Matrix Zeroes In Place'?

A First row and first column

B Last row and last column

C Diagonal elements

D Middle row and column

The first row and first column are used to mark which rows and columns should be zeroed.

If a zero is found at matrix[2][3], what should happen in the 'Set Matrix Zeroes In Place' solution?

A Set only matrix[2][3] to zero

B Set entire matrix to zero

C Set entire row 2 and column 3 to zero

D Ignore it

The entire row and column of any zero element must be set to zero.

Why do we need separate flags for the first row and first column in the solution?

A Because they are always zero

B Because they are used as markers and might need to be zeroed themselves

C Because they never contain zeros

D Because they are ignored

We track if the first row or column originally had zeros to know if they should be zeroed later.

What is the space complexity of the optimal 'Set Matrix Zeroes In Place' solution?

A O(1)

B O(m+n)

C O(m*n)

D O(log(m*n))

The solution uses constant extra space by marking in the matrix itself.

Explain step-by-step how to solve 'Set Matrix Zeroes In Place' without extra space.

Think about how to remember which rows and columns to zero without extra arrays.

Describe why tracking the first row and first column separately is important in the 'Set Matrix Zeroes In Place' problem.

Consider what happens if you overwrite the first row or column too soon.

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