Set Matrix Zeroes In Place in DSA Go - Execution Trace

Concept Flow - Set Matrix Zeroes In Place

Start

↓

Scan matrix for zeros

↓

Mark rows and columns to zero

↓

Update matrix cells to zero

↓

Done

We first scan the matrix to find zeros and mark their rows and columns. Then we update the matrix cells to zero based on these marks.

Execution Sample

DSA Go

matrix := [][]int{
  {1,1,1},
  {1,0,1},
  {1,1,1},
}
setZeroes(matrix)

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

Execution Table

Step	Operation	Matrix State	Row Markers	Column Markers	Visual State
1	Initial matrix	[[1,1,1],[1,0,1],[1,1,1]]	[false,false,false]	[false,false,false]	1 1 1 1 0 1 1 1 1
2	Scan row 0	[[1,1,1],[1,0,1],[1,1,1]]	[false,false,false]	[false,false,false]	1 1 1 1 0 1 1 1 1
3	Scan row 1, found zero at col 1	[[1,1,1],[1,0,1],[1,1,1]]	[false,true,false]	[false,true,false]	1 1 1 1 0 1 1 1 1
4	Scan row 2	[[1,1,1],[1,0,1],[1,1,1]]	[false,true,false]	[false,true,false]	1 1 1 1 0 1 1 1 1
5	Set zeros in row 1	[[1,1,1],[0,0,0],[1,1,1]]	[false,true,false]	[false,true,false]	1 1 1 0 0 0 1 1 1
6	Set zeros in column 1	[[1,0,1],[0,0,0],[1,0,1]]	[false,true,false]	[false,true,false]	1 0 1 0 0 0 1 0 1
7	Done	[[1,0,1],[0,0,0],[1,0,1]]	[false,true,false]	[false,true,false]	1 0 1 0 0 0 1 0 1

💡 All rows and columns with zeros are updated; matrix is fully processed.

Variable Tracker

Variable	Start	After Step 3	After Step 5	After Step 6	Final
matrix	[[1,1,1],[1,0,1],[1,1,1]]	[[1,1,1],[1,0,1],[1,1,1]]	[[1,1,1],[0,0,0],[1,1,1]]	[[1,0,1],[0,0,0],[1,0,1]]	[[1,0,1],[0,0,0],[1,0,1]]
rowMarkers	[false,false,false]	[false,true,false]	[false,true,false]	[false,true,false]	[false,true,false]
colMarkers	[false,false,false]	[false,true,false]	[false,true,false]	[false,true,false]	[false,true,false]

Key Moments - 3 Insights

Why do we mark rows and columns first before setting zeros?

Marking rows and columns first (see Step 3) avoids changing the matrix while scanning, which could cause incorrect zeroing.

Why do we need separate row and column markers?

Separate markers (Step 3) track which rows and columns to zero independently, ensuring all affected cells are updated correctly.

What happens if we set zeros immediately when found?

Setting zeros immediately would affect scanning and cause extra zeros (not shown here), so we mark first then update (Step 5 and 6).

Visual Quiz - 3 Questions

Look at the execution table at Step 3, which row and column are marked for zeroing?

A Row 0 and Column 0

B Row 1 and Column 1

C Row 2 and Column 2

D Row 1 and Column 2

💡 Hint

Check 'Row Markers' and 'Column Markers' columns at Step 3 in execution_table.

At which step does the matrix first change to include zeros?

A Step 2

B Step 3

C Step 5

D Step 6

💡 Hint

Look at 'Matrix State' column in execution_table to see when zeros appear.

If the zero was at matrix[0][2] instead, which marker would change at Step 3?

A rowMarkers[0] and colMarkers[2]

B rowMarkers[2] and colMarkers[0]

C rowMarkers[1] and colMarkers[1]

D rowMarkers[0] and colMarkers[0]

💡 Hint

Markers correspond to the row and column indices of the zero found during scanning.

Concept Snapshot

Set Matrix Zeroes In Place:
- Scan matrix to find zeros
- Mark rows and columns to zero
- Update matrix cells based on marks
- Modify matrix in place without extra matrix
- Avoid changing matrix during scanning

Full Transcript

This visualization shows how to set matrix zeroes in place. First, we scan the matrix to find zeros and mark their rows and columns. We keep track of these marks separately to avoid changing the matrix while scanning. After marking, we update the matrix cells to zero based on these marks. This method ensures the matrix is modified correctly without extra space for a copy. The execution table tracks each step, showing matrix state and markers. Key moments clarify why marking first is important and why separate row and column markers are needed. The visual quiz tests understanding of these steps.

Practice

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

easy

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

B. Find the sum of all elements in the matrix

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 any row or column containing a zero should be set entirely to zero.

2. Step 2: Identify the correct operation

   Only Modify the matrix so that if an element is 0, its entire row and column become 0 describes this exact operation, modifying rows and columns based on zero elements.

3. Final Answer:

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

4. Quick Check:

   Set rows and columns to zero = Modify matrix [OK]

Hint: Remember: zero means zero out whole row and column [OK]

Common Mistakes:

• Confusing with matrix transpose
• Trying to sum elements instead of modifying
• Sorting rows instead of zeroing

2. Which of the following Go code snippets correctly declares a fixed-size 2D array of integers?

easy

A. matrix := [][]int{{1, 2}, {3, 4}}

B. matrix := [2][2]int{{1, 2}, {3, 4}}

C. matrix := [][]int{1, 2, 3, 4}

D. matrix := [2]int{1, 2, 3, 4}

Solution

1. Step 1: Understand Go 2D array declaration

   In Go, fixed-size 2D arrays use syntax like [rows][cols]type, so [2][2]int is a 2x2 matrix.

2. Step 2: Check each option

   matrix := [2][2]int{{1, 2}, {3, 4}} correctly declares a 2x2 integer array with values. matrix := [][]int{{1, 2}, {3, 4}} is a slice of slices (dynamic), not a fixed-size array. matrix := [][]int{1, 2, 3, 4} and D are invalid for 2D matrix.

3. Final Answer:

   matrix := [2][2]int{{1, 2}, {3, 4}} -> Option B

4. Quick Check:

   Fixed 2D array syntax = [2][2]int [OK]

Hint: Use [rows][cols]type for fixed 2D arrays in Go [OK]

Common Mistakes:

• Using slice syntax when fixed array needed
• Incorrect nesting of braces
• Declaring 1D array instead of 2D

3. What will be the matrix after running the following Go code snippet?

matrix := [][]int{
  {1, 2, 3},
  {4, 0, 6},
  {7, 8, 9},
}
// After applying Set Matrix Zeroes In Place logic
// (zero out rows and columns containing zero)

medium

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

B. [[1, 2, 3], [0, 0, 0], [7, 0, 9]]

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

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

Solution

1. Step 1: Identify zero positions

   Zero is at matrix[1][1]. So row 1 and column 1 must be zeroed.

2. Step 2: Apply zeroing

   Row 1 becomes [0,0,0]. Column 1 elements at rows 0 and 2 become 0. So matrix[0][1] and matrix[2][1] are zero.

3. Final Answer:

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

4. Quick Check:

   Zero row and column applied correctly = [[1,0,3],[0,0,0],[7,0,9]] [OK]

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

Common Mistakes:

• Zeroing entire matrix
• Missing zero in column 1 for rows 0 and 2
• Zeroing wrong rows or columns

4. Consider this Go function snippet for setting matrix zeroes:

func setZeroes(matrix [][]int) {
  for i := 0; i < len(matrix); i++ {
    for j := 0; j < len(matrix[0]); j++ {
      if matrix[i][j] == 0 {
        for k := 0; k < len(matrix); k++ {
          matrix[k][j] = 0
        }
        for l := 0; l < len(matrix[0]); l++ {
          matrix[i][l] = 0
        }
      }
    }
  }
}

What is the main problem with this code?

medium

A. It only zeros rows but not columns

B. It uses wrong loop ranges for rows and columns

C. It does not check for zero elements at all

D. It modifies the matrix while iterating, causing incorrect zeroing

Solution

1. Step 1: Analyze matrix modification during iteration

   The code sets zeros immediately when it finds a zero, changing matrix elements during iteration.

2. Step 2: Understand side effects

   This causes new zeros to appear and triggers more zeroing incorrectly, leading to wrong final matrix.

3. Final Answer:

   It modifies the matrix while iterating, causing incorrect zeroing -> Option D

4. Quick Check:

   In-place modification during scan = incorrect zeroing [OK]

Hint: Mark zeros first, then update matrix to avoid side effects [OK]

Common Mistakes:

• Changing matrix while scanning
• Not using extra storage or flags
• Assuming immediate zeroing is safe

5. You want to set matrix zeroes in place with O(1) extra space. Which approach below correctly achieves this in Go?

hard

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

B. Create a separate boolean matrix to mark zero rows and columns, then update original matrix

C. Copy matrix to a new matrix and update zeros there to avoid modifying original during iteration

D. Use recursion to zero rows and columns when zero found

Solution

1. Step 1: Understand space constraints

   O(1) extra space means no additional matrix or large data structures allowed.

2. Step 2: Use first row and column as markers

   Mark zeros in first row and column to remember which rows and columns to zero later, then update matrix in place.

3. Step 3: Avoid extra space and recursion

   Options A and B use extra space, D uses recursion unnecessarily.

4. Final Answer:

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

5. Quick Check:

   In-place markers = O(1) space zeroing [OK]

Hint: Use matrix edges as flags to save space [OK]

Common Mistakes:

• Using extra arrays violating space constraint
• Modifying matrix during iteration without markers
• Overcomplicating with recursion