Set Matrix Zeroes In Place in DSA C++ - Build from Scratch

Set Matrix Zeroes In Place

📖 Scenario: You are working with a grid of numbers representing a spreadsheet. Sometimes, if a cell has zero, the entire row and column must be cleared to zero to mark errors.

🎯 Goal: Modify the given matrix so that if any cell is zero, its entire row and column become zero. Do this change inside the same matrix without using extra space for another matrix.

📋 What You'll Learn

Create a 2D vector called matrix with the exact values given

Create two boolean variables firstRowZero and firstColZero to track zeros in first row and column

Use the first row and first column of matrix to mark which rows and columns should be zeroed

Update the matrix in place based on these markers

Print the matrix after modification in the format: each row on a new line, values separated by spaces

💡 Why This Matters

🌍 Real World

This technique is useful in spreadsheet software and image processing where zero values indicate errors or special conditions that affect entire rows and columns.

💼 Career

Understanding in-place matrix manipulation is important for software engineers working with data grids, databases, and performance-critical applications.

1

Create the initial matrix

Create a 2D vector of integers called matrix with these exact values: {{1,1,1},{1,0,1},{1,1,1}}

DSA C++

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

Hint

Use vector> matrix = {{1,1,1},{1,0,1},{1,1,1}}; to create the matrix.

2

Add flags for first row and first column zeros

Add two boolean variables called firstRowZero and firstColZero and set both to false

DSA C++

#include 
#include 

using namespace std;

int main() {
    vector> matrix = {{1,1,1},{1,0,1},{1,1,1}};
    // Add boolean flags for first row and first column zeros
    // Your code here
    return 0;
}

Hint

Declare bool firstRowZero = false; and bool firstColZero = false; inside main().

3

Mark rows and columns to be zeroed using first row and column

Write code to check if the first row has zero and set firstRowZero accordingly. Then check if the first column has zero and set firstColZero. Next, use a for loop with i from 1 to matrix.size() and a nested for loop with j from 1 to matrix[0].size() to mark zeros in first row and column by setting matrix[i][0] and matrix[0][j] to zero if matrix[i][j] is zero.

DSA C++

#include 
#include 

using namespace std;

int main() {
    vector> matrix = {{1,1,1},{1,0,1},{1,1,1}};
    bool firstRowZero = false;
    bool firstColZero = false;
    // Check first row for zero
    // Check first column for zero
    // Mark zeros in first row and column
    // Your code here
    return 0;
}

Hint

Use loops to check first row and column for zeros. Then use nested loops starting from 1 to mark zeros in first row and column.

4

Set matrix zeroes in place and print the matrix

Use nested for loops with i from 1 to matrix.size() and j from 1 to matrix[0].size() to set matrix[i][j] to zero if matrix[i][0] or matrix[0][j] is zero. Then, if firstRowZero is true, set all elements in the first row to zero. If firstColZero is true, set all elements in the first column to zero. Finally, print the matrix row by row with values separated by spaces.

DSA C++

#include 
#include 

using namespace std;

int main() {
    vector> matrix = {{1,1,1},{1,0,1},{1,1,1}};
    bool firstRowZero = false;
    bool firstColZero = false;

    for (int j = 0; j < matrix[0].size(); j++) {
        if (matrix[0][j] == 0) {
            firstRowZero = true;
            break;
        }
    }

    for (int i = 0; i < matrix.size(); i++) {
        if (matrix[i][0] == 0) {
            firstColZero = true;
            break;
        }
    }

    for (int i = 1; i < matrix.size(); i++) {
        for (int j = 1; j < matrix[0].size(); j++) {
            if (matrix[i][j] == 0) {
                matrix[i][0] = 0;
                matrix[0][j] = 0;
            }
        }
    }

    // Set zeros based on marks
    // Set first row and first column zeros if needed
    // Print the matrix
    // Your code here

    return 0;
}

Hint

Use loops to update matrix cells to zero if marked. Then update first row and column if needed. Finally, print the matrix row by row.

Practice

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

easy

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

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

C. Count the number of zero elements in the matrix.

D. Modify the matrix so that if an element is 0, its entire row and column become 0 without using extra space.

Solution

1. Step 1: Understand the problem requirement

   The problem requires changing the matrix so that any row or column containing a zero is set entirely to zero.

2. Step 2: Note the in-place constraint

   We must do this without using extra space for another matrix or large data structures.

3. Final Answer:

   Modify the matrix so that if an element is 0, its entire row and column become 0 without using extra space. -> Option D

4. Quick Check:

   In-place zeroing = Modify matrix rows and columns [OK]

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

Common Mistakes:

• Using extra space like another matrix
• Only zeroing the element itself, not row and column
• Not handling the in-place requirement

2. Which of the following C++ code snippets correctly declares a 2D vector to represent a matrix for the Set Matrix Zeroes In Place problem?

easy

A. std::vector matrix(cols, std::vector<int>(rows));

B. std::vector<int> matrix(rows, cols);

C. std::vector matrix(rows, std::vector<int>(cols));

D. std::vector<int> matrix[rows][cols];

Solution

1. Step 1: Understand 2D vector declaration

   To create a matrix with 'rows' rows and 'cols' columns, use vector of vectors with inner vector size 'cols'.

2. Step 2: Check each option

   std::vector matrix(rows, std::vector<int>(cols)); correctly creates a vector of vectors with 'rows' outer vectors and 'cols' inner vectors each.

3. Final Answer:

   std::vector matrix(rows, std::vector<int>(cols)); -> Option C

4. Quick Check:

   Correct 2D vector syntax = std::vector matrix(rows, std::vector<int>(cols)); [OK]

Hint: Use vector of vectors with inner vector size as columns [OK]

Common Mistakes:

• Using single vector with two sizes incorrectly
• Swapping rows and columns in inner vector
• Using array syntax instead of vector

3. What will be the state of the matrix after running the following code snippet for Set Matrix Zeroes In Place?

std::vector matrix = {
  {1, 2, 3},
  {4, 0, 6},
  {7, 8, 9}
};
// Assume correct in-place zeroing function is called here
setZeroes(matrix);
// Print matrix

medium

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

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

C. [[0, 0, 0], [0, 0, 0], [0, 0, 0]]

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

Solution

1. Step 1: Identify zero positions

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

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

   Row 1 becomes [0,0,0], column 1 becomes zero in rows 0 and 2, so matrix becomes [[1,0,3],[0,0,0],[7,0,9]].

3. Final Answer:

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

4. Quick Check:

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

Hint: Zero row and column where zero found [OK]

Common Mistakes:

• Zeroing entire matrix instead of row and column
• Not zeroing column correctly
• Leaving original zero row unchanged

4. Consider this buggy code snippet for Set Matrix Zeroes In Place. What is the main error?

void setZeroes(std::vector& matrix) {
  int rows = matrix.size();
  int cols = matrix[0].size();
  for (int i = 0; i < rows; i++) {
    for (int j = 0; j < cols; j++) {
      if (matrix[i][j] == 0) {
        for (int k = 0; k < cols; k++) matrix[i][k] = 0;
        for (int k = 0; k < rows; k++) matrix[k][j] = 0;
      }
    }
  }
}

medium

A. Modifying matrix inside loops causes multiple zeroing and incorrect results.

B. The loops do not cover all rows and columns.

C. The function does not return the modified matrix.

D. The matrix size is not checked for empty input.

Solution

1. Step 1: Analyze modification during iteration

   The code sets zeros immediately when a zero is found, changing matrix during iteration.

2. Step 2: Understand side effects

   This causes new zeros to appear and cause more zeroing, leading to incorrect results.

3. Final Answer:

   Modifying matrix inside loops causes multiple zeroing and incorrect results. -> Option A

4. Quick Check:

   Immediate modification causes cascading zeroing [OK]

Hint: Mark zeros first, then modify matrix after loops [OK]

Common Mistakes:

• Changing matrix while scanning causes wrong zeroing
• Not using markers or flags to delay zeroing
• Ignoring empty matrix edge cases

5. Given a matrix with multiple zeros, how can you efficiently set matrix zeroes in place without extra space? Choose the best approach.

hard

A. Use first row and first column as markers to store zero flags, then update matrix accordingly.

B. Create a copy of the matrix and update zeros in the copy.

C. Use a hash map to store zero positions and then update matrix.

D. Iterate multiple times over the matrix zeroing rows and columns immediately when zero found.

Solution

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

   Mark zeros found in first row and column to remember which rows and columns to zero later.

2. Step 2: Update matrix based on markers

   After marking, zero out rows and columns except first row and column, then handle first row and column separately.

3. Final Answer:

   Use first row and first column as markers to store zero flags, then update matrix accordingly. -> Option A

4. Quick Check:

   In-place marking with first row/column = Use first row and first column as markers to store zero flags, then update matrix accordingly. [OK]

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

Common Mistakes:

• Using extra space violating in-place rule
• Zeroing immediately causing cascading errors
• Not handling first row and column separately