Set Matrix Zeroes — DSA Visualizer

Problem

Given an m × n integer matrix, if an element is 0, set its entire row and column to 0. You must do it in place.

Example 1

Input: matrix = [[1,1,1],[1,0,1],[1,1,1]]

Output: [[1,0,1],[0,0,0],[1,0,1]]

Explanation: Zero at (1,1) zeroes entire row 1 and col 1.

Example 2

Input: matrix = [[0,1,2,0],[3,4,5,2],[1,3,1,5]]

Output: [[0,0,0,0],[0,4,5,0],[0,3,1,0]]

Explanation: Zeros at (0,0) and (0,3) zero their rows and cols.

Constraints: 1 ≤ m, n ≤ 200 | −2³¹ ≤ matrix[i][j] ≤ 2³¹ − 1

Matrix Grid

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Original zero

Row marker (first col)

Col marker (first row)

Being zeroed

Final zero

Variables

Phase

—

firstRowZero

—

firstColZero

—

Step Logic

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Ready

0 / 0

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Algorithm

Check if row 0 / col 0 originally contain a zero → firstRowZero, firstColZero

Mark pass (r,c ≥ 1): if mat[r][c]==0 set mat[r][0]=0 and mat[0][c]=0

Zero pass (r,c ≥ 1): if mat[r][0]==0 or mat[0][c]==0 → set mat[r][c]=0

Fix row 0 if firstRowZero, fix col 0 if firstColZero

Time

O(m×n)

Space

O(1)

Why O(1) Space?

We repurpose the first row and first column as flag arrays — they already exist in the matrix, so no extra storage is needed. The only catch: before we overwrite them with markers, we must remember whether they themselves originally contained zeros (stored in firstRowZero and firstColZero). Then we mark, zero, and finally fix those edge rows/cols.