Zero Matrix - Amazon Top Interview Questions
Problem Statement :
Given a two-dimensional matrix of integers, for each zero in the original matrix, replace all values in its row and column with zero, and return the resulting matrix.
Constraints
n * m ≤ 100,000 where n and m are the number of rows and columns in matrix
Example 1
Input
matrix = [
[5, 0, 0, 5, 8],
[9, 8, 10, 3, 9],
[0, 7, 2, 3, 1],
[8, 0, 6, 7, 2],
[4, 1, 8, 5, 10]
]
Output
[
[0, 0, 0, 0, 0],
[0, 0, 0, 3, 9],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 5, 10]
]
Explanation
These rows contain a 0: [0, 2, 3] and the returned matrix contains 0 in those rows.
These columns contain a 0: [0, 1, 2] and the returned matrix contains 0 in those columns.
Solution :
Solution in C++ :
vector<vector<int>> solve(vector<vector<int>>& matrix) {
int R = matrix.size();
int C = matrix[0].size();
if (R == 0 || C == 0) return matrix;
/// STEP 1
bool hasFirstRowZero = false;
bool hasFirstColZero = false;
// Now start from matrix(0,0)
// If first row has zero ?
for (int i = 0; i < C; i++) {
if (matrix[0][i] == 0) {
hasFirstRowZero = true;
break;
}
}
// If first column has zero ?
for (int i = 0; i < R; i++) {
if (matrix[i][0] == 0) {
hasFirstColZero = true;
break;
}
}
/// STEP 2(make use of hasFirstRowZero and hasFirstColZero)
// start from matrix(1,1) and check if matrix(i,j) is zero ?
for (int i = 1; i < R; i++) {
for (int j = 1; j < C; j++) {
if (matrix[i][j] == 0) {
matrix[i][0] = 0; // leftmost element set 0
matrix[0][j] = 0; // topmost element set 0
}
}
}
/// STEP 3
// start from matrix(1,1) and check topmost and leftmost element zero ?
for (int i = 1; i < R; i++) {
for (int j = 1; j < C; j++) {
if (matrix[i][0] == 0 || matrix[0][j] == 0) {
matrix[i][j] = 0;
}
}
}
/// STEP 4
// set zeroes for first row
if (hasFirstRowZero) {
for (int i = 0; i < C; i++) {
matrix[0][i] = 0;
}
}
// set zeroes for first column
if (hasFirstColZero) {
for (int i = 0; i < R; i++) {
matrix[i][0] = 0;
}
}
return matrix;
}
Solution in Java :
import java.util.*;
class Solution {
public int[][] solve(int[][] matrix) {
boolean[] rows = new boolean[matrix.length];
boolean[] cols = new boolean[matrix[0].length];
for (int i = 0; i < rows.length; i++)
for (int j = 0; j < cols.length; j++)
if (matrix[i][j] == 0) {
rows[i] = true;
cols[j] = true;
}
// Update matrix
for (int i = 0; i < rows.length; i++)
for (int j = 0; j < cols.length; j++)
if (rows[i] || cols[j])
matrix[i][j] = 0;
return matrix;
}
}
Solution in Python :
class Solution:
def solve(self, matrix):
first_row_zero = 0 in matrix[0]
first_column_zero = 0 in [matrix[i][0] for i in range(len(matrix))]
m = len(matrix)
n = len(matrix[0])
for i in range(1, m):
for j in range(1, n):
if matrix[i][j] == 0:
matrix[i][0] = 0
matrix[0][j] = 0
for i in range(1, m):
if matrix[i][0] == 0:
for j in range(1, n):
matrix[i][j] = 0
for j in range(1, n):
if matrix[0][j] == 0:
for i in range(1, m):
matrix[i][j] = 0
if first_row_zero:
matrix[0] = [0] * n
if first_column_zero:
for i in range(m):
matrix[i][0] = 0
return matrix
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