Skip to content

01.08. Zero Matrix

Description

Write an algorithm such that if an element in an MxN matrix is 0, its entire row and column are set to 0.

 

Example 1: 

Input: 

[

  [1,1,1],

  [1,0,1],

  [1,1,1]

]

Output: 

[

  [1,0,1],

  [0,0,0],

  [1,0,1]

]

Example 2: 

Input: 

[

  [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]

]

Solutions

Solution 1: Array Marking

Thinking

A zero forces its whole row and column to zero. Clearing immediately while scanning treats newly written zeros as original zeros and spreads incorrectly.

Rows and columns to clear must be recorded completely before any write.

Arrays \(rows\) and \(cols\) are filled on the first pass and applied on the second. Two linear scans and \(O(m+n)\) extra space avoid read/write confusion.

We use arrays rows and cols to mark the rows and columns to be zeroed.

Then we traverse the matrix again, zeroing the elements corresponding to the rows and columns marked in rows and cols.

The time complexity is \(O(m \times n)\), and the space complexity is \(O(m + n)\). Here, \(m\) and \(n\) are the number of rows and columns of the matrix, respectively.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
class Solution:
    def setZeroes(self, matrix: List[List[int]]) -> None:
        m, n = len(matrix), len(matrix[0])
        rows = [0] * m
        cols = [0] * n
        for i, row in enumerate(matrix):
            for j, v in enumerate(row):
                if v == 0:
                    rows[i] = cols[j] = 1
        for i in range(m):
            for j in range(n):
                if rows[i] or cols[j]:
                    matrix[i][j] = 0

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
class Solution {
    public void setZeroes(int[][] matrix) {
        int m = matrix.length, n = matrix[0].length;
        boolean[] rows = new boolean[m];
        boolean[] cols = new boolean[n];
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (matrix[i][j] == 0) {
                    rows[i] = true;
                    cols[j] = true;
                }
            }
        }
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (rows[i] || cols[j]) {
                    matrix[i][j] = 0;
                }
            }
        }
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
        int m = matrix.size(), n = matrix[0].size();
        vector<bool> rows(m);
        vector<bool> cols(n);
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (!matrix[i][j]) {
                    rows[i] = 1;
                    cols[j] = 1;
                }
            }
        }
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (rows[i] || cols[j]) {
                    matrix[i][j] = 0;
                }
            }
        }
    }
};

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
func setZeroes(matrix [][]int) {
    m, n := len(matrix), len(matrix[0])
    rows := make([]bool, m)
    cols := make([]bool, n)
    for i, row := range matrix {
        for j, v := range row {
            if v == 0 {
                rows[i] = true
                cols[j] = true
            }
        }
    }
    for i := 0; i < m; i++ {
        for j := 0; j < n; j++ {
            if rows[i] || cols[j] {
                matrix[i][j] = 0
            }
        }
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
/**
 Do not return anything, modify matrix in-place instead.
 */
function setZeroes(matrix: number[][]): void {
    const m = matrix.length;
    const n = matrix[0].length;
    const rows = new Array(m).fill(false);
    const cols = new Array(n).fill(false);
    for (let i = 0; i < m; i++) {
        for (let j = 0; j < n; j++) {
            if (matrix[i][j] === 0) {
                rows[i] = true;
                cols[j] = true;
            }
        }
    }
    for (let i = 0; i < m; i++) {
        for (let j = 0; j < n; j++) {
            if (rows[i] || cols[j]) {
                matrix[i][j] = 0;
            }
        }
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
impl Solution {
    pub fn set_zeroes(matrix: &mut Vec<Vec<i32>>) {
        let m = matrix.len();
        let n = matrix[0].len();
        let mut rows = vec![false; m];
        let mut cols = vec![false; n];
        for i in 0..m {
            for j in 0..n {
                if matrix[i][j] == 0 {
                    rows[i] = true;
                    cols[j] = true;
                }
            }
        }
        for i in 0..m {
            for j in 0..n {
                if rows[i] || cols[j] {
                    matrix[i][j] = 0;
                }
            }
        }
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
/**
 * @param {number[][]} matrix
 * @return {void} Do not return anything, modify matrix in-place instead.
 */
var setZeroes = function (matrix) {
    const m = matrix.length;
    const n = matrix[0].length;
    const rows = new Array(m).fill(false);
    const cols = new Array(n).fill(false);
    for (let i = 0; i < m; ++i) {
        for (let j = 0; j < n; ++j) {
            if (matrix[i][j] == 0) {
                rows[i] = true;
                cols[j] = true;
            }
        }
    }
    for (let i = 0; i < m; ++i) {
        for (let j = 0; j < n; ++j) {
            if (rows[i] || cols[j]) {
                matrix[i][j] = 0;
            }
        }
    }
};

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
void setZeroes(int** matrix, int matrixSize, int* matrixColSize) {
    int m = matrixSize;
    int n = matrixColSize[0];
    int* rows = (int*) malloc(sizeof(int) * m);
    int* cols = (int*) malloc(sizeof(int) * n);
    memset(rows, 0, sizeof(int) * m);
    memset(cols, 0, sizeof(int) * n);
    for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; ++j) {
            if (matrix[i][j] == 0) {
                rows[i] = 1;
                cols[j] = 1;
            }
        }
    }
    for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; ++j) {
            if (rows[i] || cols[j]) {
                matrix[i][j] = 0;
            }
        }
    }
    free(rows);
    free(cols);
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
class Solution {
    func setZeroes(_ matrix: inout [[Int]]) {
        let m = matrix.count
        guard m > 0 else { return }
        let n = matrix[0].count
        var rows = Array(repeating: false, count: m)
        var cols = Array(repeating: false, count: n)

        for i in 0..<m {
            for j in 0..<n {
                if matrix[i][j] == 0 {
                    rows[i] = true
                    cols[j] = true
                }
            }
        }

        for i in 0..<m {
            for j in 0..<n {
                if rows[i] || cols[j] {
                    matrix[i][j] = 0
                }
            }
        }
    }
}

Solution 2: In-place Marking

Thinking

The extra arrays in Solution 1 can be replaced by the matrix’s first row and first column as markers.

Those two lines are both markers and data, so \(i0\) and \(j0\) remember whether they originally contained a zero. Other cells still take two passes: write marks, then apply them, then finish the first row and column from \(i0\) and \(j0\). Extra space drops to \(O(1)\).

In Solution 1, we used additional arrays to mark the rows and columns to be zeroed. In fact, we can directly use the first row and first column of the matrix for marking, without needing to allocate additional array space.

Since the first row and first column are used for marking, their values may change due to the marking. Therefore, we need additional variables \(i0\) and \(j0\) to mark whether the first row and first column need to be zeroed.

The time complexity is \(O(m \times n)\), where \(m\) and \(n\) are the number of rows and columns of the matrix, respectively. The space complexity is \(O(1)\).

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
class Solution:
    def setZeroes(self, matrix: List[List[int]]) -> None:
        m, n = len(matrix), len(matrix[0])
        i0 = any(v == 0 for v in matrix[0])
        j0 = any(matrix[i][0] == 0 for i in range(m))
        for i in range(1, m):
            for j in range(1, n):
                if matrix[i][j] == 0:
                    matrix[i][0] = matrix[0][j] = 0
        for i in range(1, m):
            for j in range(1, n):
                if matrix[i][0] == 0 or matrix[0][j] == 0:
                    matrix[i][j] = 0
        if i0:
            for j in range(n):
                matrix[0][j] = 0
        if j0:
            for i in range(m):
                matrix[i][0] = 0

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
class Solution {
    public void setZeroes(int[][] matrix) {
        int m = matrix.length, n = matrix[0].length;
        boolean i0 = false, j0 = false;
        for (int j = 0; j < n; ++j) {
            if (matrix[0][j] == 0) {
                i0 = true;
                break;
            }
        }
        for (int i = 0; i < m; ++i) {
            if (matrix[i][0] == 0) {
                j0 = true;
                break;
            }
        }
        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                if (matrix[i][j] == 0) {
                    matrix[i][0] = 0;
                    matrix[0][j] = 0;
                }
            }
        }
        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                if (matrix[i][0] == 0 || matrix[0][j] == 0) {
                    matrix[i][j] = 0;
                }
            }
        }
        if (i0) {
            for (int j = 0; j < n; ++j) {
                matrix[0][j] = 0;
            }
        }
        if (j0) {
            for (int i = 0; i < m; ++i) {
                matrix[i][0] = 0;
            }
        }
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
        int m = matrix.size(), n = matrix[0].size();
        bool i0 = false, j0 = false;
        for (int j = 0; j < n; ++j) {
            if (matrix[0][j] == 0) {
                i0 = true;
                break;
            }
        }
        for (int i = 0; i < m; ++i) {
            if (matrix[i][0] == 0) {
                j0 = true;
                break;
            }
        }
        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                if (matrix[i][j] == 0) {
                    matrix[i][0] = 0;
                    matrix[0][j] = 0;
                }
            }
        }
        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                if (matrix[i][0] == 0 || matrix[0][j] == 0) {
                    matrix[i][j] = 0;
                }
            }
        }
        if (i0) {
            for (int j = 0; j < n; ++j) {
                matrix[0][j] = 0;
            }
        }
        if (j0) {
            for (int i = 0; i < m; ++i) {
                matrix[i][0] = 0;
            }
        }
    }
};

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
func setZeroes(matrix [][]int) {
    m, n := len(matrix), len(matrix[0])
    i0, j0 := false, false
    for j := 0; j < n; j++ {
        if matrix[0][j] == 0 {
            i0 = true
            break
        }
    }
    for i := 0; i < m; i++ {
        if matrix[i][0] == 0 {
            j0 = true
            break
        }
    }
    for i := 1; i < m; i++ {
        for j := 1; j < n; j++ {
            if matrix[i][j] == 0 {
                matrix[i][0], matrix[0][j] = 0, 0
            }
        }
    }
    for i := 1; i < m; i++ {
        for j := 1; j < n; j++ {
            if matrix[i][0] == 0 || matrix[0][j] == 0 {
                matrix[i][j] = 0
            }
        }
    }
    if i0 {
        for j := 0; j < n; j++ {
            matrix[0][j] = 0
        }
    }
    if j0 {
        for i := 0; i < m; i++ {
            matrix[i][0] = 0
        }
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
/**
 Do not return anything, modify matrix in-place instead.
 */
function setZeroes(matrix: number[][]): void {
    const m = matrix.length;
    const n = matrix[0].length;
    let l0 = false;
    let r0 = false;
    for (let i = 0; i < m; i++) {
        if (matrix[i][0] === 0) {
            l0 = true;
            break;
        }
    }
    for (let j = 0; j < n; j++) {
        if (matrix[0][j] === 0) {
            r0 = true;
            break;
        }
    }
    for (let i = 0; i < m; i++) {
        for (let j = 0; j < n; j++) {
            if (matrix[i][j] === 0) {
                matrix[i][0] = 0;
                matrix[0][j] = 0;
            }
        }
    }
    for (let i = 1; i < m; i++) {
        for (let j = 1; j < n; j++) {
            if (matrix[i][0] === 0 || matrix[0][j] === 0) {
                matrix[i][j] = 0;
            }
        }
    }
    if (l0) {
        for (let i = 0; i < m; i++) {
            matrix[i][0] = 0;
        }
    }
    if (r0) {
        for (let j = 0; j < n; j++) {
            matrix[0][j] = 0;
        }
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
impl Solution {
    pub fn set_zeroes(matrix: &mut Vec<Vec<i32>>) {
        let m = matrix.len();
        let n = matrix[0].len();
        let l0 = {
            let mut res = false;
            for j in 0..n {
                if matrix[0][j] == 0 {
                    res = true;
                    break;
                }
            }
            res
        };
        let r0 = {
            let mut res = false;
            for i in 0..m {
                if matrix[i][0] == 0 {
                    res = true;
                    break;
                }
            }
            res
        };
        for i in 0..m {
            for j in 0..n {
                if matrix[i][j] == 0 {
                    matrix[i][0] = 0;
                    matrix[0][j] = 0;
                }
            }
        }
        for i in 1..m {
            for j in 1..n {
                if matrix[i][0] == 0 || matrix[0][j] == 0 {
                    matrix[i][j] = 0;
                }
            }
        }
        if l0 {
            for j in 0..n {
                matrix[0][j] = 0;
            }
        }
        if r0 {
            for i in 0..m {
                matrix[i][0] = 0;
            }
        }
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
/**
 * @param {number[][]} matrix
 * @return {void} Do not return anything, modify matrix in-place instead.
 */
var setZeroes = function (matrix) {
    const m = matrix.length;
    const n = matrix[0].length;
    let i0 = matrix[0].some(v => v == 0);
    let j0 = false;
    for (let i = 0; i < m; ++i) {
        if (matrix[i][0] == 0) {
            j0 = true;
            break;
        }
    }
    for (let i = 1; i < m; ++i) {
        for (let j = 1; j < n; ++j) {
            if (matrix[i][j] == 0) {
                matrix[i][0] = 0;
                matrix[0][j] = 0;
            }
        }
    }
    for (let i = 1; i < m; ++i) {
        for (let j = 1; j < n; ++j) {
            if (matrix[i][0] == 0 || matrix[0][j] == 0) {
                matrix[i][j] = 0;
            }
        }
    }
    if (i0) {
        for (let j = 0; j < n; ++j) {
            matrix[0][j] = 0;
        }
    }
    if (j0) {
        for (let i = 0; i < m; ++i) {
            matrix[i][0] = 0;
        }
    }
};

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
void setZeroes(int** matrix, int matrixSize, int* matrixColSize) {
    int m = matrixSize;
    int n = matrixColSize[0];
    int l0 = 0;
    int r0 = 0;
    for (int i = 0; i < m; i++) {
        if (matrix[i][0] == 0) {
            l0 = 1;
            break;
        }
    }
    for (int j = 0; j < n; j++) {
        if (matrix[0][j] == 0) {
            r0 = 1;
            break;
        }
    }
    for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; j++) {
            if (matrix[i][j] == 0) {
                matrix[i][0] = 0;
                matrix[0][j] = 0;
            }
        }
    }
    for (int i = 1; i < m; i++) {
        for (int j = 1; j < n; j++) {
            if (matrix[i][0] == 0 || matrix[0][j] == 0) {
                matrix[i][j] = 0;
            }
        }
    }
    if (l0) {
        for (int i = 0; i < m; i++) {
            matrix[i][0] = 0;
        }
    }
    if (r0) {
        for (int j = 0; j < n; j++) {
            matrix[0][j] = 0;
        }
    }
}

Comments