Print matrix in spiral order

Given an M × N integer matrix, print it in spiral order.

For example,

Input:

[  1   2   3   4  5 ]
[ 16  17  18  19  6 ]
[ 15  24  25  20  7 ]
[ 14  23  22  21  8 ]
[ 13  12  11  10  9 ]

Output:

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

Practice this problem

The idea is to read elements from the given matrix and print the matrix in spiral order. Four loops are used to maintain the spiral order, each for the top, right, bottom, and left corner of the matrix.

Following is the C++, Java, and Python implementation of the idea:

C++

#include <iostream>

#include <vector>

using namespace std;

void printSpiralOrder(vector<vector<int>> const &mat)

{

// base case

if (mat.size() == 0) {

return;

}

int top = 0, bottom = mat.size() - 1;

int left = 0, right = mat[0].size() - 1;

while (1)

{

if (left > right) {

break;

}

// print top row

for (int i = left; i <= right; i++) {

cout << mat[top][i] << " ";

}

top++;

if (top > bottom) {

break;

}

// print right column

for (int i = top; i <= bottom; i++) {

cout << mat[i][right] << " ";

}

right--;

if (left > right) {

break;

}

// print bottom row

for (int i = right; i >= left; i--) {

cout << mat[bottom][i] << " ";

}

bottom--;

if (top > bottom) {

break;

}

// print left column

for (int i = bottom; i >= top; i--) {

cout << mat[i][left] << " ";

}

left++;

}

int main()

{

vector<vector<int>> mat =

{

{ 1, 2, 3, 4, 5},

{16, 17, 18, 19, 6},

{15, 24, 25, 20, 7},

{14, 23, 22, 21, 8},

{13, 12, 11, 10, 9}

};

printSpiralOrder(mat);

return 0;

}

Download Run Code

Output:

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

Java

class Main

{

private static void printSpiralOrder(int[][] mat)

{

// base case

if (mat == null || mat.length == 0) {

return;

}

int top = 0, bottom = mat.length - 1;

int left = 0, right = mat[0].length - 1;

while (true)

{

if (left > right) {

break;

}

// print top row

for (int i = left; i <= right; i++) {

System.out.print(mat[top][i] + " ");

}

top++;

if (top > bottom) {

break;

}

// print right column

for (int i = top; i <= bottom; i++) {

System.out.print(mat[i][right] + " ");

}

right--;

if (left > right) {

break;

}

// print bottom row

for (int i = right; i >= left; i--) {

System.out.print(mat[bottom][i] + " ");

}

bottom--;

if (top > bottom) {

break;

}

// print left column

for (int i = bottom; i >= top; i--) {

System.out.print(mat[i][left] + " ");

}

left++;

}

public static void main(String[] args)

{

int[][] mat =

{

{ 1, 2, 3, 4, 5},

{16, 17, 18, 19, 6},

{15, 24, 25, 20, 7},

{14, 23, 22, 21, 8},

{13, 12, 11, 10, 9}

};

printSpiralOrder(mat);

}

Download Run Code

Output:

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

Python

def printSpiralOrder(mat):

# base case

if not mat or not len(mat):

return

top = left = 0

bottom = len(mat) - 1

right = len(mat[0]) - 1

while True:

if left > right:

break

# print top row

for i in range(left, right + 1):

print(mat[top][i], end=' ')

top = top + 1

if top > bottom:

break

# print right column

for i in range(top, bottom + 1):

print(mat[i][right], end=' ')

right = right - 1

if left > right:

break

# print bottom row

for i in range(right, left - 1, -1):

print(mat[bottom][i], end=' ')

bottom = bottom - 1

if top > bottom:

break

# print left column

for i in range(bottom, top - 1, -1):

print(mat[i][left], end=' ')

left = left + 1

if __name__ == '__main__':

mat = [

[1, 2, 3, 4, 5],

[16, 17, 18, 19, 6],

[15, 24, 25, 20, 7],

[14, 23, 22, 21, 8],

[13, 12, 11, 10, 9]

]

printSpiralOrder(mat)

Download Run Code

Output:

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

We can also achieve this easily with the help of recursion.

C++

#include <iostream>

#include <vector>

using namespace std;

void printSpiral(vector<vector<int>> const &mat, int top, int bottom, int left, int right)

{

// base case

if (mat.size() == 0 || left > right) {

return;

}

// print top row

for (int i = left; i <= right; i++) {

cout << mat[top][i] << " ";

}

top++;

if (top > bottom) {

return;

}

// print right column

for (int i = top; i <= bottom; i++) {

cout << mat[i][right] << " ";

}

right--;

if (left > right) {

return;

}

// print bottom row

for (int i = right; i >= left; i--) {

cout << mat[bottom][i] << " ";

}

bottom--;

if (top > bottom) {

return;

}

// print left column

for (int i = bottom; i >= top; i--) {

cout << mat[i][left] << " ";

}

left++;

printSpiral(mat, top, bottom, left, right);

}

int main()

{

vector<vector<int>> mat =

{

{ 1, 2, 3, 4, 5},

{16, 17, 18, 19, 6},

{15, 24, 25, 20, 7},

{14, 23, 22, 21, 8},

{13, 12, 11, 10, 9}

};

int top = 0, bottom = mat.size() - 1;

int left = 0, right = mat[0].size() - 1;

printSpiral(mat, top, bottom, left, right);

return 0;

}

Download Run Code

Output:

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

Java

class Main

{

private static void printSpiral(int mat[][], int top, int bottom,

int left, int right)

{

// base case

if (mat == null || mat.length == 0 || left > right) {

return;

}

// print top row

for (int i = left; i <= right; i++) {

System.out.print(mat[top][i] + " ");

}

top++;

if (top > bottom) {

return;

}

// print right column

for (int i = top; i <= bottom; i++) {

System.out.print(mat[i][right] + " ");

}

right--;

if (left > right) {

return;

}

// print bottom row

for (int i = right; i >= left; i--) {

System.out.print(mat[bottom][i] + " ");

}

bottom--;

if (top > bottom) {

return;

}

// print left column

for (int i = bottom; i >= top; i--) {

System.out.print(mat[i][left] + " ");

}

left++;

printSpiral(mat, top, bottom, left, right);

}

public static void main(String[] args)

{

int[][] mat =

{

{ 1, 2, 3, 4, 5},

{16, 17, 18, 19, 6},

{15, 24, 25, 20, 7},

{14, 23, 22, 21, 8},

{13, 12, 11, 10, 9}

};

int top = 0, bottom = mat.length - 1;

int left = 0, right = mat[0].length - 1;

printSpiral(mat, top, bottom, left, right);

}

Download Run Code

Output:

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

Python

def printSpiral(mat, top, bottom, left, right):

# base case

if not mat or not len(mat) or left > right:

return

# print top row

for i in range(left, right + 1):

print(mat[top][i], end=' ')

top = top + 1

if top > bottom:

return

# print right column

for i in range(top, bottom + 1):

print(mat[i][right], end=' ')

right = right - 1

if left > right:

return

# print bottom row

for i in range(right, left - 1, -1):

print(mat[bottom][i], end=' ')

bottom = bottom - 1

if top > bottom:

return

# print left column

for i in range(bottom, top - 1, -1):

print(mat[i][left], end=' ')

left = left + 1

printSpiral(mat, top, bottom, left, right)

if __name__ == '__main__':

mat = [

[1, 2, 3, 4, 5],

[16, 17, 18, 19, 6],

[15, 24, 25, 20, 7],

[14, 23, 22, 21, 8],

[13, 12, 11, 10, 9]

]

top = 0

bottom = len(mat) - 1

left = 0

right = len(mat[0]) - 1

printSpiral(mat, top, bottom, left, right)

Download Run Code

Output:

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

The time complexity of the proposed solution is O(M × N) for an M × N matrix. The auxiliary space required by the program is O(M × N) for recursion (call stack).

Print matrix in spiral order

C++

Java

Python

C++

Java

Python

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