Matrix Spiral Traversal starting from given Coordinates

Given the order of the matrix N and M, and a source location (X, Y), the task is to find all the coordinates of the matrix in order when visited in clockwise spiral order((i.e. East-> South-> West-> North). Whenever moved outside the matrix, continue the walk outside it to return to the matrix later.

Examples:

Input: N = 1, M = 4, X = 0, Y = 0
Output: {{0, 0}, {0, 1}, {0, 2}, {0, 3}}
Explanation:

Input: N = 5, M = 6, X = 1, Y = 4
Output: {{1, 4}, {1, 5}, {2, 5}, {2, 4}, {2, 3}, {1, 3}, {0, 3}, {0, 4}, {0, 5}, {3, 5}, {3, 4}, {3, 3}, {3, 2}, {2, 2}, {1, 2}, {0, 2}, {4, 5}, {4, 4}, {4, 3}, {4, 2}, {4, 1}, {3, 1}, {2, 1}, {1, 1}, {0, 1}, {4, 0}, {3, 0}, {2, 0}, {1, 0}, {0, 0}}
Explanation:

Approach: The given problem can be solved by traversing the matrix from the position (X, Y) in a clockwise spiral direction, and whenever reached outside the matrix, don’t include the coordinates in the solution but continue traversing outside to reach again inside the matrix. Continue this process until all cells of the matrix are not included in the solution or result.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to turn one unit left
void turn_left(int& r, int& c)
{
    c -= 1;
}

// Function to turn one unit right
void turn_right(int& r, int& c)
{
    c += 1;
}

// Function to turn one unit up
void turn_up(int& r, int& c)
{
    r -= 1;
}

// Function to turn one unit down
void turn_down(int& r, int& c)
{
    r += 1;
}

// For checking whether a cell lies
// outside the matrix or not
bool is_outside(int row, int col,
                int r, int c)
{
    if (r >= row || c >= col
        || r < 0 || c < 0)
        return true;
    return false;
}

// Function to rotate in clockwise manner
void next_turn(char& previous_direction,
               int& r, int& c)
{
    if (previous_direction == 'u') {
        turn_right(r, c);
        previous_direction = 'r';
    }
    else if (previous_direction == 'r') {
        turn_down(r, c);
        previous_direction = 'd';
    }
    else if (previous_direction == 'd') {
        turn_left(r, c);
        previous_direction = 'l';
    }
    else if (previous_direction == 'l') {
        turn_up(r, c);
        previous_direction = 'u';
    }
}

// Function to move in the same direction
// as its prev_direction
void move_in_same_direction(
    char previous_direction,
    int& r, int& c)
{
    if (previous_direction == 'r')
        c++;
    else if (previous_direction == 'u')
        r--;
    else if (previous_direction == 'd')
        r++;
    else if (previous_direction == 'l')
        c--;
}

// Function to find the spiral order of
// of matrix according to given rules
vector<vector<int> > spiralMatrixIII(
    int rows, int cols, int r, int c)
{
    // For storing the co-ordinates
    vector<vector<int> > res;
    char previous_direction = 'r';

    // For keeping track of no of steps
    // to go without turn
    int turning_elements = 2;

    // Count is for counting total cells
    // put in the res
    int count = 0;

    // Current_count is for keeping track
    // of how many cells need to
    // traversed in the same direction
    int current_count = 0;

    // For keeping track the number
    // of turns we have made
    int turn_count = 0;
    int limit = rows * cols;

    while (count < limit) {

        // If the current cell is within
        // the board
        if (!is_outside(rows, cols, r, c)) {
            res.push_back({ r, c });
            count++;
        }
        current_count++;

        // After visiting turning elements
        // of cells we change our turn
        if (current_count == turning_elements) {

            // Changing our direction
            // we have to increase the
            // turn count
            turn_count++;

            // In Every 2nd turn increasing
            // the elements the turn visiting
            if (turn_count == 2)
                turning_elements++;

            // After every 3rd turn reset
            // the turn_count to 1
            else if (turn_count == 3) {
                turn_count = 1;
            }

            // Changing direction to next
            // direction based on the
            // previous direction
            next_turn(previous_direction, r, c);

            // Reset the current_count
            current_count = 1;
        }
        else {
            move_in_same_direction(
                previous_direction, r, c);
        }
    }

    // Return the traversal
    return res;
}

// Driver Code
int main()
{
    int N = 5, M = 6, X = 1, Y = 4;
    auto res = spiralMatrixIII(N, M, X, Y);

    // Display answer
    for (auto it : res) {
        cout << '(' << it[0] << ", "
             << it[1] << ')' << ' ';
    }
    return 0;
}

Java

// Java program for the above approach
import java.io.*;
import java.util.*;
class GFG
{

    // For checking whether a cell lies
    // outside the matrix or not
    static Boolean is_outside(int row, int col, int r,
                              int c)
    {
        if (r >= row || c >= col || r < 0 || c < 0) {
            return true;
        }
        return false;
    }

    // Function to rotate in clockwise manner
    static int[] next_turn(char previous_direction, int r,
                           int c)
    {
        if (previous_direction == 'u') {
            // turn_right
            c += 1;
            previous_direction = 'r';
        }
        else if (previous_direction == 'r') {
            // turn_down
            r += 1;
            previous_direction = 'd';
        }
        else if (previous_direction == 'd') {
            // turn_left
            c -= 1;
            previous_direction = 'l';
        }
        else if (previous_direction == 'l') {
            // turn_up
            r -= 1;
            previous_direction = 'u';
        }
        int[] v = { previous_direction, r, c };
        return v;
    }

    // Function to move in the same direction
    // as its prev_direction
    static int[] move_in_same_direction(
        char previous_direction, int r, int c)
    {
        if (previous_direction == 'r')
            c += 1;
        else if (previous_direction == 'u')
            r -= 1;
        else if (previous_direction == 'd')
            r += 1;
        else if (previous_direction == 'l')
            c -= 1;

        int[] v = { r, c };
        return v;
    }

    // Function to find the spiral order of
    // of matrix according to given rules
    static int[][] spiralMatrixIII(int rows, int cols,
                                   int r, int c)
    {
        char previous_direction = 'r';

        // For keeping track of no of steps
        // to go without turn
        int turning_elements = 2;

        // Count is for counting total cells
        // put in the res
        int count = 0;

        // Current_count is for keeping track
        // of how many cells need to
        // traversed in the same direction
        int current_count = 0;

        // For keeping track the number
        // of turns we have made
        int turn_count = 0;
        int limit = rows * cols;

        // For storing the co-ordinates
        int[][] arr = new int[limit][2];

        while (count < limit) {
            // If the current cell is within
            // the board

            if (is_outside(rows, cols, r, c) == false) {
                arr[count][0] = r;
                arr[count][1] = c;
                count += 1;
            }
            current_count += 1;

            // After visiting turning elements
            // of cells we change our turn
            if (current_count == turning_elements) {

                // Changing our direction
                // we have to increase the
                // turn count
                turn_count += 1;

                // In Every 2nd turn increasing
                // the elements the turn visiting
                if (turn_count == 2)
                    turning_elements += 1;

                // After every 3rd turn reset
                // the turn_count to 1
                else if (turn_count == 3)
                    turn_count = 1;

                // Changing direction to next
                // direction based on the
                // previous direction
                int[] store
                    = next_turn(previous_direction, r, c);

                // converting integer back to Character
                previous_direction = (char)store[0];
                r = store[1];
                c = store[2];
                // Reset the current_count
                current_count = 1;
            }
            else {
                int[] store = move_in_same_direction(
                    previous_direction, r, c);
                r = store[0];
                c = store[1];
            }
            // Return the traversal
        }
        return arr;
    }

    // Driver Code
    public static void main(String[] args)
    {
        int N = 5;
        int M = 6;
        int X = 1;
        int Y = 4;
        int[][] arr = spiralMatrixIII(N, M, X, Y);
        String ans = "";
        int len = arr.length;
        for (int i = 0; i < len; i++) {
            ans += "(" + arr[i][0] + "," + arr[i][1] + ") ";
        }
        System.out.println(ans);
    }
}

// This code is contributed by rj13to.

Python3

# Python program for the above approach

# For checking whether a cell lies
# outside the matrix or not
def is_outside(row, col, r, c):
    if (r >= row or c >= col or r < 0 or c < 0):
        return True
    return False

# Function to rotate in clockwise manner
def next_turn(previous_direction,
              r, c):
    if (previous_direction == 'u'):

        # turn_right
        c += 1
        previous_direction = 'r'
    elif (previous_direction == 'r'):

        # turn_down
        r += 1
        previous_direction = 'd'
    elif (previous_direction == 'd'):

        # turn_left
        c -= 1
        previous_direction = 'l'
    elif (previous_direction == 'l'):

        # turn_up
        r -= 1
        previous_direction = 'u'
    return [previous_direction, r, c]

# Function to move in the same direction
# as its prev_direction
def move_in_same_direction(
        previous_direction, r, c):
    if (previous_direction == 'r'):
        c += 1
    elif (previous_direction == 'u'):
        r -= 1
    elif(previous_direction == 'd'):
        r += 1
    elif(previous_direction == 'l'):
        c -= 1
    return [r, c]

# Function to find the spiral order of
# of matrix according to given rules
def spiralMatrixIII(rows, cols, r, c):
    # For storing the co-ordinates
    res = []
    previous_direction = 'r'

    # For keeping track of no of steps
    # to go without turn
    turning_elements = 2

    # Count is for counting total cells
    # put in the res
    count = 0

    # Current_count is for keeping track
    # of how many cells need to
    # traversed in the same direction
    current_count = 0

    # For keeping track the number
    # of turns we have made
    turn_count = 0
    limit = rows * cols

    while (count < limit):

        # If the current cell is within
        # the board
        if (is_outside(rows, cols, r, c) == False):
            res.append([r, c])
            count += 1

        current_count += 1

        # After visiting turning elements
        # of cells we change our turn
        if (current_count == turning_elements):

            # Changing our direction
            # we have to increase the
            # turn count
            turn_count += 1

            # In Every 2nd turn increasing
            # the elements the turn visiting
            if (turn_count == 2):
                turning_elements += 1

            # After every 3rd turn reset
            # the turn_count to 1
            elif (turn_count == 3):
                turn_count = 1

            # Changing direction to next
            # direction based on the
            # previous direction
            store = next_turn(previous_direction, r, c)
            previous_direction = store[0]
            r = store[1]
            c = store[2]

            # Reset the current_count
            current_count = 1

        else:
            store = move_in_same_direction(
                previous_direction, r, c)
            r = store[0]
            c = store[1]

    # Return the traversal
    return res

# Driver Code
N = 5
M = 6
X = 1
Y = 4
res = spiralMatrixIII(N, M, X, Y)

# Display answer
for vec in res:
    print('(', vec[0], ", ", vec[1], ')', end=" ")

    # This code is contributed by rj13to.

C#

// C# program for the above approach

using System;
using System.Collections.Generic;

public class GFG {

  // For checking whether a cell lies
  // outside the matrix or not
  static Boolean is_outside(int row, int col, int r, int c) {
    if (r >= row || c >= col || r < 0 || c < 0) {
      return true;
    }
    return false;
  }

  // Function to rotate in clockwise manner
  static int[] next_turn(char previous_direction, int r, int c) {
    if (previous_direction == 'u') {
      // turn_right
      c += 1;
      previous_direction = 'r';
    } else if (previous_direction == 'r') {
      // turn_down
      r += 1;
      previous_direction = 'd';
    } else if (previous_direction == 'd') {
      // turn_left
      c -= 1;
      previous_direction = 'l';
    } else if (previous_direction == 'l') {
      // turn_up
      r -= 1;
      previous_direction = 'u';
    }
    int[] v = { previous_direction, r, c };
    return v;
  }

  // Function to move in the same direction
  // as its prev_direction
  static int[] move_in_same_direction(char previous_direction, int r, int c) {
    if (previous_direction == 'r')
      c += 1;
    else if (previous_direction == 'u')
      r -= 1;
    else if (previous_direction == 'd')
      r += 1;
    else if (previous_direction == 'l')
      c -= 1;

    int[] v = { r, c };
    return v;
  }

  // Function to find the spiral order of
  // of matrix according to given rules
  static int[,] spiralMatrixIII(int rows, int cols, int r, int c) {
    char previous_direction = 'r';

    // For keeping track of no of steps
    // to go without turn
    int turning_elements = 2;

    // Count is for counting total cells
    // put in the res
    int count = 0;

    // Current_count is for keeping track
    // of how many cells need to
    // traversed in the same direction
    int current_count = 0;

    // For keeping track the number
    // of turns we have made
    int turn_count = 0;
    int limit = rows * cols;

    // For storing the co-ordinates
    int[,] arr = new int[limit,2];

    while (count < limit) {
      // If the current cell is within
      // the board

      if (is_outside(rows, cols, r, c) == false) {
        arr[count,0] = r;
        arr[count,1] = c;
        count += 1;
      }
      current_count += 1;

      // After visiting turning elements
      // of cells we change our turn
      if (current_count == turning_elements) {

        // Changing our direction
        // we have to increase the
        // turn count
        turn_count += 1;

        // In Every 2nd turn increasing
        // the elements the turn visiting
        if (turn_count == 2)
          turning_elements += 1;

        // After every 3rd turn reset
        // the turn_count to 1
        else if (turn_count == 3)
          turn_count = 1;

        // Changing direction to next
        // direction based on the
        // previous direction
        int[] store = next_turn(previous_direction, r, c);

        // converting integer back to char
        previous_direction = (char) store[0];
        r = store[1];
        c = store[2];
        // Reset the current_count
        current_count = 1;
      } else {
        int[] store = move_in_same_direction(previous_direction, r, c);
        r = store[0];
        c = store[1];
      }
      // Return the traversal
    }
    return arr;
  }

  // Driver Code
  public static void Main(String[] args) {
    int N = 5;
    int M = 6;
    int X = 1;
    int Y = 4;
    int[,] arr = spiralMatrixIII(N, M, X, Y);
    String ans = "";
    int len = arr.GetLength(0);
    for (int i = 0; i < len; i++) {
      ans += "(" + arr[i,0] + "," + arr[i,1] + ") ";
    }
    Console.WriteLine(ans);
  }
}

// This code is contributed by gauravrajput1

Javascript

<script>
// javascript program for the above approach
// For checking whether a cell lies
    // outside the matrix or not
     function is_outside(row , col , r , c) {
        if (r >= row || c >= col || r < 0 || c < 0) {
            return true;
        }
        return false;
    }

    // Function to rotate in clockwise manner
     function next_turn( previous_direction , r , c) {
        if (previous_direction == 'u') {
            // turn_right
            c += 1;
            previous_direction = 'r';
        } else if (previous_direction == 'r') {
            // turn_down
            r += 1;
            previous_direction = 'd';
        } else if (previous_direction == 'd') {
            // turn_left
            c -= 1;
            previous_direction = 'l';
        } else if (previous_direction == 'l') {
            // turn_up
            r -= 1;
            previous_direction = 'u';
        }
        var v = [ previous_direction, r, c ];
        return v;
    }

    // Function to move in the same direction
    // as its prev_direction
     function move_in_same_direction( previous_direction , r , c) {
        if (previous_direction == 'r')
            c += 1;
        else if (previous_direction == 'u')
            r -= 1;
        else if (previous_direction == 'd')
            r += 1;
        else if (previous_direction == 'l')
            c -= 1;

        var v = [ r, c ];
        return v;
    }

    // Function to find the spiral order of
    // of matrix according to given rules
     function spiralMatrixIII(rows , cols , r , c) {
        var previous_direction = 'r';

        // For keeping track of no of steps
        // to go without turn
        var turning_elements = 2;

        // Count is for counting total cells
        // put in the res
        var count = 0;

        // Current_count is for keeping track
        // of how many cells need to
        // traversed in the same direction
        var current_count = 0;

        // For keeping track the number
        // of turns we have made
        var turn_count = 0;
        var limit = rows * cols;

        // For storing the co-ordinates
        var arr = Array(limit).fill().map(()=>Array(2).fill(0));

        while (count < limit) {
            // If the current cell is within
            // the board

            if (is_outside(rows, cols, r, c) == false) {
                arr[count][0] = r;
                arr[count][1] = c;
                count += 1;
            }
            current_count += 1;

            // After visiting turning elements
            // of cells we change our turn
            if (current_count == turning_elements) {

                // Changing our direction
                // we have to increase the
                // turn count
                turn_count += 1;

                // In Every 2nd turn increasing
                // the elements the turn visiting
                if (turn_count == 2)
                    turning_elements += 1;

                // After every 3rd turn reset
                // the turn_count to 1
                else if (turn_count == 3)
                    turn_count = 1;

                // Changing direction to next
                // direction based on the
                // previous direction
                var store = next_turn(previous_direction, r, c);

                // converting integer back to Character
                previous_direction =  store[0];
                r = store[1];
                c = store[2];
                // Reset the current_count
                current_count = 1;
            } else {
                var store = move_in_same_direction(previous_direction, r, c);
                r = store[0];
                c = store[1];
            }
            // Return the traversal
        }
        return arr;
    }

    // Driver Code

        var N = 5;
        var M = 6;
        var X = 1;
        var Y = 4;
        var arr = spiralMatrixIII(N, M, X, Y);
        var ans = "";
        var len = arr.length;
        for (i = 0; i < len; i++) {
            ans += "(" + arr[i][0] + "," + arr[i][1] + ") ";
        }
        document.write(ans);

// This code is contributed by gauravrajput1
</script>

Output:
(1, 4) (1, 5) (2, 5) (2, 4) (2, 3) (1, 3) (0, 3) (0, 4) (0, 5) (3, 5) (3, 4) (3, 3) (3, 2) (2, 2) (1, 2) (0, 2) (4, 5) (4, 4) (4, 3) (4, 2) (4, 1) (3, 1) (2, 1) (1, 1) (0, 1) (4, 0) (3, 0) (2, 0) (1, 0) (0, 0) 

Time Complexity: O(N²)
Auxiliary Space: O(1)