Depth First Traversal ( DFS ) on a 2D array
Given a 2D array grid[][] of dimension N * M, the task is to perform the Depth – First Search traversal on the given 2D array.
Examples:
Input: grid[][] = {{-1, 2, 3}, {0, 9, 8}, {1, 0, 1}}
Output: -1 2 3 8 1 0 9 0 1
Explanation: The sequence of traversal of matrix elements using DFS is -1, 2, 3, 8, 1, 0, 9, 0, 1.
Input: grid[][] = {{1, 2, 3}, {5, 6, 7}, {9, 10, 11}}
Output: 1 2 3 7 11 10 6 5 9
Approach: The idea is to use Stack Data Structure to perform DFS Traversal on the 2D array. Follow the steps below to solve the given problem:
- Initialize a stack, say S, with the starting cell coordinates as (0, 0).
- Initialize an auxiliary boolean 2D array of dimension N * M with all values as false, which is used to mark the visited cells.
- Declare a function isValid() to check if the cell coordinates are valid or not, i.e lies within the boundaries of the given matrix and is unvisited or not.
- Iterate while the stack is not empty and perform the following steps:
- Pop the cell present at the top of the stack and print the element at that cell.
- Push the cell adjacent to the above-popped cells into the stack, if they are valid by checking using isValid() function.
Note: Direction vectors are used to traverse the adjacent cells of a given cell in a given order. For example, (x, y) is a cell whose adjacent cells (x – 1, y), (x, y + 1), (x + 1, y), (x, y – 1) need to be traversed, then it can be done using the direction vectors (-1, 0), (0, 1), (1, 0), (0, -1) in the up, left, down and right order.
Below is the implementation of the above approach:
C++
// C++ program of the above approach#include <bits/stdc++.h>using namespace std;#define ROW 3#define COL 3// Initialize direction vectorsint dRow[] = { 0, 1, 0, -1 };int dCol[] = { -1, 0, 1, 0 };// Function to check if mat[row][col]// is unvisited and lies within the// boundary of the given matrixbool isValid(bool vis[][COL], int row, int col){ // If cell is out of bounds if (row < 0 || col < 0 || row >= ROW || col >= COL) return false; // If the cell is already visited if (vis[row][col]) return false; // Otherwise, it can be visited return true;}// Function to perform DFS// Traversal on the matrix grid[]void DFS(int row, int col, int grid[][COL], bool vis[][COL]){ // Initialize a stack of pairs and // push the starting cell into it stack<pair<int, int> > st; st.push({ row, col }); // Iterate until the // stack is not empty while (!st.empty()) { // Pop the top pair pair<int, int> curr = st.top(); st.pop(); int row = curr.first; int col = curr.second; // Check if the current popped // cell is a valid cell or not if (!isValid(vis, row, col)) continue; // Mark the current // cell as visited vis[row][col] = true; // Print the element at // the current top cell cout << grid[row][col] << " "; // Push all the adjacent cells for (int i = 0; i < 4; i++) { int adjx = row + dRow[i]; int adjy = col + dCol[i]; st.push({ adjx, adjy }); } }}// Driver Codeint main(){ int grid[ROW][COL] = { { -1, 2, 3 }, { 0, 9, 8 }, { 1, 0, 1 } }; // Stores whether the current // cell is visited or not bool vis[ROW][COL]; memset(vis, false, sizeof vis); // Function call DFS(0, 0, grid, vis); return 0;} |
Java
// Java program of the above approachimport java.util.Stack;class GFG{ static int ROW = 3;static int COL = 3;// Initialize direction vectorsstatic int dRow[] = { 0, 1, 0, -1 };static int dCol[] = { -1, 0, 1, 0 };static class pair{ public int first; public int second; public pair(int first, int second) { this.first = first; this.second = second; }}static Boolean isValid(Boolean vis[][], int row, int col){ // If cell is out of bounds if (row < 0 || col < 0 || row >= ROW || col >= COL) return false; // If the cell is already visited if (vis[row][col]) return false; // Otherwise, it can be visited return true;}// Function to perform DFS// Traversal on the matrix grid[]static void DFS(int row, int col, int grid[][], Boolean vis[][]){ // Initialize a stack of pairs and // push the starting cell into it Stack<pair> st = new Stack<pair>(); st.push(new pair(row, col)); // Iterate until the // stack is not empty while (!st.empty()) { // Pop the top pair pair curr = st.pop(); row = curr.first; col = curr.second; // Check if the current popped // cell is a valid cell or not if (!isValid(vis, row, col)) continue; // Mark the current // cell as visited vis[row][col] = true; // Print the element at // the current top cell System.out.print(grid[row][col] + " "); // Push all the adjacent cells for(int i = 0; i < 4; i++) { int adjx = row + dRow[i]; int adjy = col + dCol[i]; st.push(new pair(adjx, adjy)); } }}// Driver codepublic static void main(String[] args){ int grid[][] = { { -1, 2, 3 }, { 0, 9, 8 }, { 1, 0, 1 } }; Boolean vis[][] = new Boolean[ROW][COL]; for(int i = 0; i < ROW; i++) { for(int j = 0; j < COL; j++) { vis[i][j] = false; } } // Function call DFS(0, 0, grid, vis);}}// This code is contributed by abhinavjain194 |
Python3
# Python 3 program of the above approachROW = 3COL = 3# Initialize direction vectorsdRow = [0, 1, 0, -1]dCol = [-1, 0, 1, 0]vis = [[False for i in range(3)] for j in range(3)]# Function to check if mat[row][col]# is unvisited and lies within the# boundary of the given matrixdef isValid(row, col): global ROW global COL global vis # If cell is out of bounds if (row < 0 or col < 0 or row >= ROW or col >= COL): return False # If the cell is already visited if (vis[row][col]): return False # Otherwise, it can be visited return True# Function to perform DFS# Traversal on the matrix grid[]def DFS(row, col, grid): global dRow global dCol global vis # Initialize a stack of pairs and # push the starting cell into it st = [] st.append([row, col]) # Iterate until the # stack is not empty while (len(st) > 0): # Pop the top pair curr = st[len(st) - 1] st.remove(st[len(st) - 1]) row = curr[0] col = curr[1] # Check if the current popped # cell is a valid cell or not if (isValid(row, col) == False): continue # Mark the current # cell as visited vis[row][col] = True # Print the element at # the current top cell print(grid[row][col], end = " ") # Push all the adjacent cells for i in range(4): adjx = row + dRow[i] adjy = col + dCol[i] st.append([adjx, adjy])# Driver Codeif __name__ == '__main__': grid = [[-1, 2, 3], [0, 9, 8], [1, 0, 1]] # Function call DFS(0, 0, grid) # This code is contributed by SURENDRA_GANGWAR. |
C#
// C# program of the above approachusing System;using System.Collections;class GFG{ static int ROW = 3;static int COL = 3; // Initialize direction vectorsstatic int[] dRow = { 0, 1, 0, -1 };static int[] dCol = { -1, 0, 1, 0 };static bool isValid(bool[,] vis, int row, int col){ // If cell is out of bounds if (row < 0 || col < 0 || row >= ROW || col >= COL) return false; // If the cell is already visited if (vis[row,col]) return false; // Otherwise, it can be visited return true;} // Function to perform DFS// Traversal on the matrix grid[]static void DFS(int row, int col, int[,] grid, bool[,] vis){ // Initialize a stack of pairs and // push the starting cell into it Stack st = new Stack(); st.Push(new Tuple<int, int>(row, col)); // Iterate until the // stack is not empty while (st.Count > 0) { // Pop the top pair Tuple<int, int> curr = (Tuple<int, int>)st.Peek(); st.Pop(); row = curr.Item1; col = curr.Item2; // Check if the current popped // cell is a valid cell or not if (!isValid(vis, row, col)) continue; // Mark the current // cell as visited vis[row, col] = true; // Print the element at // the current top cell Console.Write(grid[row, col] + " "); // Push all the adjacent cells for(int i = 0; i < 4; i++) { int adjx = row + dRow[i]; int adjy = col + dCol[i]; st.Push(new Tuple<int, int>(adjx, adjy)); } }}// Driver codestatic void Main(){ int[,] grid = { { -1, 2, 3 }, { 0, 9, 8 }, { 1, 0, 1 } }; bool[,] vis = new bool[ROW, COL]; for(int i = 0; i < ROW; i++) { for(int j = 0; j < COL; j++) { vis[i, j] = false; } } // Function call DFS(0, 0, grid, vis);}}// This code is contributed by mukesh07 |
Javascript
<script>// Javascript program of the above approachvar ROW = 3;var COL = 3// Initialize direction vectorsvar dRow = [0, 1, 0, -1];var dCol = [ -1, 0, 1, 0];// Function to check if mat[row][col]// is unvisited and lies within the// boundary of the given matrixfunction isValid(vis, row, col){ // If cell is out of bounds if (row < 0 || col < 0 || row >= ROW || col >= COL) return false; // If the cell is already visited if (vis[row][col]) return false; // Otherwise, it can be visited return true;}// Function to perform DFS// Traversal on the matrix grid[]function DFS(row, col,grid, vis){ // Initialize a stack of pairs and // push the starting cell into it var st = []; st.push([ row, col ]); // Iterate until the // stack is not empty while (st.length!=0) { // Pop the top pair var curr = st[st.length-1]; st.pop(); var row = curr[0]; var col = curr[1]; // Check if the current popped // cell is a valid cell or not if (!isValid(vis, row, col)) continue; // Mark the current // cell as visited vis[row][col] = true; // Print the element at // the current top cell document.write( grid[row][col] + " "); // Push all the adjacent cells for (var i = 0; i < 4; i++) { var adjx = row + dRow[i]; var adjy = col + dCol[i]; st.push([ adjx, adjy ]); } }}// Driver Codevar grid = [ [ -1, 2, 3 ], [ 0, 9, 8 ], [ 1, 0, 1 ] ];// Stores whether the current// cell is visited or notvar vis = Array.from(Array(ROW), ()=> Array(COL).fill(false));// Function callDFS(0, 0, grid, vis);</script> |
Output:
-1 2 3 8 1 0 9 0 1
Time Complexity: O(N * M)
Auxiliary Space: O(N * M )
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