Breadth First Traversal ( BFS ) on a 2D array
Given a matrix of size M x N consisting of integers, the task is to print the matrix elements using Breadth-First Search traversal.
Examples:
Input: grid[][] = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16}}
Output: 1 2 5 3 6 9 4 7 10 13 8 11 14 12 15 16
Input: grid[][] = {{-1, 0, 0, 1}, {-1, -1, -2, -1}, {-1, -1, -1, -1}, {0, 0, 0, 0}}
Output: -1 0 -1 0 -1 -1 1 -2 -1 0 -1 -1 0 -1 0 0
Approach: Follow the steps below to solve the problem:
- Initialize the direction vectors dRow[] = {-1, 0, 1, 0} and dCol[] = {0, 1, 0, -1} and a queue of pairs to store the indices of matrix cells.
- Start BFS traversal from the first cell, i.e. (0, 0), and enqueue the index of this cell into the queue.
- Initialize a boolean array to mark the visited cells of the matrix. Mark the cell (0, 0) as visited.
- 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 are unvisited or not.
- Iterate while the queue is not empty and perform the following operations:
- Dequeue the cell present at the front of the queue and print it.
- Move to its adjacent cells that are not visited.
- Mark them visited and enqueue them into the queue.
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++
#include <bits/stdc++.h>
using namespace std;
#define ROW 4
#define COL 4
int dRow[] = { -1, 0, 1, 0 };
int dCol[] = { 0, 1, 0, -1 };
bool isValid( bool vis[][COL],
int row, int col)
{
if (row < 0 || col < 0
|| row >= ROW || col >= COL)
return false ;
if (vis[row][col])
return false ;
return true ;
}
void BFS( int grid[][COL], bool vis[][COL],
int row, int col)
{
queue<pair< int , int > > q;
q.push({ row, col });
vis[row][col] = true ;
while (!q.empty()) {
pair< int , int > cell = q.front();
int x = cell.first;
int y = cell.second;
cout << grid[x][y] << " " ;
q.pop();
for ( int i = 0; i < 4; i++) {
int adjx = x + dRow[i];
int adjy = y + dCol[i];
if (isValid(vis, adjx, adjy)) {
q.push({ adjx, adjy });
vis[adjx][adjy] = true ;
}
}
}
}
int main()
{
int grid[ROW][COL] = { { 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 },
{ 13, 14, 15, 16 } };
bool vis[ROW][COL];
memset (vis, false , sizeof vis);
BFS(grid, vis, 0, 0);
return 0;
}
|
Java
import java.util.*;
class GFG{
static class pair
{
int first, second;
public pair( int first, int second)
{
this .first = first;
this .second = second;
}
}
static final int ROW = 4 ;
static final int COL = 4 ;
static int dRow[] = { - 1 , 0 , 1 , 0 };
static int dCol[] = { 0 , 1 , 0 , - 1 };
static boolean isValid( boolean vis[][],
int row, int col)
{
if (row < 0 || col < 0 ||
row >= ROW || col >= COL)
return false ;
if (vis[row][col])
return false ;
return true ;
}
static void BFS( int grid[][], boolean vis[][],
int row, int col)
{
Queue<pair > q = new LinkedList<>();
q.add( new pair(row, col));
vis[row][col] = true ;
while (!q.isEmpty())
{
pair cell = q.peek();
int x = cell.first;
int y = cell.second;
System.out.print(grid[x][y] + " " );
q.remove();
for ( int i = 0 ; i < 4 ; i++)
{
int adjx = x + dRow[i];
int adjy = y + dCol[i];
if (isValid(vis, adjx, adjy))
{
q.add( new pair(adjx, adjy));
vis[adjx][adjy] = true ;
}
}
}
}
public static void main(String[] args)
{
int grid[][] = { { 1 , 2 , 3 , 4 },
{ 5 , 6 , 7 , 8 },
{ 9 , 10 , 11 , 12 },
{ 13 , 14 , 15 , 16 } };
boolean [][]vis = new boolean [ROW][COL];
BFS(grid, vis, 0 , 0 );
}
}
|
Python3
from collections import deque as queue
dRow = [ - 1 , 0 , 1 , 0 ]
dCol = [ 0 , 1 , 0 , - 1 ]
def isValid(vis, row, col):
if (row < 0 or col < 0 or row > = 4 or col > = 4 ):
return False
if (vis[row][col]):
return False
return True
def BFS(grid, vis, row, col):
q = queue()
q.append(( row, col ))
vis[row][col] = True
while ( len (q) > 0 ):
cell = q.popleft()
x = cell[ 0 ]
y = cell[ 1 ]
print (grid[x][y], end = " " )
for i in range ( 4 ):
adjx = x + dRow[i]
adjy = y + dCol[i]
if (isValid(vis, adjx, adjy)):
q.append((adjx, adjy))
vis[adjx][adjy] = True
if __name__ = = '__main__' :
grid = [ [ 1 , 2 , 3 , 4 ],
[ 5 , 6 , 7 , 8 ],
[ 9 , 10 , 11 , 12 ],
[ 13 , 14 , 15 , 16 ] ]
vis = [[ False for i in range ( 4 )] for i in range ( 4 )]
BFS(grid, vis, 0 , 0 )
|
C#
using System;
using System.Collections.Generic;
public class GFG
{
class pair
{
public int first, second;
public pair( int first, int second)
{
this .first = first;
this .second = second;
}
}
static readonly int ROW = 4;
static readonly int COL = 4;
static int []dRow = { -1, 0, 1, 0 };
static int []dCol = { 0, 1, 0, -1 };
static bool isValid( bool [,]vis,
int row, int col)
{
if (row < 0 || col < 0 ||
row >= ROW || col >= COL)
return false ;
if (vis[row,col])
return false ;
return true ;
}
static void BFS( int [,]grid, bool [,]vis,
int row, int col)
{
Queue<pair> q = new Queue<pair>();
q.Enqueue( new pair(row, col));
vis[row,col] = true ;
while (q.Count!=0)
{
pair cell = q.Peek();
int x = cell.first;
int y = cell.second;
Console.Write(grid[x,y] + " " );
q.Dequeue();
for ( int i = 0; i < 4; i++)
{
int adjx = x + dRow[i];
int adjy = y + dCol[i];
if (isValid(vis, adjx, adjy))
{
q.Enqueue( new pair(adjx, adjy));
vis[adjx,adjy] = true ;
}
}
}
}
public static void Main(String[] args)
{
int [,]grid = { { 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 },
{ 13, 14, 15, 16 } };
bool [,]vis = new bool [ROW,COL];
BFS(grid, vis, 0, 0);
}
}
|
Javascript
<script>
var ROW = 4;
var COL = 4;
var dRow = [-1, 0, 1, 0 ];
var dCol = [0, 1, 0, -1 ];
function isValid(vis, row, col)
{
if (row < 0 || col < 0
|| row >= ROW || col >= COL)
return false ;
if (vis[row][col])
return false ;
return true ;
}
function BFS( grid, vis,row, col)
{
var q = [];
q.push([row, col ]);
vis[row][col] = true ;
while (q.length!=0) {
var cell = q[0];
var x = cell[0];
var y = cell[1];
document.write( grid[x][y] + " " );
q.shift();
for ( var i = 0; i < 4; i++) {
var adjx = x + dRow[i];
var adjy = y + dCol[i];
if (isValid(vis, adjx, adjy)) {
q.push([adjx, adjy ]);
vis[adjx][adjy] = true ;
}
}
}
}
var grid = [[1, 2, 3, 4 ],
[5, 6, 7, 8 ],
[9, 10, 11, 12 ],
[13, 14, 15, 16 ] ];
var vis = Array.from(Array(ROW), ()=> Array(COL).fill( false ));
BFS(grid, vis, 0, 0);
</script>
|
Output:
1 2 5 3 6 9 4 7 10 13 8 11 14 12 15 16
Time Complexity: O(N * M)
Auxiliary Space: O(N * M)
Last Updated :
31 May, 2021
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