Minimum distance to the end of a grid from source
Given a binary grid of order r * c and an initial position. The task is to find the minimum distance from the source to get to the end of the grid (first row, last row, first column or last column). A move can be made to a cell grid[i][j] only if grid[i][j] = 0 and only left, right, up and down movements are permitted. If no valid path exists then print -1.
Examples:
Input: i = 1, j = 1, grid[][] = { {1, 0, 1}, {0, 0, 0}, {1, 1, 1}}
Output: 1Input: i = 0, j = 0, grid[][] = { {0, 1}, {1, 1}}
Output: 0
Approach:
- If source is already the first/last row/column then print 0.
- Start traversing the grid starting with source using BFS as :
- Insert cell position in queue.
- Pop element from queue and mark it visited.
- For each valid move adjacent to popped one, insert the cell position into queue.
- On each move, update the minimum distance of the cell from initial position.
- After the completion of the BFS, find the minimum distance from source to every cell in the first row, last row, first column and last column.
- Print the minimum among these in the end.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; #define row 5 #define col 5 // Global variables for grid, minDistance and visited array int minDistance[row + 1][col + 1], visited[row + 1][col + 1]; // Queue for BFS queue<pair< int , int > > que; // Function to find whether the move is valid or not bool isValid( int grid[][col], int i, int j) { if (i < 0 || j < 0 || j >= col || i >= row || grid[i][j] || visited[i][j]) return false ; return true ; } // Function to return the minimum distance // from source to the end of the grid int findMinPathminDistance( int grid[][col], int sourceRow, int sourceCol) { // If source is one of the destinations if (sourceCol == 0 || sourceCol == col - 1 || sourceRow == 0 || sourceRow == row - 1) return 0; // Set minimum value int minFromSource = row * col; // Precalculate minDistance of each grid with R * C for ( int i = 0; i < row; i++) for ( int j = 0; j < col; j++) minDistance[i][j] = row * col; // Insert source position in queue que.push(make_pair(sourceRow, sourceCol)); // Update minimum distance to visit source minDistance[sourceRow][sourceCol] = 0; // Set source to visited visited[sourceRow][sourceCol] = 1; // BFS approach for calculating the minDistance // of each cell from source while (!que.empty()) { // Iterate over all four cells adjacent // to current cell pair< int , int > cell = que.front(); // Initialize position of current cell int cellRow = cell.first; int cellCol = cell.second; // Cell below the current cell if (isValid(grid, cellRow + 1, cellCol)) { // Push new cell to the queue que.push(make_pair(cellRow + 1, cellCol)); // Update one of its neighbor's distance minDistance[cellRow + 1][cellCol] = min(minDistance[cellRow + 1][cellCol], minDistance[cellRow][cellCol] + 1); visited[cellRow + 1][cellCol] = 1; } // Above the current cell if (isValid(grid, cellRow - 1, cellCol)) { que.push(make_pair(cellRow - 1, cellCol)); minDistance[cellRow - 1][cellCol] = min(minDistance[cellRow - 1][cellCol], minDistance[cellRow][cellCol] + 1); visited[cellRow - 1][cellCol] = 1; } // Right cell if (isValid(grid, cellRow, cellCol + 1)) { que.push(make_pair(cellRow, cellCol + 1)); minDistance[cellRow][cellCol + 1] = min(minDistance[cellRow][cellCol + 1], minDistance[cellRow][cellCol] + 1); visited[cellRow][cellCol + 1] = 1; } // Left cell if (isValid(grid, cellRow, cellCol - 1)) { que.push(make_pair(cellRow, cellCol - 1)); minDistance[cellRow][cellCol - 1] = min(minDistance[cellRow][cellCol - 1], minDistance[cellRow][cellCol] + 1); visited[cellRow][cellCol - 1] = 1; } // Pop the visited cell que.pop(); } int i; // Minimum distance in the first row for (i = 0; i < col; i++) minFromSource = min(minFromSource, minDistance[0][i]); // Minimum distance in the last row for (i = 0; i < col; i++) minFromSource = min(minFromSource, minDistance[row - 1][i]); // Minimum distance in the first column for (i = 0; i < row; i++) minFromSource = min(minFromSource, minDistance[i][0]); // Minimum distance in the last column for (i = 0; i < row; i++) minFromSource = min(minFromSource, minDistance[i][col - 1]); // If no path exists if (minFromSource == row * col) return -1; // Return the minimum distance return minFromSource; } // Driver code int main() { int sourceRow = 3, sourceCol = 3; int grid[row][col] = { 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0 }; cout << findMinPathminDistance(grid, sourceRow, sourceCol); return 0; } |
Java
// Java implementation of the approach import java.util.*; class GFG { // Pair class static class Pair { int first,second; Pair( int a, int b) { first = a; second = b; } } static int row = 5 ; static int col = 5 ; // Global variables for grid, minDistance and visited array static int minDistance[][] = new int [row + 1 ][col + 1 ], visited[][] = new int [row + 1 ][col + 1 ]; // Queue for BFS static Queue<Pair > que= new LinkedList<>(); // Function to find whether the move is valid or not static boolean isValid( int grid[][], int i, int j) { if (i < 0 || j < 0 || j >= col || i >= row || grid[i][j] != 0 || visited[i][j] != 0 ) return false ; return true ; } // Function to return the minimum distance // from source to the end of the grid static int findMinPathminDistance( int grid[][], int sourceRow, int sourceCol) { // If source is one of the destinations if (sourceCol == 0 || sourceCol == col - 1 || sourceRow == 0 || sourceRow == row - 1 ) return 0 ; // Set minimum value int minFromSource = row * col; // Precalculate minDistance of each grid with R * C for ( int i = 0 ; i < row; i++) for ( int j = 0 ; j < col; j++) minDistance[i][j] = row * col; // Insert source position in queue que.add( new Pair(sourceRow, sourceCol)); // Update minimum distance to visit source minDistance[sourceRow][sourceCol] = 0 ; // Set source to visited visited[sourceRow][sourceCol] = 1 ; // BFS approach for calculating the minDistance // of each cell from source while (que.size() > 0 ) { // Iterate over all four cells adjacent // to current cell Pair cell = que.peek(); // Initialize position of current cell int cellRow = cell.first; int cellCol = cell.second; // Cell below the current cell if (isValid(grid, cellRow + 1 , cellCol)) { // add new cell to the queue que.add( new Pair(cellRow + 1 , cellCol)); // Update one of its neighbor's distance minDistance[cellRow + 1 ][cellCol] = Math.min(minDistance[cellRow + 1 ][cellCol], minDistance[cellRow][cellCol] + 1 ); visited[cellRow + 1 ][cellCol] = 1 ; } // Above the current cell if (isValid(grid, cellRow - 1 , cellCol)) { que.add( new Pair(cellRow - 1 , cellCol)); minDistance[cellRow - 1 ][cellCol] = Math.min(minDistance[cellRow - 1 ][cellCol], minDistance[cellRow][cellCol] + 1 ); visited[cellRow - 1 ][cellCol] = 1 ; } // Right cell if (isValid(grid, cellRow, cellCol + 1 )) { que.add( new Pair(cellRow, cellCol + 1 )); minDistance[cellRow][cellCol + 1 ] = Math.min(minDistance[cellRow][cellCol + 1 ], minDistance[cellRow][cellCol] + 1 ); visited[cellRow][cellCol + 1 ] = 1 ; } // Left cell if (isValid(grid, cellRow, cellCol - 1 )) { que.add( new Pair(cellRow, cellCol - 1 )); minDistance[cellRow][cellCol - 1 ] = Math.min(minDistance[cellRow][cellCol - 1 ], minDistance[cellRow][cellCol] + 1 ); visited[cellRow][cellCol - 1 ] = 1 ; } // Pop the visited cell que.remove(); } int i; // Minimum distance in the first row for (i = 0 ; i < col; i++) minFromSource = Math.min(minFromSource, minDistance[ 0 ][i]); // Minimum distance in the last row for (i = 0 ; i < col; i++) minFromSource = Math.min(minFromSource, minDistance[row - 1 ][i]); // Minimum distance in the first column for (i = 0 ; i < row; i++) minFromSource = Math.min(minFromSource, minDistance[i][ 0 ]); // Minimum distance in the last column for (i = 0 ; i < row; i++) minFromSource = Math.min(minFromSource, minDistance[i][col - 1 ]); // If no path exists if (minFromSource == row * col) return - 1 ; // Return the minimum distance return minFromSource; } // Driver code public static void main(String args[]) { int sourceRow = 3 , sourceCol = 3 ; int grid[][] = { { 1 , 1 , 1 , 1 , 0 }, { 0 , 0 , 1 , 0 , 1 }, { 0 , 0 , 1 , 0 , 1 }, { 1 , 0 , 0 , 0 , 1 }, { 1 , 1 , 0 , 1 , 0 }}; System.out.println(findMinPathminDistance(grid, sourceRow, sourceCol)); } } // This code is contributed by Arnab Kundu |
Python3
# Python3 implementation of the approach from collections import deque as queue row = 5 col = 5 # Global variables for grid, minDistance and visited array minDistance = [[ 0 for i in range (col + 1 )] for i in range (row + 1 )] visited = [[ 0 for i in range (col + 1 )] for i in range (row + 1 )] # Queue for BFS que = queue() # Function to find whether the move is valid or not def isValid(grid, i, j): if (i < 0 or j < 0 or j > = col or i > = row or grid[i][j] or visited[i][j]): return False return True # Function to return the minimum distance # from source to the end of the grid def findMinPathminDistance(grid,sourceRow, sourceCol): # If source is one of the destinations if (sourceCol = = 0 or sourceCol = = col - 1 or sourceRow = = 0 or sourceRow = = row - 1 ): return 0 # Set minimum value minFromSource = row * col # Precalculate minDistance of each grid with R * C for i in range (row): for j in range (col): minDistance[i][j] = row * col # Insert source position in queue que.appendleft([sourceRow, sourceCol]) # Update minimum distance to visit source minDistance[sourceRow][sourceCol] = 0 ; # Set source to visited visited[sourceRow][sourceCol] = 1 ; # BFS approach for calculating the minDistance # of each cell from source while ( len (que) > 0 ): # Iterate over all four cells adjacent # to current cell cell = que.pop() # Initialize position of current cell cellRow = cell[ 0 ] cellCol = cell[ 1 ] # Cell below the current cell if (isValid(grid, cellRow + 1 , cellCol)): # Push new cell to the queue que.appendleft([cellRow + 1 , cellCol]) # Update one of its neighbor's distance minDistance[cellRow + 1 ][cellCol] = min (minDistance[cellRow + 1 ][cellCol], minDistance[cellRow][cellCol] + 1 ) visited[cellRow + 1 ][cellCol] = 1 # Above the current cell if (isValid(grid, cellRow - 1 , cellCol)): que.appendleft([cellRow - 1 , cellCol]) minDistance[cellRow - 1 ][cellCol] = min (minDistance[cellRow - 1 ][cellCol], minDistance[cellRow][cellCol] + 1 ) visited[cellRow - 1 ][cellCol] = 1 # Right cell if (isValid(grid, cellRow, cellCol + 1 )): que.appendleft([cellRow, cellCol + 1 ]) minDistance[cellRow][cellCol + 1 ] = min (minDistance[cellRow][cellCol + 1 ], minDistance[cellRow][cellCol] + 1 ) visited[cellRow][cellCol + 1 ] = 1 ; # Left cell if (isValid(grid, cellRow, cellCol - 1 )): que.appendleft([cellRow, cellCol - 1 ]) minDistance[cellRow][cellCol - 1 ] = min (minDistance[cellRow][cellCol - 1 ], minDistance[cellRow][cellCol] + 1 ) visited[cellRow][cellCol - 1 ] = 1 # Pop the visited cell # Minimum distance in the first row for i in range (col): minFromSource = min (minFromSource, minDistance[ 0 ][i]); # Minimum distance in the last row for i in range (col): minFromSource = min (minFromSource, minDistance[row - 1 ][i]); # Minimum distance in the first column for i in range (row): minFromSource = min (minFromSource, minDistance[i][ 0 ]); # Minimum distance in the last column for i in range (row): minFromSource = min (minFromSource, minDistance[i][col - 1 ]); # If no path exists if (minFromSource = = row * col): return - 1 # Return the minimum distance return minFromSource # Driver code sourceRow = 3 sourceCol = 3 grid = [[ 1 , 1 , 1 , 1 , 0 ], [ 0 , 0 , 1 , 0 , 1 ], [ 0 , 0 , 1 , 0 , 1 ], [ 1 , 0 , 0 , 0 , 1 ], [ 1 , 1 , 0 , 1 , 0 ]] print (findMinPathminDistance(grid, sourceRow, sourceCol)) # This code is contributed by mohit kumar 29 |
C#
// C# implementation of the approach using System; using System.Collections.Generic; class GFG{ // Pair class class Pair { public int first, second; public Pair( int a, int b) { first = a; second = b; } } static int row = 5; static int col = 5; // Global variables for grid, minDistance // and visited array static int [,]minDistance = new int [row + 1, col + 1]; static int [,]visited = new int [row + 1, col + 1]; // Queue for BFS static Queue<Pair> que = new Queue<Pair>(); // Function to find whether the move is valid or not static bool isValid( int [,]grid, int i, int j) { if (i < 0 || j < 0 || j >= col || i >= row || grid[i, j] != 0 || visited[i, j] != 0) return false ; return true ; } // Function to return the minimum distance // from source to the end of the grid static int findMinPathminDistance( int [,]grid, int sourceRow, int sourceCol) { // If source is one of the destinations if (sourceCol == 0 || sourceCol == col - 1 || sourceRow == 0 || sourceRow == row - 1) return 0; // Set minimum value int minFromSource = row * col; int i = 0; // Precalculate minDistance of each // grid with R * C for (i = 0; i < row; i++) for ( int j = 0; j < col; j++) minDistance[i, j] = row * col; // Insert source position in queue que.Enqueue( new Pair(sourceRow, sourceCol)); // Update minimum distance to visit source minDistance[sourceRow, sourceCol] = 0; // Set source to visited visited[sourceRow, sourceCol] = 1; // BFS approach for calculating the minDistance // of each cell from source while (que.Count > 0) { // Iterate over all four cells adjacent // to current cell Pair cell = que.Peek(); // Initialize position of current cell int cellRow = cell.first; int cellCol = cell.second; // Cell below the current cell if (isValid(grid, cellRow + 1, cellCol)) { // Add new cell to the queue que.Enqueue( new Pair(cellRow + 1, cellCol)); // Update one of its neighbor's distance minDistance[cellRow + 1, cellCol] = Math.Min( minDistance[cellRow + 1, cellCol], minDistance[cellRow, cellCol] + 1); visited[cellRow + 1, cellCol] = 1; } // Above the current cell if (isValid(grid, cellRow - 1, cellCol)) { que.Enqueue( new Pair(cellRow - 1, cellCol)); minDistance[cellRow - 1, cellCol] = Math.Min( minDistance[cellRow - 1, cellCol], minDistance[cellRow, cellCol] + 1); visited[cellRow - 1, cellCol] = 1; } // Right cell if (isValid(grid, cellRow, cellCol + 1)) { que.Enqueue( new Pair(cellRow, cellCol + 1)); minDistance[cellRow, cellCol + 1] = Math.Min( minDistance[cellRow, cellCol + 1], minDistance[cellRow, cellCol] + 1); visited[cellRow, cellCol + 1] = 1; } // Left cell if (isValid(grid, cellRow, cellCol - 1)) { que.Enqueue( new Pair(cellRow, cellCol - 1)); minDistance[cellRow, cellCol - 1] = Math.Min( minDistance[cellRow, cellCol - 1], minDistance[cellRow, cellCol] + 1); visited[cellRow, cellCol - 1] = 1; } // Pop the visited cell que.Dequeue(); } i = 0; // Minimum distance in the first row for (i = 0; i < col; i++) minFromSource = Math.Min(minFromSource, minDistance[0, i]); // Minimum distance in the last row for (i = 0; i < col; i++) minFromSource = Math.Min(minFromSource, minDistance[row - 1, i]); // Minimum distance in the first column for (i = 0; i < row; i++) minFromSource = Math.Min(minFromSource, minDistance[i, 0]); // Minimum distance in the last column for (i = 0; i < row; i++) minFromSource = Math.Min(minFromSource, minDistance[i, col - 1]); // If no path exists if (minFromSource == row * col) return -1; // Return the minimum distance return minFromSource; } // Driver code public static void Main(String []args) { int sourceRow = 3, sourceCol = 3; int [,]grid = { { 1, 1, 1, 1, 0 }, { 0, 0, 1, 0, 1 }, { 0, 0, 1, 0, 1 }, { 1, 0, 0, 0, 1 }, { 1, 1, 0, 1, 0 } }; Console.WriteLine(findMinPathminDistance( grid, sourceRow, sourceCol)); } } // This code is contributed by 29AjayKumar |
Javascript
<script> // Javascript implementation of the approach // Pair class class Pair { constructor(a, b) { this .first = a; this .second = b; } } let row = 5; let col = 5; // Global variables for grid, minDistance and visited array let minDistance= new Array(row + 1); for (let i = 0; i < row + 1; i++) { minDistance[i] = new Array(col+1); for (let j = 0; j < col + 1; j++) minDistance[i][j] = 0; } let visited = new Array(row + 1); for (let i = 0; i < row + 1; i++) { visited[i] = new Array(col + 1); for (let j = 0; j < col + 1; j++) visited[i][j] = 0; } // Queue for BFS let que = []; // Function to find whether the move is valid or not function isValid(grid, i, j) { if (i < 0 || j < 0 || j >= col || i >= row || grid[i][j] != 0 || visited[i][j] != 0) return false ; return true ; } // Function to return the minimum distance // from source to the end of the grid function findMinPathminDistance(grid,sourceRow,sourceCol) { // If source is one of the destinations if (sourceCol == 0 || sourceCol == col - 1 || sourceRow == 0 || sourceRow == row - 1) return 0; // Set minimum value let minFromSource = row * col; // Precalculate minDistance of each grid with R * C for (let i = 0; i < row; i++) for (let j = 0; j < col; j++) minDistance[i][j] = row * col; // Insert source position in queue que.push( new Pair(sourceRow, sourceCol)); // Update minimum distance to visit source minDistance[sourceRow][sourceCol] = 0; // Set source to visited visited[sourceRow][sourceCol] = 1; // BFS approach for calculating the minDistance // of each cell from source while (que.length > 0) { // Iterate over all four cells adjacent // to current cell let cell = que[0]; // Initialize position of current cell let cellRow = cell.first; let cellCol = cell.second; // Cell below the current cell if (isValid(grid, cellRow + 1, cellCol)) { // add new cell to the queue que.push( new Pair(cellRow + 1, cellCol)); // Update one of its neighbor's distance minDistance[cellRow + 1][cellCol] = Math.min(minDistance[cellRow + 1][cellCol], minDistance[cellRow][cellCol] + 1); visited[cellRow + 1][cellCol] = 1; } // Above the current cell if (isValid(grid, cellRow - 1, cellCol)) { que.push( new Pair(cellRow - 1, cellCol)); minDistance[cellRow - 1][cellCol] = Math.min(minDistance[cellRow - 1][cellCol], minDistance[cellRow][cellCol] + 1); visited[cellRow - 1][cellCol] = 1; } // Right cell if (isValid(grid, cellRow, cellCol + 1)) { que.push( new Pair(cellRow, cellCol + 1)); minDistance[cellRow][cellCol + 1] = Math.min(minDistance[cellRow][cellCol + 1], minDistance[cellRow][cellCol] + 1); visited[cellRow][cellCol + 1] = 1; } // Left cell if (isValid(grid, cellRow, cellCol - 1)) { que.push( new Pair(cellRow, cellCol - 1)); minDistance[cellRow][cellCol - 1] = Math.min(minDistance[cellRow][cellCol - 1], minDistance[cellRow][cellCol] + 1); visited[cellRow][cellCol - 1] = 1; } // Pop the visited cell que.shift(); } let i; // Minimum distance in the first row for (i = 0; i < col; i++) minFromSource = Math.min(minFromSource, minDistance[0][i]); // Minimum distance in the last row for (i = 0; i < col; i++) minFromSource = Math.min(minFromSource, minDistance[row - 1][i]); // Minimum distance in the first column for (i = 0; i < row; i++) minFromSource = Math.min(minFromSource, minDistance[i][0]); // Minimum distance in the last column for (i = 0; i < row; i++) minFromSource = Math.min(minFromSource, minDistance[i][col - 1]); // If no path exists if (minFromSource == row * col) return -1; // Return the minimum distance return minFromSource; } // Driver code let sourceRow = 3, sourceCol = 3; let grid=[[1, 1, 1, 1, 0], [0, 0, 1, 0, 1], [0, 0, 1, 0, 1], [1, 0, 0, 0, 1], [1, 1, 0, 1, 0 ]]; document.write(findMinPathminDistance(grid, sourceRow, sourceCol)); // This code is contributed by avanitrachhadiya2155 </script> |
Output
2