Minimum distance to the corner of a grid from source

16 Jun, 2022
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 any corner of the grid. 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[][] = {{0, 0, 1}, {0, 0, 0}, {1, 1, 1}} Output: 2 (1, 1) -> (1, 0) -> (0, 0) 
Input: i = 0, j = 0, grid[][] = {{0, 1}, {1, 1}} Output: 0 Source is already a corner of the grid.  
 
Approach:  
If source is already any of the corner 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.
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 corner.
Print the minimum among these in the end.
Below is the implementation of the above approach:  
C++
Java
Python3
C#
Javascript
// 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 arrayint minDistance[row + 1][col + 1], visited[row + 1][col + 1]; // Queue for BFSqueue<pair<int, int> > que; // Function to find whether the move is valid or notbool 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 gridint minDistance(int grid[][col],                           int sourceRow, int sourceCol){    // If source is one of the destinations    if ((sourceCol == 0 && sourceRow == 0)        || (sourceCol == col - 1 && sourceRow == 0)        || (sourceCol == 0 && sourceRow == row - 1)        || (sourceCol == col - 1 && 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 neightbor'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 to the corner    // of the first row, first column    minFromSource = min(minFromSource,                        minDistance[0][0]);     // Minimum distance to the corner    // of the last row, first column    minFromSource = min(minFromSource,                        minDistance[row - 1][0]);     // Minimum distance to the corner    // of the last row, last column    minFromSource = min(minFromSource,                        minDistance[row - 1][col - 1]);     // Minimum distance to the corner    // of the first row, last column    minFromSource = min(minFromSource,                        minDistance[0][col - 1]);     // If no path exists    if (minFromSource == row * col)        return -1;     // Return the minimum distance    return minFromSource;} // Driver codeint main(){    int sourceRow = 3, sourceCol = 3;    int grid[row][col] = { 1, 1, 1, 0, 0,                           0, 0, 1, 0, 1,                           0, 0, 1, 0, 1,                           1, 0, 0, 0, 1,                           1, 1, 0, 1, 0 };     cout << minDistance(grid, sourceRow, sourceCol);     return 0;}
// Java implementation of the approachimport java.util.*;class GFG{     // Pair classstatic 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 arraystatic int minDistance[][] =            new int[row + 1][col + 1],            visited[][] = new int[row + 1][col + 1]; // Queue for BFSstatic Queue<Pair > que = new LinkedList<>(); // Function to find whether the move is valid or notstatic 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 gridstatic int minDistance(int grid[][],                        int sourceRow, int sourceCol){    // If source is one of the destinations    if ((sourceCol == 0 && sourceRow == 0)        || (sourceCol == col - 1 && sourceRow == 0)        || (sourceCol == 0 && sourceRow == row - 1)        || (sourceCol == col - 1 && 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 neightbor'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;        }         // remove the visited cell        que.remove();    }     int i;     // Minimum distance to the corner    // of the first row, first column    minFromSource = Math.min(minFromSource,                        minDistance[0][0]);     // Minimum distance to the corner    // of the last row, first column    minFromSource = Math.min(minFromSource,                        minDistance[row - 1][0]);     // Minimum distance to the corner    // of the last row, last column    minFromSource = Math.min(minFromSource,                        minDistance[row - 1][col - 1]);     // Minimum distance to the corner    // of the first row, last column    minFromSource = Math.min(minFromSource,                        minDistance[0][col - 1]);     // If no path exists    if (minFromSource == row * col)        return -1;     // Return the minimum distance    return minFromSource;}  // Driver codepublic static void main(String args[]){    int sourceRow = 3, sourceCol = 3;    int grid[][] = { {1, 1, 1, 0, 0},                    {0, 0, 1, 0, 1},                    {0, 0, 1, 0, 1},                    {1, 0, 0, 0, 1},                    {1, 1, 0, 1, 0} };     System.out.println(minDistance(grid, sourceRow, sourceCol));}} // This code is contributed by Arnab Kundu
# Python 3 implementation of the approach row = 5col = 5 # Global variables for grid, minDistance and visited arrayminDistance = [[0 for i in range(col+1)] for j in range(row+1)]visited = [[0 for i in range(col+1)]for j in range(row+1)] # Queue for BFSque = [[0,0]] # Function to find whether the move is valid or notdef 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 griddef minDistance1(grid,sourceRow,sourceCol):    # If source is one of the destinations    if ((sourceCol == 0 and sourceRow == 0) or        (sourceCol == col - 1 and sourceRow == 0) or        (sourceCol == 0 or sourceRow == row - 1) or        (sourceCol == col - 1 and 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.append([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[0]         # 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.append([cellRow + 1, cellCol])             # Update one of its neightbor'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.append([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.append([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.append([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.remove(que[0])     # Minimum distance to the corner    # of the first row, first column    minFromSource = min(minFromSource, minDistance[0][0])     # Minimum distance to the corner    # of the last row, first column    minFromSource = min(minFromSource, minDistance[row - 1][0])     # Minimum distance to the corner    # of the last row, last column    minFromSource = min(minFromSource,minDistance[row - 1][col - 1])     # Minimum distance to the corner    # of the first row, last column    minFromSource = min(minFromSource, minDistance[0][col - 1])     # If no path exists    if (minFromSource == row * col):        return -1     # Return the minimum distance    return minFromSource # Driver codeif __name__ == '__main__':    sourceRow = 3    sourceCol = 3    grid = [[1, 1, 1, 0, 0],            [0, 0, 1, 0, 1],            [0, 0, 1, 0, 1],            [1, 0, 0, 0, 1],            [1, 1, 0, 1, 0]]     print(minDistance1(grid, sourceRow, sourceCol)) # This code is contributed by# Surendra_Gangwar
// C# implementation of above approachusing System;using System.Collections;using System.Collections.Generic; class GFG {    // Global variables for grid, minDistance and visited    // array    static class Globals {        // global int        public static int row = 5;        public static int col = 5;         // Global variables for grid, minDistance and        // visited array        public static int[, ] minDistance            = new int[row + 1, col + 1];        public static int[, ] visited            = new int[row + 1, col + 1];         // Queue for BFS        public static Queue<KeyValuePair<int, int> > que            = new Queue<KeyValuePair<int, int> >();    }      // 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 >= Globals.col            || i >= Globals.row || grid[i, j] != 0            || Globals.visited[i, j] != 0)            return false;         return true;    }     // Function to return the minimum distance    // from source to the end of the grid    static int minDistance1(int[, ] grid, int sourceRow,                            int sourceCol)    {        // If source is one of the destinations        if ((sourceCol == 0 && sourceRow == 0)            || (sourceCol == Globals.col - 1                && sourceRow == 0)            || (sourceCol == 0                && sourceRow == Globals.row - 1)            || (sourceCol == Globals.col - 1                && sourceRow == Globals.row - 1))            return 0;         // Set minimum value        int minFromSource = Globals.row * Globals.col;         // Precalculate minDistance of each grid with R * C        for (int i = 0; i < Globals.row; i++)            for (int j = 0; j < Globals.col; j++)                Globals.minDistance[i, j]                    = Globals.row * Globals.col;         // Insert source position in queue        Globals.que.Enqueue(new KeyValuePair<int, int>(            sourceRow, sourceCol));         // Update minimum distance to visit source        Globals.minDistance[sourceRow, sourceCol] = 0;         // Set source to visited        Globals.visited[sourceRow, sourceCol] = 1;         // BFS approach for calculating the minDistance        // of each cell from source        while (Globals.que.Count > 0) {             // Iterate over all four cells adjacent            // to current cell            KeyValuePair<int, int> cell                = Globals.que.Dequeue();             // Initialize position of current cell            int cellRow = cell.Key;            int cellCol = cell.Value;             // Cell below the current cell            if (isValid(grid, cellRow + 1, cellCol)) {                 // Push new cell to the queue                Globals.que.Enqueue(                    new KeyValuePair<int, int>(cellRow + 1,                                               cellCol));                 // Update one of its neightbor's distance                Globals.minDistance[cellRow + 1, cellCol]                    = Math.Min(                        Globals.minDistance[cellRow + 1,                                            cellCol],                        Globals.minDistance[cellRow,                                            cellCol]                            + 1);                Globals.visited[cellRow + 1, cellCol] = 1;            }             // Above the current cell            if (isValid(grid, cellRow - 1, cellCol)) {                Globals.que.Enqueue(                    new KeyValuePair<int, int>(cellRow - 1,                                               cellCol));                Globals.minDistance[cellRow - 1, cellCol]                    = Math.Min(                        Globals.minDistance[cellRow - 1,                                            cellCol],                        Globals.minDistance[cellRow,                                            cellCol]                            + 1);                Globals.visited[cellRow - 1, cellCol] = 1;            }             // Right cell            if (isValid(grid, cellRow, cellCol + 1)) {                Globals.que.Enqueue(                    new KeyValuePair<int, int>(                        cellRow, cellCol + 1));                Globals.minDistance[cellRow, cellCol + 1]                    = Math.Min(                        Globals.minDistance[cellRow,                                            cellCol + 1],                        Globals.minDistance[cellRow,                                            cellCol]                            + 1);                Globals.visited[cellRow, cellCol + 1] = 1;            }             // Left cell            if (isValid(grid, cellRow, cellCol - 1)) {                Globals.que.Enqueue(                    new KeyValuePair<int, int>(                        cellRow, cellCol - 1));                Globals.minDistance[cellRow, cellCol - 1]                    = Math.Min(                        Globals.minDistance[cellRow,                                            cellCol - 1],                        Globals.minDistance[cellRow,                                            cellCol]                            + 1);                Globals.visited[cellRow, cellCol - 1] = 1;            }        }         // Minimum distance to the corner        // of the first row, first column        minFromSource = Math.Min(minFromSource,                                 Globals.minDistance[0, 0]);         // Minimum distance to the corner        // of the last row, first column        minFromSource = Math.Min(            minFromSource,            Globals.minDistance[Globals.row - 1, 0]);         // Minimum distance to the corner        // of the last row, last column        minFromSource = Math.Min(            minFromSource,            Globals.minDistance[Globals.row - 1,                                Globals.col - 1]);         // Minimum distance to the corner        // of the first row, last column        minFromSource = Math.Min(            minFromSource,            Globals.minDistance[0, Globals.col - 1]);         // If no path exists        if (minFromSource == Globals.row * Globals.col)            return -1;         // Return the minimum distance        return minFromSource;    }     // Driver Code    static void Main()    {        int sourceRow = 3, sourceCol = 3;        int[, ] grid = { { 1, 1, 1, 0, 0 },                         { 0, 0, 1, 0, 1 },                         { 0, 0, 1, 0, 1 },                         { 1, 0, 0, 0, 1 },                         { 1, 1, 0, 1, 0 } };         Console.WriteLine(            minDistance1(grid, sourceRow, sourceCol));    }} // The code is contributed by Gautam goel (gautamgoel962)
<script>// Javascript implementation of the approach // Pair classclass Pair{    constructor(a, b)    {        this.first = a;        this.second = b;    }} let row = 5;let col = 5; // Global variables for grid, minDistance and visited arraylet minDistance = new Array(row + 1);let visited = new Array(row + 1);for(let i = 0; i < row + 1; i++){    minDistance[i] = new Array(col+1);    visited[i] = new Array(col+1);    for(let j = 0; j < col + 1; j++)    {        minDistance[i][j] = 0;        visited[i][j] = 0;    }          } // Queue for BFSlet que = []; // Function to find whether the move is valid or notfunction 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 gridfunction _minDistance(grid,sourceRow,sourceCol){    // If source is one of the destinations    if ((sourceCol == 0 && sourceRow == 0)        || (sourceCol == col - 1 && sourceRow == 0)        || (sourceCol == 0 && sourceRow == row - 1)        || (sourceCol == col - 1 && 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 neightbor'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;        }           // remove the visited cell        que.shift();    }       let i;       // Minimum distance to the corner    // of the first row, first column    minFromSource = Math.min(minFromSource,                        minDistance[0][0]);       // Minimum distance to the corner    // of the last row, first column    minFromSource = Math.min(minFromSource,                        minDistance[row - 1][0]);       // Minimum distance to the corner    // of the last row, last column    minFromSource = Math.min(minFromSource,                        minDistance[row - 1][col - 1]);       // Minimum distance to the corner    // of the first row, last column    minFromSource = Math.min(minFromSource,                        minDistance[0][col - 1]);       // If no path exists    if (minFromSource == row * col)        return -1;       // Return the minimum distance    return minFromSource;} // Driver codelet sourceRow = 3, sourceCol = 3;let grid = [[1, 1, 1, 0, 0],                    [0, 0, 1, 0, 1],                    [0, 0, 1, 0, 1],                    [1, 0, 0, 0, 1],                    [1, 1, 0, 1, 0]];document.write(_minDistance(grid, sourceRow, sourceCol)); // This code is contributed by avanitrachhadiya2155</script>
4
 
SURENDRA_GANGWAR
Akanksha_Rai
andrew1234
avanitrachhadiya2155
gautamgoel962
BFS
Geometric
Graph
Matrix
Queue
Matrix
Graph
Queue
Geometric
BFS
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