Data Modelling & AI Data Structure & Algorithm

Minimum distance to the end of a grid from source

23 June 2025

0

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: 1

Input: 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

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Minimum distance to the end of a grid from source

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