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: 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:

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// 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 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 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;
}

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Output:

2


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