# 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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++ implementation of the approach #include 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 > 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 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; }

Output:

2

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