# 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:

## CPP

 `// 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<``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 in the first row ` `    ``for` `(i = 0; i < col; i++) ` `        ``minFromSource = min(minFromSource, minDistance[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]); ` ` `  `    ``// 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; ` `} `

## Python

 `# 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 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.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 `

Output:

```2
```

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