# Shortest distance between two cells in a matrix or grid

Given a matrix of N*M order. Find the shortest distance from a source cell to a destination cell, traversing through limited cells only. Also you can move only up, down, left and right. If found output the distance else -1.

s represents ‘source’

d represents ‘destination’

* represents cell you can travel

0 represents cell you can not travel

This problem is meant for single source and destination.

Examples:

Input : {'0', '*', '0', 's'}, {'*', '0', '*', '*'}, {'0', '*', '*', '*'}, {'d', '*', '*', '*'} Output : 6 Input : {'0', '*', '0', 's'}, {'*', '0', '*', '*'}, {'0', '*', '*', '*'}, {'d', '0', '0', '0'} Output : -1

The idea is to BFS (breadth first search) on matrix cells. Note that we can always use BFS to find shortest path if graph is unweighted.

- Store each cell as a node with their row, column values and distance from source cell.
- Start BFS with source cell.
- Make a visited array with all having “false” values except ‘0’cells which are assigned “true” values as they can not be traversed.
- Keep updating distance from source value in each move.
- Return distance when destination is met, else return -1 (no path exists in between source and destination).

## CPP

`// C++ Code implementation for above problem` `#include <bits/stdc++.h>` `using` `namespace` `std;` `#define N 4` `#define M 4` `// QItem for current location and distance` `// from source location` `class` `QItem {` `public` `:` ` ` `int` `row;` ` ` `int` `col;` ` ` `int` `dist;` ` ` `QItem(` `int` `x, ` `int` `y, ` `int` `w)` ` ` `: row(x), col(y), dist(w)` ` ` `{` ` ` `}` `};` `int` `minDistance(` `char` `grid[N][M])` `{` ` ` `QItem source(0, 0, 0);` ` ` `// To keep track of visited QItems. Marking` ` ` `// blocked cells as visited.` ` ` `bool` `visited[N][M];` ` ` `for` `(` `int` `i = 0; i < N; i++) {` ` ` `for` `(` `int` `j = 0; j < M; j++)` ` ` `{` ` ` `if` `(grid[i][j] == ` `'0'` `)` ` ` `visited[i][j] = ` `true` `;` ` ` `else` ` ` `visited[i][j] = ` `false` `;` ` ` `// Finding source` ` ` `if` `(grid[i][j] == ` `'s'` `)` ` ` `{` ` ` `source.row = i;` ` ` `source.col = j;` ` ` `}` ` ` `}` ` ` `}` ` ` `// applying BFS on matrix cells starting from source` ` ` `queue<QItem> q;` ` ` `q.push(source);` ` ` `visited[source.row][source.col] = ` `true` `;` ` ` `while` `(!q.empty()) {` ` ` `QItem p = q.front();` ` ` `q.pop();` ` ` `// Destination found;` ` ` `if` `(grid[p.row][p.col] == ` `'d'` `)` ` ` `return` `p.dist;` ` ` `// moving up` ` ` `if` `(p.row - 1 >= 0 &&` ` ` `visited[p.row - 1][p.col] == ` `false` `) {` ` ` `q.push(QItem(p.row - 1, p.col, p.dist + 1));` ` ` `visited[p.row - 1][p.col] = ` `true` `;` ` ` `}` ` ` `// moving down` ` ` `if` `(p.row + 1 < N &&` ` ` `visited[p.row + 1][p.col] == ` `false` `) {` ` ` `q.push(QItem(p.row + 1, p.col, p.dist + 1));` ` ` `visited[p.row + 1][p.col] = ` `true` `;` ` ` `}` ` ` `// moving left` ` ` `if` `(p.col - 1 >= 0 &&` ` ` `visited[p.row][p.col - 1] == ` `false` `) {` ` ` `q.push(QItem(p.row, p.col - 1, p.dist + 1));` ` ` `visited[p.row][p.col - 1] = ` `true` `;` ` ` `}` ` ` `// moving right` ` ` `if` `(p.col + 1 < M &&` ` ` `visited[p.row][p.col + 1] == ` `false` `) {` ` ` `q.push(QItem(p.row, p.col + 1, p.dist + 1));` ` ` `visited[p.row][p.col + 1] = ` `true` `;` ` ` `}` ` ` `}` ` ` `return` `-1;` `}` `// Driver code` `int` `main()` `{` ` ` `char` `grid[N][M] = { { ` `'0'` `, ` `'*'` `, ` `'0'` `, ` `'s'` `},` ` ` `{ ` `'*'` `, ` `'0'` `, ` `'*'` `, ` `'*'` `},` ` ` `{ ` `'0'` `, ` `'*'` `, ` `'*'` `, ` `'*'` `},` ` ` `{ ` `'d'` `, ` `'*'` `, ` `'*'` `, ` `'*'` `} };` ` ` `cout << minDistance(grid);` ` ` `return` `0;` `}` |

## Java

`/*package whatever //do not write package name here */` `// Java Code implementation for above problem` `import` `java.util.LinkedList;` `import` `java.util.Queue;` `import` `java.util.Scanner;` `// QItem for current location and distance` `// from source location` `class` `QItem {` ` ` `int` `row;` ` ` `int` `col;` ` ` `int` `dist;` ` ` `public` `QItem(` `int` `row, ` `int` `col, ` `int` `dist)` ` ` `{` ` ` `this` `.row = row;` ` ` `this` `.col = col;` ` ` `this` `.dist = dist;` ` ` `}` `}` `public` `class` `Maze {` ` ` `private` `static` `int` `minDistance(` `char` `[][] grid)` ` ` `{` ` ` `QItem source = ` `new` `QItem(` `0` `, ` `0` `, ` `0` `);` ` ` ` ` `// To keep track of visited QItems. Marking` ` ` `// blocked cells as visited.` ` ` `firstLoop:` ` ` `for` `(` `int` `i = ` `0` `; i < grid.length; i++) {` ` ` `for` `(` `int` `j = ` `0` `; j < grid[i].length; j++)` ` ` `{` ` ` ` ` `// Finding source` ` ` `if` `(grid[i][j] == ` `'s'` `) {` ` ` `source.row = i;` ` ` `source.col = j;` ` ` `break` `firstLoop;` ` ` `}` ` ` `}` ` ` `}` ` ` ` ` `// applying BFS on matrix cells starting from source` ` ` `Queue<QItem> queue = ` `new` `LinkedList<>();` ` ` `queue.add(` `new` `QItem(source.row, source.col, ` `0` `));` ` ` `boolean` `[][] visited` ` ` `= ` `new` `boolean` `[grid.length][grid[` `0` `].length];` ` ` `visited[source.row][source.col] = ` `true` `;` ` ` `while` `(queue.isEmpty() == ` `false` `) {` ` ` `QItem p = queue.remove();` ` ` ` ` `// Destination found;` ` ` `if` `(grid[p.row][p.col] == ` `'d'` `)` ` ` `return` `p.dist;` ` ` `// moving up` ` ` `if` `(isValid(p.row - ` `1` `, p.col, grid, visited)) {` ` ` `queue.add(` `new` `QItem(p.row - ` `1` `, p.col,` ` ` `p.dist + ` `1` `));` ` ` `visited[p.row - ` `1` `][p.col] = ` `true` `;` ` ` `}` ` ` `// moving down` ` ` `if` `(isValid(p.row + ` `1` `, p.col, grid, visited)) {` ` ` `queue.add(` `new` `QItem(p.row + ` `1` `, p.col,` ` ` `p.dist + ` `1` `));` ` ` `visited[p.row + ` `1` `][p.col] = ` `true` `;` ` ` `}` ` ` `// moving left` ` ` `if` `(isValid(p.row, p.col - ` `1` `, grid, visited)) {` ` ` `queue.add(` `new` `QItem(p.row, p.col - ` `1` `,` ` ` `p.dist + ` `1` `));` ` ` `visited[p.row][p.col - ` `1` `] = ` `true` `;` ` ` `}` ` ` `// moving right` ` ` `if` `(isValid(p.row - ` `1` `, p.col + ` `1` `, grid,` ` ` `visited)) {` ` ` `queue.add(` `new` `QItem(p.row, p.col + ` `1` `,` ` ` `p.dist + ` `1` `));` ` ` `visited[p.row][p.col + ` `1` `] = ` `true` `;` ` ` `}` ` ` `}` ` ` `return` `-` `1` `;` ` ` `}` ` ` ` ` `// checking where it's valid or not` ` ` `private` `static` `boolean` `isValid(` `int` `x, ` `int` `y,` ` ` `char` `[][] grid,` ` ` `boolean` `[][] visited)` ` ` `{` ` ` `if` `(x >= ` `0` `&& y >= ` `0` `&& x < grid.length` ` ` `&& y < grid[` `0` `].length && grid[x][y] != ` `'0'` ` ` `&& visited[x][y] == ` `false` `) {` ` ` `return` `true` `;` ` ` `}` ` ` `return` `false` `;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `char` `[][] grid = { { ` `'0'` `, ` `'*'` `, ` `'0'` `, ` `'s'` `},` ` ` `{ ` `'*'` `, ` `'0'` `, ` `'*'` `, ` `'*'` `},` ` ` `{ ` `'0'` `, ` `'*'` `, ` `'*'` `, ` `'*'` `},` ` ` `{ ` `'d'` `, ` `'*'` `, ` `'*'` `, ` `'*'` `} };` ` ` `System.out.println(minDistance(grid));` ` ` `}` `}` `// This code is contributed by abhikelge21.` |

Output:

6

This article is contributed by **Prashant Singh**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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