# Minimum Distance from a given Cell to all other Cells of a Matrix

Given two integers R and C, denoting the number of rows and columns in a matrix, and two integers X and Y, the task is to find the minimum distance from the given cell to all other cells of the matrix.

Examples:

Input: R = 5, C = 5, X = 2, Y = 2
Output:
2 2 2 2 2
2 1 1 1 2
2 1 0 1 2
2 1 1 1 2
2 2 2 2 2

Input: R = 5, C = 5, X = 1, Y = 1
Output:
1 1 1 2 3
1 0 1 2 3
1 1 1 2 3
2 2 2 2 3
3 3 3 3 3

Approach:
Follow the steps below to solve the problem:

• Assign the distance of the initial cells as 0.
• Initialize a Queue and insert the pair {X, Y} into the Queue.
• Iterate until the Queue is not empty, and for every unvisited cell, assign the current distance and insert the index {i, j} into the Queue using BFS technique.
• Print the distance of each cell at the end.

Below is the implementation of the above approach:

 `// C++ Program to implement ` `// the above approach ` `#include ` `using` `namespace` `std; ` ` `  `int` `mat[1001][1001]; ` `int` `r, c, x, y; ` ` `  `// Stores the accessible directions ` `int` `dx[] = { 0, -1, -1, -1, 0, 1, 1, 1 }; ` `int` `dy[] = { 1, 1, 0, -1, -1, -1, 0, 1 }; ` ` `  `// Function to find the minimum distance from a ` `// given cell to all other cells in the matrix ` `void` `FindMinimumDistance() ` `{ ` `    ``// Stores the accessible cells ` `    ``// from current cell ` `    ``queue > q; ` ` `  `    ``// Insert pair (x, y) ` `    ``q.push({ x, y }); ` `    ``mat[x][y] = 0; ` ` `  `    ``// Iterate untill queue is empty ` `    ``while` `(!q.empty()) { ` ` `  `        ``// Extract the pair ` `        ``x = q.front().first; ` `        ``y = q.front().second; ` ` `  `        ``// Pop them ` `        ``q.pop(); ` ` `  `        ``for` `(``int` `i = 0; i < 8; i++) { ` `            ``int` `a = x + dx[i]; ` `            ``int` `b = y + dy[i]; ` ` `  `            ``// Checking boundary condition ` `            ``if` `(a < 0 || a >= r || b >= c || b < 0) ` `                ``continue``; ` ` `  `            ``// If the cell is not visited ` `            ``if` `(mat[a][b] == 0) { ` ` `  `                ``// Assign the minimum distance ` `                ``mat[a][b] = mat[x][y] + 1; ` ` `  `                ``// Insert the traversed neighbour ` `                ``// into the queue ` `                ``q.push({ a, b }); ` `            ``} ` `        ``} ` `    ``} ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``r = 5, c = 5, x = 1, y = 1; ` ` `  `    ``int` `t = x; ` `    ``int` `l = y; ` `    ``mat[x][y] = 0; ` ` `  `    ``FindMinimumDistance(); ` ` `  `    ``mat[t][l] = 0; ` ` `  `    ``// Print the required distances ` `    ``for` `(``int` `i = 0; i < r; i++) { ` `        ``for` `(``int` `j = 0; j < c; j++) { ` `            ``cout << mat[i][j] << ``" "``; ` `        ``} ` `        ``cout << endl; ` `    ``} ` `} `

 `// Java program to implement ` `// the above approach ` `import` `java.util.*; ` ` `  `class` `GFG{ ` `     `  `static` `class` `pair ` `{  ` `    ``int` `first, second;  ` `    ``public` `pair(``int` `first, ``int` `second)  ` `    ``{  ` `        ``this``.first = first;  ` `        ``this``.second = second;  ` `    ``}  ` `}  ` ` `  `static` `int` `[][]mat = ``new` `int``[``1001``][``1001``]; ` `static` `int` `r, c, x, y; ` ` `  `// Stores the accessible directions ` `static` `int` `dx[] = { ``0``, -``1``, -``1``, -``1``, ``0``, ``1``, ``1``, ``1` `}; ` `static` `int` `dy[] = { ``1``, ``1``, ``0``, -``1``, -``1``, -``1``, ``0``, ``1` `}; ` ` `  `// Function to find the minimum distance from a ` `// given cell to all other cells in the matrix ` `static` `void` `FindMinimumDistance() ` `{ ` `     `  `    ``// Stores the accessible cells ` `    ``// from current cell ` `    ``Queue q = ``new` `LinkedList<>(); ` ` `  `    ``// Insert pair (x, y) ` `    ``q.add(``new` `pair(x, y)); ` `    ``mat[x][y] = ``0``; ` ` `  `    ``// Iterate untill queue is empty ` `    ``while` `(!q.isEmpty()) ` `    ``{ ` `         `  `        ``// Extract the pair ` `        ``x = q.peek().first; ` `        ``y = q.peek().second; ` ` `  `        ``// Pop them ` `        ``q.remove(); ` ` `  `        ``for``(``int` `i = ``0``; i < ``8``; i++) ` `        ``{ ` `            ``int` `a = x + dx[i]; ` `            ``int` `b = y + dy[i]; ` ` `  `            ``// Checking boundary condition ` `            ``if` `(a < ``0` `|| a >= r || ` `               ``b >= c || b < ``0``) ` `                ``continue``; ` ` `  `            ``// If the cell is not visited ` `            ``if` `(mat[a][b] == ``0``)  ` `            ``{ ` `                 `  `                ``// Assign the minimum distance ` `                ``mat[a][b] = mat[x][y] + ``1``; ` ` `  `                ``// Insert the traversed neighbour ` `                ``// into the queue ` `                ``q.add(``new` `pair(a, b)); ` `            ``} ` `        ``} ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``r = ``5``; c = ``5``; x = ``1``; y = ``1``; ` ` `  `    ``int` `t = x; ` `    ``int` `l = y; ` `    ``mat[x][y] = ``0``; ` ` `  `    ``FindMinimumDistance(); ` ` `  `    ``mat[t][l] = ``0``; ` ` `  `    ``// Print the required distances ` `    ``for``(``int` `i = ``0``; i < r; i++) ` `    ``{ ` `        ``for``(``int` `j = ``0``; j < c; j++) ` `        ``{ ` `            ``System.out.print(mat[i][j] + ``" "``); ` `        ``} ` `        ``System.out.println(); ` `    ``} ` `} ` `} ` ` `  `// This code is contributed by Amit Katiyar`

 `# Python3 program to implement ` `# the above approach ` `mat ``=` `[[``0` `for` `x ``in` `range``(``1001``)]  ` `          ``for` `y ``in` `range``(``1001``)] ` ` `  `# Stores the accessible directions ` `dx ``=` `[ ``0``, ``-``1``, ``-``1``, ``-``1``, ``0``, ``1``, ``1``, ``1` `] ` `dy ``=` `[ ``1``, ``1``, ``0``, ``-``1``, ``-``1``, ``-``1``, ``0``, ``1` `] ` ` `  `# Function to find the minimum distance ` `# from a given cell to all other cells ` `# in the matrix ` `def` `FindMinimumDistance(): ` `     `  `    ``global` `x, y, r, c ` ` `  `    ``# Stores the accessible cells ` `    ``# from current cell ` `    ``q ``=` `[] ` ` `  `    ``# Insert pair (x, y) ` `    ``q.append([x, y]) ` `    ``mat[x][y] ``=` `0` ` `  `    ``# Iterate untill queue is empty ` `    ``while``(``len``(q) !``=` `0``): ` ` `  `        ``# Extract the pair ` `        ``x ``=` `q[``0``][``0``] ` `        ``y ``=` `q[``0``][``1``] ` ` `  `        ``# Pop them ` `        ``q.pop(``0``) ` ` `  `        ``for` `i ``in` `range``(``8``): ` `            ``a ``=` `x ``+` `dx[i] ` `            ``b ``=` `y ``+` `dy[i] ` ` `  `            ``# Checking boundary condition ` `            ``if``(a < ``0` `or` `a >``=` `r ``or`  `              ``b >``=` `c ``or` `b < ``0``): ` `                ``continue` ` `  `            ``# If the cell is not visited ` `            ``if``(mat[a][b] ``=``=` `0``): ` ` `  `                ``# Assign the minimum distance ` `                ``mat[a][b] ``=` `mat[x][y] ``+` `1` ` `  `                ``# Insert the traversed neighbour ` `                ``# into the queue ` `                ``q.append([a, b]) ` ` `  `# Driver Code ` `r ``=` `5` `c ``=` `5` `x ``=` `1` `y ``=` `1` `t ``=` `x ` `l ``=` `y ` ` `  `mat[x][y] ``=` `0` ` `  `FindMinimumDistance() ` `mat[t][l] ``=` `0` ` `  `# Print the required distances  ` `for` `i ``in` `range``(r): ` `    ``for` `j ``in` `range``(c): ` `        ``print``(mat[i][j], end ``=` `" "``) ` `         `  `    ``print``() ` ` `  `# This code is contributed by Shivam Singh `

 `// C# program to implement ` `// the above approach ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG{ ` `     `  `class` `pair ` `{  ` `    ``public` `int` `first, second;  ` `    ``public` `pair(``int` `first, ``int` `second)  ` `    ``{  ` `        ``this``.first = first;  ` `        ``this``.second = second;  ` `    ``}  ` `}  ` ` `  `static` `int` `[,]mat = ``new` `int``[1001, 1001]; ` `static` `int` `r, c, x, y; ` ` `  `// Stores the accessible directions ` `static` `int` `[]dx = { 0, -1, -1, -1, 0, 1, 1, 1 }; ` `static` `int` `[]dy = { 1, 1, 0, -1, -1, -1, 0, 1 }; ` ` `  `// Function to find the minimum distance from a ` `// given cell to all other cells in the matrix ` `static` `void` `FindMinimumDistance() ` `{ ` `     `  `    ``// Stores the accessible cells ` `    ``// from current cell ` `    ``Queue q = ``new` `Queue(); ` ` `  `    ``// Insert pair (x, y) ` `    ``q.Enqueue(``new` `pair(x, y)); ` `    ``mat[x, y] = 0; ` ` `  `    ``// Iterate untill queue is empty ` `    ``while` `(q.Count != 0) ` `    ``{ ` `         `  `        ``// Extract the pair ` `        ``x = q.Peek().first; ` `        ``y = q.Peek().second; ` ` `  `        ``// Pop them ` `        ``q.Dequeue(); ` ` `  `        ``for``(``int` `i = 0; i < 8; i++) ` `        ``{ ` `            ``int` `a = x + dx[i]; ` `            ``int` `b = y + dy[i]; ` ` `  `            ``// Checking boundary condition ` `            ``if` `(a < 0 || a >= r || ` `                ``b >= c || b < 0) ` `                ``continue``; ` ` `  `            ``// If the cell is not visited ` `            ``if` `(mat[a, b] == 0)  ` `            ``{ ` `                 `  `                ``// Assign the minimum distance ` `                ``mat[a, b] = mat[x, y] + 1; ` ` `  `                ``// Insert the traversed neighbour ` `                ``// into the queue ` `                ``q.Enqueue(``new` `pair(a, b)); ` `            ``} ` `        ``} ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``r = 5; c = 5; x = 1; y = 1; ` ` `  `    ``int` `t = x; ` `    ``int` `l = y; ` `    ``mat[x, y] = 0; ` ` `  `    ``FindMinimumDistance(); ` ` `  `    ``mat[t, l] = 0; ` ` `  `    ``// Print the required distances ` `    ``for``(``int` `i = 0; i < r; i++) ` `    ``{ ` `        ``for``(``int` `j = 0; j < c; j++) ` `        ``{ ` `            ``Console.Write(mat[i, j] + ``" "``); ` `        ``} ` `        ``Console.WriteLine(); ` `    ``} ` `} ` `} ` ` `  `// This code is contributed by shikhasingrajput `

Output:
```1 1 1 2 3
1 0 1 2 3
1 1 1 2 3
2 2 2 2 3
3 3 3 3 3
```

Time Complexity: O(R * C)
Auxiliary Space: O(R * C)

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