Skip to content
Related Articles
Minimum distance to the corner of a grid from source
• Difficulty Level : Medium
• Last Updated : 13 Feb, 2020

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 any corner of the grid. 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[][] = {{0, 0, 1}, {0, 0, 0}, {1, 1, 1}}
Output: 2
(1, 1) -> (1, 0) -> (0, 0)

Input: i = 0, j = 0, grid[][] = {{0, 1}, {1, 1}}
Output: 0
Source is already a corner of the grid.

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

Approach:

• If source is already any of the corner 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 corner.
• Print the minimum among these in the end.

Below is the implementation of the above approach:

## C++

 `// 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` `minDistance(``int` `grid[][col],``                           ``int` `sourceRow, ``int` `sourceCol)``{``    ``// If source is one of the destinations``    ``if` `((sourceCol == 0 && sourceRow == 0)``        ``|| (sourceCol == col - 1 && sourceRow == 0)``        ``|| (sourceCol == 0 && sourceRow == row - 1)``        ``|| (sourceCol == col - 1 && 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 to the corner``    ``// of the first row, first column``    ``minFromSource = min(minFromSource,``                        ``minDistance);`` ` `    ``// Minimum distance to the corner``    ``// of the last row, first column``    ``minFromSource = min(minFromSource,``                        ``minDistance[row - 1]);`` ` `    ``// Minimum distance to the corner``    ``// of the last row, last column``    ``minFromSource = min(minFromSource,``                        ``minDistance[row - 1][col - 1]);`` ` `    ``// Minimum distance to the corner``    ``// of the first row, last column``    ``minFromSource = min(minFromSource,``                        ``minDistance[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, 0, 0,``                           ``0, 0, 1, 0, 1,``                           ``0, 0, 1, 0, 1,``                           ``1, 0, 0, 0, 1,``                           ``1, 1, 0, 1, 0 };`` ` `    ``cout << minDistance(grid, sourceRow, sourceCol);`` ` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.util.*;``class` `GFG``{``     ` `// Pair class``static` `class` `Pair``{``    ``int` `first,second;``    ``Pair(``int` `a, ``int` `b)``    ``{``        ``first = a;``        ``second = b;``    ``}``}``     ` `static` `int` `row = ``5``;``static` `int` `col = ``5``;`` ` `// Global variables for grid, minDistance and visited array``static` `int` `minDistance[][] = ``            ``new` `int``[row + ``1``][col + ``1``], ``            ``visited[][] = ``new` `int``[row + ``1``][col + ``1``];`` ` `// Queue for BFS``static` `Queue que = ``new` `LinkedList<>();`` ` `// Function to find whether the move is valid or not``static` `boolean` `isValid(``int` `grid[][], ``int` `i, ``int` `j)``{``    ``if` `(i < ``0` `|| j < ``0``        ``|| j >= col || i >= row``        ``|| grid[i][j] != ``0` `|| visited[i][j] != ``0``)``        ``return` `false``;`` ` `    ``return` `true``;``}`` ` `// Function to return the minimum distance``// from source to the end of the grid``static` `int` `minDistance(``int` `grid[][],``                        ``int` `sourceRow, ``int` `sourceCol)``{``    ``// If source is one of the destinations``    ``if` `((sourceCol == ``0` `&& sourceRow == ``0``)``        ``|| (sourceCol == col - ``1` `&& sourceRow == ``0``)``        ``|| (sourceCol == ``0` `&& sourceRow == row - ``1``)``        ``|| (sourceCol == col - ``1` `&& 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.add(``new` `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.size() > ``0``) ``    ``{`` ` `        ``// Iterate over all four cells adjacent``        ``// to current cell``        ``Pair cell = que.peek();`` ` `        ``// Initialize position of current cell``        ``int` `cellRow = cell.first;``        ``int` `cellCol = cell.second;`` ` `        ``// Cell below the current cell``        ``if` `(isValid(grid, cellRow + ``1``, cellCol)) ``        ``{`` ` `            ``// add new cell to the queue``            ``que.add(``new` `Pair(cellRow + ``1``, cellCol));`` ` `            ``// Update one of its neightbor's distance``            ``minDistance[cellRow + ``1``][cellCol]``                ``= Math.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.add(``new` `Pair(cellRow - ``1``, cellCol));``            ``minDistance[cellRow - ``1``][cellCol]``                ``= Math.min(minDistance[cellRow - ``1``][cellCol],``                    ``minDistance[cellRow][cellCol] + ``1``);``            ``visited[cellRow - ``1``][cellCol] = ``1``;``        ``}`` ` `        ``// Right cell``        ``if` `(isValid(grid, cellRow, cellCol + ``1``))``        ``{``            ``que.add(``new` `Pair(cellRow, cellCol + ``1``));``            ``minDistance[cellRow][cellCol + ``1``]``                ``= Math.min(minDistance[cellRow][cellCol + ``1``],``                    ``minDistance[cellRow][cellCol] + ``1``);``            ``visited[cellRow][cellCol + ``1``] = ``1``;``        ``}`` ` `        ``// Left cell``        ``if` `(isValid(grid, cellRow, cellCol - ``1``))``        ``{``            ``que.add(``new` `Pair(cellRow, cellCol - ``1``));``            ``minDistance[cellRow][cellCol - ``1``]``                ``= Math.min(minDistance[cellRow][cellCol - ``1``],``                    ``minDistance[cellRow][cellCol] + ``1``);``            ``visited[cellRow][cellCol - ``1``] = ``1``;``        ``}`` ` `        ``// remove the visited cell``        ``que.remove();``    ``}`` ` `    ``int` `i;`` ` `    ``// Minimum distance to the corner``    ``// of the first row, first column``    ``minFromSource = Math.min(minFromSource,``                        ``minDistance[``0``][``0``]);`` ` `    ``// Minimum distance to the corner``    ``// of the last row, first column``    ``minFromSource = Math.min(minFromSource,``                        ``minDistance[row - ``1``][``0``]);`` ` `    ``// Minimum distance to the corner``    ``// of the last row, last column``    ``minFromSource = Math.min(minFromSource,``                        ``minDistance[row - ``1``][col - ``1``]);`` ` `    ``// Minimum distance to the corner``    ``// of the first row, last column``    ``minFromSource = Math.min(minFromSource,``                        ``minDistance[``0``][col - ``1``]);`` ` `    ``// If no path exists``    ``if` `(minFromSource == row * col)``        ``return` `-``1``;`` ` `    ``// Return the minimum distance``    ``return` `minFromSource;``}`` ` ` ` `// Driver code``public` `static` `void` `main(String args[])``{``    ``int` `sourceRow = ``3``, sourceCol = ``3``;``    ``int` `grid[][] = { {``1``, ``1``, ``1``, ``0``, ``0``},``                    ``{``0``, ``0``, ``1``, ``0``, ``1``},``                    ``{``0``, ``0``, ``1``, ``0``, ``1``},``                    ``{``1``, ``0``, ``0``, ``0``, ``1``},``                    ``{``1``, ``1``, ``0``, ``1``, ``0``} };`` ` `    ``System.out.println(minDistance(grid, sourceRow, sourceCol));``}``}`` ` `// This code is contributed by Arnab Kundu`

## Python3

 `# Python 3 implementation of the approach`` ` `row ``=` `5``col ``=` `5`` ` `# Global variables for grid, minDistance and visited array``minDistance ``=` `[[``0` `for` `i ``in` `range``(col``+``1``)] ``for` `j ``in` `range``(row``+``1``)]``visited ``=` `[[``0` `for` `i ``in` `range``(col``+``1``)]``for` `j ``in` `range``(row``+``1``)]`` ` `# Queue for BFS``que ``=` `[[``0``,``0``]]`` ` `# 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` `minDistance1(grid,sourceRow,sourceCol):``    ``# If source is one of the destinations``    ``if` `((sourceCol ``=``=` `0` `and` `sourceRow ``=``=` `0``) ``or``        ``(sourceCol ``=``=` `col ``-` `1` `and` `sourceRow ``=``=` `0``) ``or``        ``(sourceCol ``=``=` `0` `or` `sourceRow ``=``=` `row ``-` `1``) ``or` `        ``(sourceCol ``=``=` `col ``-` `1` `and` `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.append([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[``0``]`` ` `        ``# 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.append([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.append([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.append([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.append([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.remove(que[``0``])`` ` `    ``# Minimum distance to the corner``    ``# of the first row, first column``    ``minFromSource ``=` `min``(minFromSource, minDistance[``0``][``0``])`` ` `    ``# Minimum distance to the corner``    ``# of the last row, first column``    ``minFromSource ``=` `min``(minFromSource, minDistance[row ``-` `1``][``0``])`` ` `    ``# Minimum distance to the corner``    ``# of the last row, last column``    ``minFromSource ``=` `min``(minFromSource,minDistance[row ``-` `1``][col ``-` `1``])`` ` `    ``# Minimum distance to the corner``    ``# of the first row, last column``    ``minFromSource ``=` `min``(minFromSource, minDistance[``0``][col ``-` `1``])`` ` `    ``# If no path exists``    ``if` `(minFromSource ``=``=` `row ``*` `col):``        ``return` `-``1`` ` `    ``# Return the minimum distance``    ``return` `minFromSource`` ` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``sourceRow ``=` `3``    ``sourceCol ``=` `3``    ``grid ``=` `[[``1``, ``1``, ``1``, ``0``, ``0``],``            ``[``0``, ``0``, ``1``, ``0``, ``1``],``            ``[``0``, ``0``, ``1``, ``0``, ``1``],``            ``[``1``, ``0``, ``0``, ``0``, ``1``],``            ``[``1``, ``1``, ``0``, ``1``, ``0``]]`` ` `    ``print``(minDistance1(grid, sourceRow, sourceCol))`` ` `# This code is contributed by``# Surendra_Gangwar`
Output:
```4
```

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer DSA Live Classes

My Personal Notes arrow_drop_up