Minimum distance to the corner 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 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.
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 <bits/stdc++.h>using namespace std;#define row 5#define col 5// Global variables for grid, minDistance and visited arrayint minDistance[row + 1][col + 1], visited[row + 1][col + 1];// Queue for BFSqueue<pair<int, int> > que;// Function to find whether the move is valid or notbool 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 gridint 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 neighbor'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[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 codeint 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 approachimport java.util.*;class GFG{ // Pair classstatic 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 arraystatic int minDistance[][] = new int[row + 1][col + 1], visited[][] = new int[row + 1][col + 1];// Queue for BFSstatic Queue<Pair > que = new LinkedList<>();// Function to find whether the move is valid or notstatic 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 gridstatic 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 neighbor'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 codepublic 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 approachrow = 5col = 5# Global variables for grid, minDistance and visited arrayminDistance = [[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 BFSque = [[0,0]]# Function to find whether the move is valid or notdef 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 griddef 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 neighbor'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 codeif __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 |
C#
// C# implementation of above approachusing System;using System.Collections;using System.Collections.Generic;class GFG { // Global variables for grid, minDistance and visited // array static class Globals { // global int public static int row = 5; public static int col = 5; // Global variables for grid, minDistance and // visited array public static int[, ] minDistance = new int[row + 1, col + 1]; public static int[, ] visited = new int[row + 1, col + 1]; // Queue for BFS public static Queue<KeyValuePair<int, int> > que = new Queue<KeyValuePair<int, int> >(); } // Function to find whether the move is valid or not static bool isValid(int[, ] grid, int i, int j) { if (i < 0 || j < 0 || j >= Globals.col || i >= Globals.row || grid[i, j] != 0 || Globals.visited[i, j] != 0) return false; return true; } // Function to return the minimum distance // from source to the end of the grid static int minDistance1(int[, ] grid, int sourceRow, int sourceCol) { // If source is one of the destinations if ((sourceCol == 0 && sourceRow == 0) || (sourceCol == Globals.col - 1 && sourceRow == 0) || (sourceCol == 0 && sourceRow == Globals.row - 1) || (sourceCol == Globals.col - 1 && sourceRow == Globals.row - 1)) return 0; // Set minimum value int minFromSource = Globals.row * Globals.col; // Precalculate minDistance of each grid with R * C for (int i = 0; i < Globals.row; i++) for (int j = 0; j < Globals.col; j++) Globals.minDistance[i, j] = Globals.row * Globals.col; // Insert source position in queue Globals.que.Enqueue(new KeyValuePair<int, int>( sourceRow, sourceCol)); // Update minimum distance to visit source Globals.minDistance[sourceRow, sourceCol] = 0; // Set source to visited Globals.visited[sourceRow, sourceCol] = 1; // BFS approach for calculating the minDistance // of each cell from source while (Globals.que.Count > 0) { // Iterate over all four cells adjacent // to current cell KeyValuePair<int, int> cell = Globals.que.Dequeue(); // Initialize position of current cell int cellRow = cell.Key; int cellCol = cell.Value; // Cell below the current cell if (isValid(grid, cellRow + 1, cellCol)) { // Push new cell to the queue Globals.que.Enqueue( new KeyValuePair<int, int>(cellRow + 1, cellCol)); // Update one of its neighbor's distance Globals.minDistance[cellRow + 1, cellCol] = Math.Min( Globals.minDistance[cellRow + 1, cellCol], Globals.minDistance[cellRow, cellCol] + 1); Globals.visited[cellRow + 1, cellCol] = 1; } // Above the current cell if (isValid(grid, cellRow - 1, cellCol)) { Globals.que.Enqueue( new KeyValuePair<int, int>(cellRow - 1, cellCol)); Globals.minDistance[cellRow - 1, cellCol] = Math.Min( Globals.minDistance[cellRow - 1, cellCol], Globals.minDistance[cellRow, cellCol] + 1); Globals.visited[cellRow - 1, cellCol] = 1; } // Right cell if (isValid(grid, cellRow, cellCol + 1)) { Globals.que.Enqueue( new KeyValuePair<int, int>( cellRow, cellCol + 1)); Globals.minDistance[cellRow, cellCol + 1] = Math.Min( Globals.minDistance[cellRow, cellCol + 1], Globals.minDistance[cellRow, cellCol] + 1); Globals.visited[cellRow, cellCol + 1] = 1; } // Left cell if (isValid(grid, cellRow, cellCol - 1)) { Globals.que.Enqueue( new KeyValuePair<int, int>( cellRow, cellCol - 1)); Globals.minDistance[cellRow, cellCol - 1] = Math.Min( Globals.minDistance[cellRow, cellCol - 1], Globals.minDistance[cellRow, cellCol] + 1); Globals.visited[cellRow, cellCol - 1] = 1; } } // Minimum distance to the corner // of the first row, first column minFromSource = Math.Min(minFromSource, Globals.minDistance[0, 0]); // Minimum distance to the corner // of the last row, first column minFromSource = Math.Min( minFromSource, Globals.minDistance[Globals.row - 1, 0]); // Minimum distance to the corner // of the last row, last column minFromSource = Math.Min( minFromSource, Globals.minDistance[Globals.row - 1, Globals.col - 1]); // Minimum distance to the corner // of the first row, last column minFromSource = Math.Min( minFromSource, Globals.minDistance[0, Globals.col - 1]); // If no path exists if (minFromSource == Globals.row * Globals.col) return -1; // Return the minimum distance return minFromSource; } // Driver Code static void Main() { 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 } }; Console.WriteLine( minDistance1(grid, sourceRow, sourceCol)); }}// The code is contributed by Gautam goel (gautamgoel962) |
Javascript
<script>// Javascript implementation of the approach// Pair classclass Pair{ constructor(a, b) { this.first = a; this.second = b; }}let row = 5;let col = 5;// Global variables for grid, minDistance and visited arraylet minDistance = new Array(row + 1);let visited = new Array(row + 1);for(let i = 0; i < row + 1; i++){ minDistance[i] = new Array(col+1); visited[i] = new Array(col+1); for(let j = 0; j < col + 1; j++) { minDistance[i][j] = 0; visited[i][j] = 0; } }// Queue for BFSlet que = [];// Function to find whether the move is valid or notfunction isValid(grid,i,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 gridfunction _minDistance(grid,sourceRow,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 let minFromSource = row * col; // Precalculate minDistance of each grid with R * C for (let i = 0; i < row; i++) for (let j = 0; j < col; j++) minDistance[i][j] = row * col; // Insert source position in queue que.push(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.length > 0) { // Iterate over all four cells adjacent // to current cell let cell = que[0]; // Initialize position of current cell let cellRow = cell.first; let cellCol = cell.second; // Cell below the current cell if (isValid(grid, cellRow + 1, cellCol)) { // add new cell to the queue que.push(new Pair(cellRow + 1, cellCol)); // Update one of its neighbor'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.push(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.push(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.push(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.shift(); } let 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 codelet sourceRow = 3, sourceCol = 3;let 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]];document.write(_minDistance(grid, sourceRow, sourceCol));// This code is contributed by avanitrachhadiya2155</script> |
Output:
4
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