Dada una cuadrícula binaria de orden r * c y una posición inicial. La tarea es encontrar la distancia mínima desde la fuente para llegar al final de la cuadrícula (primera fila, última fila, primera columna o última columna). Se puede realizar un movimiento a una celda grid[i][j] solo si grid[i][j] = 0 y solo se permiten movimientos hacia la izquierda , derecha , arriba y abajo . Si no existe una ruta válida, imprima -1 .
Ejemplos:
Entrada: i = 1, j = 1, grid[][] = { {1, 0, 1}, {0, 0, 0}, {1, 1, 1}}
Salida: 1Entrada: i = 0, j = 0, grid[][] = { {0, 1}, {1, 1}}
Salida: 0
Acercarse:
- Si la fuente ya es la primera/última fila/columna, imprima 0 .
- Comience a atravesar la cuadrícula comenzando con la fuente usando BFS como:
- Inserte la posición de la celda en la cola.
- Extraiga el elemento de la cola y márquelo como visitado.
- Para cada movimiento válido adyacente al que apareció, inserte la posición de la celda en la cola.
- En cada movimiento, actualice la distancia mínima de la celda desde la posición inicial.
- Después de completar el BFS, encuentre la distancia mínima desde la fuente hasta cada celda en la primera fila, la última fila, la primera columna y la última columna.
- Imprime el mínimo entre estos al final.
A continuación se muestra la implementación del enfoque anterior:
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 array
int minDistance[row + 1][col + 1], visited[row + 1][col + 1];
// Queue for BFS
queue<pair<int, int> > 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[0][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][0]);
// 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;
}
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<Pair > 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 findMinPathminDistance(int grid[][],
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.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;
}
// Pop the visited cell
que.remove();
}
int i;
// Minimum distance in the first row
for (i = 0; i < col; i++)
minFromSource = Math.min(minFromSource,
minDistance[0][i]);
// Minimum distance in the last row
for (i = 0; i < col; i++)
minFromSource = Math.min(minFromSource,
minDistance[row - 1][i]);
// Minimum distance in the first column
for (i = 0; i < row; i++)
minFromSource = Math.min(minFromSource,
minDistance[i][0]);
// Minimum distance in the last column
for (i = 0; i < row; i++)
minFromSource = Math.min(minFromSource,
minDistance[i][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, 1, 0},
{0, 0, 1, 0, 1},
{0, 0, 1, 0, 1},
{1, 0, 0, 0, 1},
{1, 1, 0, 1, 0 }};
System.out.println(findMinPathminDistance(grid,
sourceRow, sourceCol));
}
}
// This code is contributed by Arnab Kundu
Python3
# 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
C#
// C# implementation of the approach
using System;
using System.Collections.Generic;
class GFG{
// Pair class
class Pair
{
public int first, second;
public 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];
static int [,]visited = new int[row + 1, col + 1];
// Queue for BFS
static Queue<Pair> que = new Queue<Pair>();
// 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 >= 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 findMinPathminDistance(int [,]grid,
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;
int i = 0;
// Precalculate minDistance of each
// grid with R * C
for(i = 0; i < row; i++)
for(int j = 0; j < col; j++)
minDistance[i, j] = row * col;
// Insert source position in queue
que.Enqueue(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.Count > 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.Enqueue(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.Enqueue(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.Enqueue(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.Enqueue(new Pair(cellRow, cellCol - 1));
minDistance[cellRow, cellCol - 1] = Math.Min(
minDistance[cellRow, cellCol - 1],
minDistance[cellRow, cellCol] + 1);
visited[cellRow, cellCol - 1] = 1;
}
// Pop the visited cell
que.Dequeue();
}
i = 0;
// Minimum distance in the first row
for(i = 0; i < col; i++)
minFromSource = Math.Min(minFromSource,
minDistance[0, i]);
// Minimum distance in the last row
for(i = 0; i < col; i++)
minFromSource = Math.Min(minFromSource,
minDistance[row - 1, i]);
// Minimum distance in the first column
for(i = 0; i < row; i++)
minFromSource = Math.Min(minFromSource,
minDistance[i, 0]);
// Minimum distance in the last column
for(i = 0; i < row; i++)
minFromSource = Math.Min(minFromSource,
minDistance[i, 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, 1, 0 },
{ 0, 0, 1, 0, 1 },
{ 0, 0, 1, 0, 1 },
{ 1, 0, 0, 0, 1 },
{ 1, 1, 0, 1, 0 } };
Console.WriteLine(findMinPathminDistance(
grid, sourceRow, sourceCol));
}
}
// This code is contributed by 29AjayKumar
Javascript
<script>
// Javascript implementation of the approach
// Pair class
class Pair
{
constructor(a, b)
{
this.first = a;
this.second = b;
}
}
let row = 5;
let col = 5;
// Global variables for grid, minDistance and visited array
let minDistance=new Array(row + 1);
for(let i = 0; i < row + 1; i++)
{
minDistance[i] = new Array(col+1);
for(let j = 0; j < col + 1; j++)
minDistance[i][j] = 0;
}
let visited = new Array(row + 1);
for(let i = 0; i < row + 1; i++)
{
visited[i] = new Array(col + 1);
for(let j = 0; j < col + 1; j++)
visited[i][j] = 0;
}
// Queue for BFS
let que = [];
// Function to find whether the move is valid or not
function 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 grid
function findMinPathminDistance(grid,sourceRow,sourceCol)
{
// If source is one of the destinations
if (sourceCol == 0 || sourceCol == col - 1
|| sourceRow == 0 || 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 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.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;
}
// Pop the visited cell
que.shift();
}
let i;
// Minimum distance in the first row
for (i = 0; i < col; i++)
minFromSource = Math.min(minFromSource,
minDistance[0][i]);
// Minimum distance in the last row
for (i = 0; i < col; i++)
minFromSource = Math.min(minFromSource,
minDistance[row - 1][i]);
// Minimum distance in the first column
for (i = 0; i < row; i++)
minFromSource = Math.min(minFromSource,
minDistance[i][0]);
// Minimum distance in the last column
for (i = 0; i < row; i++)
minFromSource = Math.min(minFromSource,
minDistance[i][col - 1]);
// If no path exists
if (minFromSource == row * col)
return -1;
// Return the minimum distance
return minFromSource;
}
// Driver code
let sourceRow = 3, sourceCol = 3;
let 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 ]];
document.write(findMinPathminDistance(grid,
sourceRow, sourceCol));
// This code is contributed by avanitrachhadiya2155
</script>
Producción:
2
Publicación traducida automáticamente
Artículo escrito por Shivam.Pradhan y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA