Dada una ruta en forma de array rectangular con pocas minas terrestres colocadas arbitrariamente (marcada como 0), calcule la longitud de la ruta segura más corta posible desde cualquier celda de la primera columna hasta cualquier celda de la última columna de la array. Tenemos que evitar las minas terrestres y sus cuatro celdas adyacentes (izquierda, derecha, arriba y abajo) ya que tampoco son seguras. Solo se nos permite movernos a celdas adyacentes que no son minas terrestres. es decir, la ruta no puede contener movimientos diagonales.
Ejemplos:
Input: A 12 x 10 matrix with landmines marked as 0 [ 1 1 1 1 1 1 1 1 1 1 ] [ 1 0 1 1 1 1 1 1 1 1 ] [ 1 1 1 0 1 1 1 1 1 1 ] [ 1 1 1 1 0 1 1 1 1 1 ] [ 1 1 1 1 1 1 1 1 1 1 ] [ 1 1 1 1 1 0 1 1 1 1 ] [ 1 0 1 1 1 1 1 1 0 1 ] [ 1 1 1 1 1 1 1 1 1 1 ] [ 1 1 1 1 1 1 1 1 1 1 ] [ 0 1 1 1 1 0 1 1 1 1 ] [ 1 1 1 1 1 1 1 1 1 1 ] [ 1 1 1 0 1 1 1 1 1 1 ] Output: Length of shortest safe route is 13 (Highlighted in Bold)
La idea es usar Backtracking. Primero marcamos todas las celdas adyacentes de las minas terrestres como inseguras. Luego, para cada celda segura de la primera columna de la array, avanzamos en todas las direcciones permitidas y verificamos recursivamente si conducen al destino o no. Si se encuentra el destino, actualizamos el valor de la ruta más corta; de lo contrario, si ninguna de las soluciones anteriores funciona, devolvemos falso desde nuestra función.
A continuación se muestra la implementación de la idea anterior:
C++
// C++ program to find shortest safe Route in
// the matrix with landmines
#include <bits/stdc++.h>
using namespace std;
#define R 12
#define C 10
// These arrays are used to get row and column
// numbers of 4 neighbours of a given cell
int rowNum[] = { -1, 0, 0, 1 };
int colNum[] = { 0, -1, 1, 0 };
// A function to check if a given cell (x, y)
// can be visited or not
bool isSafe(int mat[R][C], int visited[R][C],
int x, int y)
{
if (mat[x][y] == 0 || visited[x][y])
return false;
return true;
}
// A function to check if a given cell (x, y) is
// a valid cell or not
bool isValid(int x, int y)
{
if (x < R && y < C && x >= 0 && y >= 0)
return true;
return false;
}
// A function to mark all adjacent cells of
// landmines as unsafe. Landmines are shown with
// number 0
void markUnsafeCells(int mat[R][C])
{
for (int i = 0; i < R; i++)
{
for (int j = 0; j < C; j++)
{
// if a landmines is found
if (mat[i][j] == 0)
{
// mark all adjacent cells
for (int k = 0; k < 4; k++)
if (isValid(i + rowNum[k], j + colNum[k]))
mat[i + rowNum[k]][j + colNum[k]] = -1;
}
}
}
// mark all found adjacent cells as unsafe
for (int i = 0; i < R; i++)
{
for (int j = 0; j < C; j++)
{
if (mat[i][j] == -1)
mat[i][j] = 0;
}
}
// Uncomment below lines to print the path
/*for (int i = 0; i < R; i++)
{
for (int j = 0; j < C; j++)
{
cout << std::setw(3) << mat[i][j];
}
cout << endl;
}*/
}
// Function to find shortest safe Route in the
// matrix with landmines
// mat[][] - binary input matrix with safe cells marked as 1
// visited[][] - store info about cells already visited in
// current route
// (i, j) are coordinates of the current cell
// min_dist --> stores minimum cost of shortest path so far
// dist --> stores current path cost
void findShortestPathUtil(int mat[R][C], int visited[R][C],
int i, int j, int &min_dist, int dist)
{
// if destination is reached
if (j == C-1)
{
// update shortest path found so far
min_dist = min(dist, min_dist);
return;
}
// if current path cost exceeds minimum so far
if (dist > min_dist)
return;
// include (i, j) in current path
visited[i][j] = 1;
// Recurse for all safe adjacent neighbours
for (int k = 0; k < 4; k++)
{
if (isValid(i + rowNum[k], j + colNum[k]) &&
isSafe(mat, visited, i + rowNum[k], j + colNum[k]))
{
findShortestPathUtil(mat, visited, i + rowNum[k],
j + colNum[k], min_dist, dist + 1);
}
}
// Backtrack
visited[i][j] = 0;
}
// A wrapper function over findshortestPathUtil()
void findShortestPath(int mat[R][C])
{
// stores minimum cost of shortest path so far
int min_dist = INT_MAX;
// create a boolean matrix to store info about
// cells already visited in current route
int visited[R][C];
// mark adjacent cells of landmines as unsafe
markUnsafeCells(mat);
// start from first column and take minimum
for (int i = 0; i < R; i++)
{
// if path is safe from current cell
if (mat[i][0] == 1)
{
// initialize visited to false
memset(visited, 0, sizeof visited);
// find shortest route from (i, 0) to any
// cell of last column (x, C - 1) where
// 0 <= x < R
findShortestPathUtil(mat, visited, i, 0,
min_dist, 0);
// if min distance is already found
if(min_dist == C - 1)
break;
}
}
// if destination can be reached
if (min_dist != INT_MAX)
cout << "Length of shortest safe route is "
<< min_dist;
else // if the destination is not reachable
cout << "Destination not reachable from "
<< "given source";
}
// Driver code
int main()
{
// input matrix with landmines shown with number 0
int mat[R][C] =
{
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 },
{ 1, 0, 1, 1, 1, 1, 1, 1, 0, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 }
};
// find shortest path
findShortestPath(mat);
return 0;
}
Java
// Java program to find shortest safe Route
// in the matrix with landmines
import java.util.Arrays;
class GFG{
static final int R = 12;
static final int C = 10;
// These arrays are used to get row and column
// numbers of 4 neighbours of a given cell
static int rowNum[] = { -1, 0, 0, 1 };
static int colNum[] = { 0, -1, 1, 0 };
static int min_dist;
// A function to check if a given cell (x, y)
// can be visited or not
static boolean isSafe(int[][] mat, boolean[][] visited,
int x, int y)
{
if (mat[x][y] == 0 || visited[x][y])
return false;
return true;
}
// A function to check if a given cell (x, y) is
// a valid cell or not
static boolean isValid(int x, int y)
{
if (x < R && y < C && x >= 0 && y >= 0)
return true;
return false;
}
// A function to mark all adjacent cells of
// landmines as unsafe. Landmines are shown with
// number 0
static void markUnsafeCells(int[][] mat)
{
for(int i = 0; i < R; i++)
{
for(int j = 0; j < C; j++)
{
// If a landmines is found
if (mat[i][j] == 0)
{
// Mark all adjacent cells
for(int k = 0; k < 4; k++)
if (isValid(i + rowNum[k], j + colNum[k]))
mat[i + rowNum[k]][j + colNum[k]] = -1;
}
}
}
// Mark all found adjacent cells as unsafe
for(int i = 0; i < R; i++)
{
for(int j = 0; j < C; j++)
{
if (mat[i][j] == -1)
mat[i][j] = 0;
}
}
// Uncomment below lines to print the path
/*
* for (int i = 0; i < R; i++) {
* for (int j = 0; j < C; j++) { cout <<
* std::setw(3) << mat[i][j]; } cout << endl; }
*/
}
// Function to find shortest safe Route in the
// matrix with landmines
// mat[][] - binary input matrix with safe cells marked as 1
// visited[][] - store info about cells already visited in
// current route
// (i, j) are coordinates of the current cell
// min_dist --> stores minimum cost of shortest path so far
// dist --> stores current path cost
static void findShortestPathUtil(int[][] mat,
boolean[][] visited,
int i, int j, int dist)
{
// If destination is reached
if (j == C - 1)
{
// Update shortest path found so far
min_dist = Math.min(dist, min_dist);
return;
}
// If current path cost exceeds minimum so far
if (dist > min_dist)
return;
// include (i, j) in current path
visited[i][j] = true;
// Recurse for all safe adjacent neighbours
for(int k = 0; k < 4; k++)
{
if (isValid(i + rowNum[k], j + colNum[k]) &&
isSafe(mat, visited, i + rowNum[k],
j + colNum[k]))
{
findShortestPathUtil(mat, visited, i + rowNum[k],
j + colNum[k], dist + 1);
}
}
// Backtrack
visited[i][j] = false;
}
// A wrapper function over findshortestPathUtil()
static void findShortestPath(int[][] mat)
{
// Stores minimum cost of shortest path so far
min_dist = Integer.MAX_VALUE;
// Create a boolean matrix to store info about
// cells already visited in current route
boolean[][] visited = new boolean[R][C];
// Mark adjacent cells of landmines as unsafe
markUnsafeCells(mat);
// Start from first column and take minimum
for(int i = 0; i < R; i++)
{
// If path is safe from current cell
if (mat[i][0] == 1)
{
// Initialize visited to false
for(int k = 0; k < R; k++)
{
Arrays.fill(visited[k], false);
}
// Find shortest route from (i, 0) to any
// cell of last column (x, C - 1) where
// 0 <= x < R
findShortestPathUtil(mat, visited, i, 0, 0);
// If min distance is already found
if (min_dist == C - 1)
break;
}
}
// If destination can be reached
if (min_dist != Integer.MAX_VALUE)
System.out.println("Length of shortest " +
"safe route is " + min_dist);
else
// If the destination is not reachable
System.out.println("Destination not " +
"reachable from given source");
}
// Driver code
public static void main(String[] args)
{
// Input matrix with landmines shown with number 0
int[][] mat = {
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 },
{ 1, 0, 1, 1, 1, 1, 1, 1, 0, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 } };
// Find shortest path
findShortestPath(mat);
}
}
// This code is contributed by sanjeev2552
Python3
# Python3 program to find shortest safe Route
# in the matrix with landmines
import sys
R = 12
C = 10
# These arrays are used to get row and column
# numbers of 4 neighbours of a given cell
rowNum = [ -1, 0, 0, 1 ]
colNum = [ 0, -1, 1, 0 ]
min_dist = sys.maxsize
# A function to check if a given cell (x, y)
# can be visited or not
def isSafe(mat, visited, x, y):
if (mat[x][y] == 0 or visited[x][y]):
return False
return True
# A function to check if a given cell (x, y) is
# a valid cell or not
def isValid(x, y):
if (x < R and y < C and x >= 0 and y >= 0):
return True
return False
# A function to mark all adjacent cells of
# landmines as unsafe. Landmines are shown with
# number 0
def markUnsafeCells(mat):
for i in range(R):
for j in range(C):
# If a landmines is found
if (mat[i][j] == 0):
# Mark all adjacent cells
for k in range(4):
if (isValid(i + rowNum[k], j + colNum[k])):
mat[i + rowNum[k]][j + colNum[k]] = -1
# Mark all found adjacent cells as unsafe
for i in range(R):
for j in range(C):
if (mat[i][j] == -1):
mat[i][j] = 0
""" Uncomment below lines to print the path
/*
* for (int i = 0; i < R; i++) {
* for (int j = 0; j < C; j++) { cout <<
* std::setw(3) << mat[i][j]; } cout << endl; }
*"""
# Function to find shortest safe Route in the
# matrix with landmines
# mat[][] - binary input matrix with safe cells marked as 1
# visited[][] - store info about cells already visited in
# current route
# (i, j) are coordinates of the current cell
# min_dist --> stores minimum cost of shortest path so far
# dist --> stores current path cost
def findShortestPathUtil(mat, visited, i, j, dist):
global min_dist
# If destination is reached
if (j == C - 1):
# Update shortest path found so far
min_dist = min(dist, min_dist)
return
# If current path cost exceeds minimum so far
if (dist > min_dist):
return
# include (i, j) in current path
visited[i][j] = True
# Recurse for all safe adjacent neighbours
for k in range(4):
if (isValid(i + rowNum[k], j + colNum[k]) and isSafe(mat, visited, i + rowNum[k], j + colNum[k])):
findShortestPathUtil(mat, visited, i + rowNum[k], j + colNum[k], dist + 1)
# Backtrack
visited[i][j] = False
# A wrapper function over findshortestPathUtil()
def findShortestPath(mat):
global min_dist
# Stores minimum cost of shortest path so far
min_dist = sys.maxsize
# Create a boolean matrix to store info about
# cells already visited in current route
visited = [[False for i in range(C)] for j in range(R)]
# Mark adjacent cells of landmines as unsafe
markUnsafeCells(mat)
# Start from first column and take minimum
for i in range(R):
# If path is safe from current cell
if (mat[i][0] == 1):
# Find shortest route from (i, 0) to any
# cell of last column (x, C - 1) where
# 0 <= x < R
findShortestPathUtil(mat, visited, i, 0, 0)
# If min distance is already found
if (min_dist == C - 1):
break
# If destination can be reached
if (min_dist != sys.maxsize):
print("Length of shortest safe route is", min_dist)
else:
# If the destination is not reachable
print("Destination not reachable from given source")
mat = [
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 ],
[ 1, 0, 1, 1, 1, 1, 1, 1, 0, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 ] ]
# Find shortest path
findShortestPath(mat)
# This code is contributed by mukesh07.
C#
// C# program to find shortest safe Route
// in the matrix with landmines
using System;
using System.Collections.Generic;
class GFG {
static int R = 12;
static int C = 10;
// These arrays are used to get row and column
// numbers of 4 neighbours of a given cell
static int[] rowNum = { -1, 0, 0, 1 };
static int[] colNum = { 0, -1, 1, 0 };
static int min_dist;
// A function to check if a given cell (x, y)
// can be visited or not
static bool isSafe(int[,] mat, bool[,] visited, int x, int y)
{
if (mat[x,y] == 0 || visited[x,y])
return false;
return true;
}
// A function to check if a given cell (x, y) is
// a valid cell or not
static bool isValid(int x, int y)
{
if (x < R && y < C && x >= 0 && y >= 0)
return true;
return false;
}
// A function to mark all adjacent cells of
// landmines as unsafe. Landmines are shown with
// number 0
static void markUnsafeCells(int[,] mat)
{
for(int i = 0; i < R; i++)
{
for(int j = 0; j < C; j++)
{
// If a landmines is found
if (mat[i,j] == 0)
{
// Mark all adjacent cells
for(int k = 0; k < 4; k++)
if (isValid(i + rowNum[k], j + colNum[k]))
mat[i + rowNum[k],j + colNum[k]] = -1;
}
}
}
// Mark all found adjacent cells as unsafe
for(int i = 0; i < R; i++)
{
for(int j = 0; j < C; j++)
{
if (mat[i,j] == -1)
mat[i,j] = 0;
}
}
// Uncomment below lines to print the path
/*
* for (int i = 0; i < R; i++) {
* for (int j = 0; j < C; j++) { cout <<
* std::setw(3) << mat[i][j]; } cout << endl; }
*/
}
// Function to find shortest safe Route in the
// matrix with landmines
// mat[][] - binary input matrix with safe cells marked as 1
// visited[][] - store info about cells already visited in
// current route
// (i, j) are coordinates of the current cell
// min_dist --> stores minimum cost of shortest path so far
// dist --> stores current path cost
static void findShortestPathUtil(int[,] mat,
bool[,] visited,
int i, int j, int dist)
{
// If destination is reached
if (j == C - 1)
{
// Update shortest path found so far
min_dist = Math.Min(dist, min_dist);
return;
}
// If current path cost exceeds minimum so far
if (dist > min_dist)
return;
// include (i, j) in current path
visited[i,j] = true;
// Recurse for all safe adjacent neighbours
for(int k = 0; k < 4; k++)
{
if (isValid(i + rowNum[k], j + colNum[k]) &&
isSafe(mat, visited, i + rowNum[k], j + colNum[k]))
{
findShortestPathUtil(mat, visited, i + rowNum[k], j + colNum[k], dist + 1);
}
}
// Backtrack
visited[i,j] = false;
}
// A wrapper function over findshortestPathUtil()
static void findShortestPath(int[,] mat)
{
// Stores minimum cost of shortest path so far
min_dist = Int32.MaxValue;
// Create a boolean matrix to store info about
// cells already visited in current route
bool[,] visited = new bool[R,C];
// Mark adjacent cells of landmines as unsafe
markUnsafeCells(mat);
// Start from first column and take minimum
for(int i = 0; i < R; i++)
{
// If path is safe from current cell
if (mat[i,0] == 1)
{
// Find shortest route from (i, 0) to any
// cell of last column (x, C - 1) where
// 0 <= x < R
findShortestPathUtil(mat, visited, i, 0, 0);
// If min distance is already found
if (min_dist == C - 1)
break;
}
}
// If destination can be reached
if (min_dist != Int32.MaxValue)
Console.WriteLine("Length of shortest " +
"safe route is " + min_dist);
else
// If the destination is not reachable
Console.WriteLine("Destination not " +
"reachable from given source");
}
static void Main()
{
// Input matrix with landmines shown with number 0
int[,] mat = {
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 },
{ 1, 0, 1, 1, 1, 1, 1, 1, 0, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 } };
// Find shortest path
findShortestPath(mat);
}
}
// This code is contributed by rameshtravel07.
Javascript
<script>
// Javascript program to find shortest safe Route
// in the matrix with landmines
let R = 12;
let C = 10;
// These arrays are used to get row and column
// numbers of 4 neighbours of a given cell
let rowNum = [ -1, 0, 0, 1 ];
let colNum = [ 0, -1, 1, 0 ];
let min_dist;
// A function to check if a given cell (x, y)
// can be visited or not
function isSafe(mat, visited, x, y)
{
if (mat[x][y] == 0 || visited[x][y])
return false;
return true;
}
// A function to check if a given cell (x, y) is
// a valid cell or not
function isValid(x, y)
{
if (x < R && y < C && x >= 0 && y >= 0)
return true;
return false;
}
// A function to mark all adjacent cells of
// landmines as unsafe. Landmines are shown with
// number 0
function markUnsafeCells(mat)
{
for(let i = 0; i < R; i++)
{
for(let j = 0; j < C; j++)
{
// If a landmines is found
if (mat[i][j] == 0)
{
// Mark all adjacent cells
for(let k = 0; k < 4; k++)
if (isValid(i + rowNum[k], j + colNum[k]))
mat[i + rowNum[k]][j + colNum[k]] = -1;
}
}
}
// Mark all found adjacent cells as unsafe
for(let i = 0; i < R; i++)
{
for(let j = 0; j < C; j++)
{
if (mat[i][j] == -1)
mat[i][j] = 0;
}
}
// Uncomment below lines to print the path
/*
* for (int i = 0; i < R; i++) {
* for (int j = 0; j < C; j++) { cout <<
* std::setw(3) << mat[i][j]; } cout << endl; }
*/
}
// Function to find shortest safe Route in the
// matrix with landmines
// mat[][] - binary input matrix with safe cells marked as 1
// visited[][] - store info about cells already visited in
// current route
// (i, j) are coordinates of the current cell
// min_dist --> stores minimum cost of shortest path so far
// dist --> stores current path cost
function findShortestPathUtil(mat, visited, i, j, dist)
{
// If destination is reached
if (j == C - 1)
{
// Update shortest path found so far
min_dist = Math.min(dist, min_dist);
return;
}
// If current path cost exceeds minimum so far
if (dist > min_dist)
return;
// include (i, j) in current path
visited[i][j] = true;
// Recurse for all safe adjacent neighbours
for(let k = 0; k < 4; k++)
{
if (isValid(i + rowNum[k], j + colNum[k]) &&
isSafe(mat, visited, i + rowNum[k],
j + colNum[k]))
{
findShortestPathUtil(mat, visited, i + rowNum[k],
j + colNum[k], dist + 1);
}
}
// Backtrack
visited[i][j] = false;
}
// A wrapper function over findshortestPathUtil()
function findShortestPath(mat)
{
// Stores minimum cost of shortest path so far
min_dist = Number.MAX_VALUE;
// Create a boolean matrix to store info about
// cells already visited in current route
let visited = new Array(R);
for(let i = 0; i < R; i++)
{
visited[i] = new Array(C);
for(let j = 0; j < C; j++)
{
visited[i][j] = false;
}
}
// Mark adjacent cells of landmines as unsafe
markUnsafeCells(mat);
// Start from first column and take minimum
for(let i = 0; i < R; i++)
{
// If path is safe from current cell
if (mat[i][0] == 1)
{
// Find shortest route from (i, 0) to any
// cell of last column (x, C - 1) where
// 0 <= x < R
findShortestPathUtil(mat, visited, i, 0, 0);
// If min distance is already found
if (min_dist == C - 1)
break;
}
}
// If destination can be reached
if (min_dist != Number.MAX_VALUE)
document.write("Length of shortest " +
"safe route is " + min_dist + "</br>");
else
// If the destination is not reachable
document.write("Destination not " +
"reachable from given source" + "</br>");
}
// Input matrix with landmines shown with number 0
let mat = [
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 ],
[ 1, 0, 1, 1, 1, 1, 1, 1, 0, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 ] ];
// Find shortest path
findShortestPath(mat);
// This code is contributed by decode2207.
</script>
Producción
Length of shortest safe route is 13
Otro método: se puede resolver en tiempo polinomial con la ayuda de Breadth First Search. Ponga en cola las celdas con 1 valor en la cola con la distancia como 0. A medida que avanza el BFS, se calcula la ruta más corta a cada celda desde la primera columna. Finalmente, para las celdas alcanzables en la última columna, genere la distancia mínima.
La implementación en C++ es la siguiente:
C++
// C++ program to find shortest safe Route in
// the matrix with landmines
#include <bits/stdc++.h>
using namespace std;
#define R 12
#define C 10
struct Key{
int x,y;
Key(int i,int j){ x=i;y=j;};
};
// These arrays are used to get row and column
// numbers of 4 neighbours of a given cell
int rowNum[] = { -1, 0, 0, 1 };
int colNum[] = { 0, -1, 1, 0 };
// A function to check if a given cell (x, y) is
// a valid cell or not
bool isValid(int x, int y)
{
if (x < R && y < C && x >= 0 && y >= 0)
return true;
return false;
}
// A function to mark all adjacent cells of
// landmines as unsafe. Landmines are shown with
// number 0
void findShortestPath(int mat[R][C]){
int i,j;
for (i = 0; i < R; i++)
{
for (j = 0; j < C; j++)
{
// if a landmines is found
if (mat[i][j] == 0)
{
// mark all adjacent cells
for (int k = 0; k < 4; k++)
if (isValid(i + rowNum[k], j + colNum[k]))
mat[i + rowNum[k]][j + colNum[k]] = -1;
}
}
}
// mark all found adjacent cells as unsafe
for (i = 0; i < R; i++)
{
for (j = 0; j < C; j++)
{
if (mat[i][j] == -1)
mat[i][j] = 0;
}
}
int dist[R][C];
for(i=0;i<R;i++){
for(j=0;j<C;j++)
dist[i][j] = -1;
}
queue<Key> q;
for(i=0;i<R;i++){
if(mat[i][0] == 1){
q.push(Key(i,0));
dist[i][0] = 0;
}
}
while(!q.empty()){
Key k = q.front();
q.pop();
int d = dist[k.x][k.y];
int x = k.x;
int y = k.y;
for (int k = 0; k < 4; k++) {
int xp = x + rowNum[k];
int yp = y + colNum[k];
if(isValid(xp,yp) && dist[xp][yp] == -1 && mat[xp][yp] == 1){
dist[xp][yp] = d+1;
q.push(Key(xp,yp));
}
}
}
// stores minimum cost of shortest path so far
int ans = INT_MAX;
// start from first column and take minimum
for(i=0;i<R;i++){
if(mat[i][C-1] == 1 && dist[i][C-1] != -1){
ans = min(ans,dist[i][C-1]);
}
}
// if destination can be reached
if(ans == INT_MAX)
cout << "NOT POSSIBLE\n";
else// if the destination is not reachable
cout << "Length of shortest safe route is " << ans << endl;
}
// Driver code
int main(){
// input matrix with landmines shown with number 0
int mat[R][C] =
{
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 },
{ 1, 0, 1, 1, 1, 1, 1, 1, 0, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 }
};
// find shortest path
findShortestPath(mat);
}
Java
// Java program to find shortest safe Route in
// the matrix with landmines
import java.util.LinkedList;
import java.util.Queue;
public class GFG {
static class Key {
int x, y;
Key(int i, int j)
{
x = i;
y = j;
};
}
static int R = 12, C = 10;
// These arrays are used to get row and column
// numbers of 4 neighbours of a given cell
static int rowNum[] = { -1, 0, 0, 1 };
static int colNum[] = { 0, -1, 1, 0 };
// A function to check if a given cell (x, y) is
// a valid cell or not
static boolean isValid(int x, int y)
{
if (x < R && y < C && x >= 0 && y >= 0)
return true;
return false;
}
// A function to mark all adjacent cells of
// landmines as unsafe. Landmines are shown with
// number 0
static void findShortestPath(int mat[][])
{
int i, j;
for (i = 0; i < R; i++) {
for (j = 0; j < C; j++) {
// if a landmines is found
if (mat[i][j] == 0) {
// mark all adjacent cells
for (int k = 0; k < 4; k++)
if (isValid(i + rowNum[k],
j + colNum[k]))
mat[i + rowNum[k]]
[j + colNum[k]]
= -1;
}
}
}
// mark all found adjacent cells as unsafe
for (i = 0; i < R; i++) {
for (j = 0; j < C; j++) {
if (mat[i][j] == -1)
mat[i][j] = 0;
}
}
int dist[][] = new int[R][C];
for (i = 0; i < R; i++) {
for (j = 0; j < C; j++)
dist[i][j] = -1;
}
Queue<Key> q = new LinkedList<Key>();
for (i = 0; i < R; i++) {
if (mat[i][0] == 1) {
q.add(new Key(i, 0));
dist[i][0] = 0;
}
}
while (!q.isEmpty()) {
Key k = q.peek();
q.poll();
int d = dist[k.x][k.y];
int x = k.x;
int y = k.y;
for (int ki = 0; ki < 4; ki++) {
int xp = x + rowNum[ki];
int yp = y + colNum[ki];
if (isValid(xp, yp) && dist[xp][yp] == -1
&& mat[xp][yp] == 1) {
dist[xp][yp] = d + 1;
q.add(new Key(xp, yp));
}
}
}
// stores minimum cost of shortest path so far
int ans = Integer.MAX_VALUE;
// start from first column and take minimum
for (i = 0; i < R; i++) {
if (mat[i][C - 1] == 1
&& dist[i][C - 1] != -1) {
ans = Math.min(ans, dist[i][C - 1]);
}
}
// if destination can be reached
if (ans == Integer.MAX_VALUE)
System.out.println("NOT POSSIBLE");
else // if the destination is not reachable
System.out.println(
"Length of shortest safe route is " + ans);
}
// Driver code
public static void main(String[] args)
{
// input matrix with landmines shown with number 0
int mat[][] = { { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 },
{ 1, 0, 1, 1, 1, 1, 1, 1, 0, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 },
{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 },
{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 } };
// find shortest path
findShortestPath(mat);
}
}
// This code is contributed by Lovely Jain
Python3
# Python program to find shortest safe Route in
# the matrix with landmines
import sys
R = 12
C = 10
class Key:
def __init__(self,i, j):
self.x = i
self.y = j
# These arrays are used to get row and column
# numbers of 4 neighbours of a given cell
rowNum = [ -1, 0, 0, 1 ]
colNum = [ 0, -1, 1, 0 ]
# A function to check if a given cell (x, y) is
# a valid cell or not
def isValid(x, y):
if (x < R and y < C and x >= 0 and y >= 0):
return True
return False
# A function to mark all adjacent cells of
# landmines as unsafe. Landmines are shown with
# number 0
def findShortestPath(mat):
for i in range(R):
for j in range(C):
# if a landmines is found
if (mat[i][j] == 0):
# mark all adjacent cells
for k in range(4):
if (isValid(i + rowNum[k], j + colNum[k])):
mat[i + rowNum[k]][j + colNum[k]] = -1
# mark all found adjacent cells as unsafe
for i in range(R):
for j in range(C):
if (mat[i][j] == -1):
mat[i][j] = 0
dist = [[-1 for i in range(C)]for j in range(R)]
q = []
for i in range(R):
if(mat[i][0] == 1):
q.append(Key(i,0))
dist[i][0] = 0
while(len(q) != 0):
k = q[0]
q = q[1:]
d = dist[k.x][k.y]
x = k.x
y = k.y
for k in range(4):
xp = x + rowNum[k]
yp = y + colNum[k]
if(isValid(xp,yp) and dist[xp][yp] == -1 and mat[xp][yp] == 1):
dist[xp][yp] = d+1
q.append(Key(xp,yp))
# stores minimum cost of shortest path so far
ans = sys.maxsize
# start from first column and take minimum
for i in range(R):
if(mat[i][C-1] == 1 and dist[i][C-1] != -1):
ans = min(ans,dist[i][C-1])
# if destination can be reached
if(ans == sys.maxsize):
print("NOT POSSIBLE")
else: # if the destination is not reachable
print(f"Length of shortest safe route is {ans}")
# Driver code
# input matrix with landmines shown with number 0
mat =[
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 ],
[ 1, 0, 1, 1, 1, 1, 1, 1, 0, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 ]
]
# find shortest path
findShortestPath(mat)
# This code is contributed by shinjanpatra
Javascript
<script>
// JavaScript program to find shortest safe Route in
// the matrix with landmines
const R = 12
const C = 10
class Key
{
constructor(i, j)
{
this.x = i
this.y = j
}
}
// These arrays are used to get row and column
// numbers of 4 neighbours of a given cell
let rowNum = [ -1, 0, 0, 1 ]
let colNum = [ 0, -1, 1, 0 ]
// A function to check if a given cell (x, y) is
// a valid cell or not
function isValid(x, y)
{
if (x < R && y < C && x >= 0 && y >= 0)
return true
return false
}
// A function to mark all adjacent cells of
// landmines as unsafe. Landmines are shown with
// number 0
function findShortestPath(mat){
let i,j
for (i = 0;i < R;i++)
{
for (j = 0;j < C;j++)
{
// if a landmines is found
if (mat[i][j] == 0)
{
// mark all adjacent cells
for (let k = 0;k < 4;k++)
if (isValid(i + rowNum[k], j + colNum[k]))
mat[i + rowNum[k]][j + colNum[k]] = -1
}
}
}
// mark all found adjacent cells as unsafe
for (i = 0;i < R;i++)
{
for (j = 0;j < C;j++)
{
if (mat[i][j] == -1)
mat[i][j] = 0
}
}
let dist = new Array(R);
for(i = 0; i < R; i++){
dist[i] = new Array(C).fill(-1);
}
let q = [];
for(i = 0; i < R; i++){
if(mat[i][0] == 1){
q.push(new Key(i,0))
dist[i][0] = 0
}
}
while(q.length != 0){
let k = q.shift()
let d = dist[k.x][k.y]
let x = k.x
let y = k.y
for (let k = 0;k < 4;k++) {
let xp = x + rowNum[k]
let yp = y + colNum[k]
if(isValid(xp,yp) && dist[xp][yp] == -1 && mat[xp][yp] == 1){
dist[xp][yp] = d+1
q.push(new Key(xp,yp))
}
}
}
// stores minimum cost of shortest path so far
let ans = Number.MAX_VALUE
// start from first column and take minimum
for(let i = 0; i < R; i++)
{
if(mat[i][C-1] == 1 && dist[i][C-1] != -1){
ans = Math.min(ans,dist[i][C-1])
}
}
// if destination can be reached
if(ans == Number.MAX_VALUE)
document.write("NOT POSSIBLE","</br>")
else // if the destination is not reachable
document.write("Length of shortest safe route is ",ans,"</br>")
}
// Driver code
// input matrix with landmines shown with number 0
let mat =[
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 0, 1, 1, 1, 1 ],
[ 1, 0, 1, 1, 1, 1, 1, 1, 0, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 1, 1, 1, 1, 0, 1, 1, 1, 1 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 ]
]
// find shortest path
findShortestPath(mat)
// This code is contributed by shinjanpatra
</script>
Producción
Length of shortest safe route is 13
Este artículo es una contribución de Aditya Goel . Si te gusta GeeksforGeeks y te gustaría contribuir, también puedes escribir un artículo usando write.geeksforgeeks.org o enviar tu artículo por correo a review-team@geeksforgeeks.org. Vea su artículo que aparece en la página principal de GeeksforGeeks y ayude a otros Geeks.
Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA