Find shortest safe route in a path with landmines

Last Updated : 22 Dec, 2023

Given a path in the form of a rectangular matrix having few landmines arbitrarily placed (marked as 0), calculate length of the shortest safe route possible from any cell in the first column to any cell in the last column of the matrix. We have to avoid landmines and their four adjacent cells (left, right, above and below) as they are also unsafe. We are allowed to move to only adjacent cells which are not landmines. i.e. the route cannot contains any diagonal moves.

Examples:

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)

The idea is to use Backtracking. We first mark all adjacent cells of the landmines as unsafe. Then for each safe cell of first column of the matrix, we move forward in all allowed directions and recursively checks if they leads to the destination or not. If destination is found, we update the value of shortest path else if none of the above solutions work we return false from our function.

Below is the implementation of above idea:

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# 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>

Output

Length of shortest safe route is 13

Time Complexity: O(4^(R * C)), where R is number of rows and C are the number of columns in the given matrix.
Auxiliary Space: O(R * C), as we are using extra space like visted[R][C].

Another method: It can be solved in polynomial time with the help of Breadth First Search. Enqueue the cells with 1 value in the queue with the distance as 0. As the BFS proceeds, shortest path to each cell from the first column is computed. Finally for the reachable cells in the last column, output the minimum distance.

The implementation in C++ is as follows:

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

// C# program to find shortest safe Route in // the matrix with landmines using System; using System.Collections.Generic;  class Key {     public int x, y;     public Key(int i, int j)     {         x = i;         y = j;     } }  public class GFG {            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 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 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;         }         List<Key> q = new List<Key>();          for (i = 0; i < R; i++) {             if (mat[i, 0] == 1) {                 q.Add(new Key(i, 0));                 dist[i, 0] = 0;             }         }          while (q.Count != 0) {             Key k = q[0];             q.RemoveAt(0);              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 = Int32.MaxValue;         // 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 == Int32.MaxValue)             Console.WriteLine("NOT POSSIBLE");          else // if the destination is not reachable             Console.WriteLine(                 "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 phasing17

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>

Output

Length of shortest safe route is 13

Time Complexity: O(r * c), where r and c are the number of rows and columns in the given matrix respectively.
Auxiliary Space: O(r * c)

Printing all solutions in N-Queen Problem

Aditya Goel

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Find shortest safe route in a path with landmines

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