Find shortest safe route in a path with landmines

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)

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

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 C++ implementation of above idea –

 // C++ program to find shortest safe Route in // the matrix with landmines #include 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 cordinates 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] == 1)         {             // initailize 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; }

Output:

Length of shortest safe route is 13

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++ program to find shortest safe Route in // the matrix with landmines #include 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 q;        for(i=0;i

Output:

Length of shortest safe route is 13

This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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