Find shortest safe route in a path with landmines - GeeksforGeeks
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.
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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.
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.
// These arrays are used to get row and column// numbers of 4 neighbours of a given cellint 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 notbool 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 notbool 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 0void 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 costvoid 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) { // 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";}