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you will develop algorithms that find road routes through the bridges to travel between islands.The input is a text file containing data about the given map. Each file begins with the number of rows and columns in the map considered as maximum latitudes and maximum longitudes respectively on the map. The character “X” in the file represents the water that means if a cell contains “X” then the traveler is not allowed to occupy that cell as this car is not drivable on water. The character “0” in the file represents the road connected island. That means if a cell contains “0” then the traveler is allowed to occupy that cell as this car can drive on roads.
The traveler starts at the island located at latitude = 0 and longitude = 0 (i.e., (0,0)) in the upper left corner, and the goal is to drive to the island located at (MaxLattitude-1, MaxLongitudes-1) in the lower right corner. A legal move from an island is to move left, right, up, or down to an immediately adjacent cell that has road connectivity which means a cell that contains “0”. Moving off any edge of the map is not allowed.
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Print paths as explicitly specified for all the functions in Part A, Part B, and extra credit on the console.
Input: The map files
Output: Print paths as explicitly specified for all the functions in Part A, Part B, and extra credit on the console.
Part A
Consider the following class map,
class map
{
public:
map(ifstream &fin);
void print(int,int,int,int);
bool isLegal(int i, int j);
void setMap(int i, int j, int n);
int getMap(int i, int j) const;
int getReverseMapI(int n) const;
int getReverseMapJ(int n) const;
void mapToGraph(graph &g);
bool findPathRecursive(graph &g, stack<int> &moves);
bool findPathNonRecursive1(graph &g, stack<int> &moves);
bool findPathNonRecursive2(graph &g, queue<int> &moves);
bool findShortestPath1(graph &g, stack<int> &bestMoves);
bool findShortestPath2(graph &, vector<int> &bestMoves);
void map::printPath(stack<int> &s);
int numRows(){return rows;};
int numCols(){return cols;};
private:
int rows; // number of latitudes/rows in the map
int cols; // number of longitudes/columns in the map
matrix<bool> value;
matrix<int> mapping; // Mapping from latitude and longitude co-ordinates (i,j) values to node index values
vector<int> reverseMapI; // Mapping from node index values to map latitude i value
vector<int> reverseMapJ; // Mapping from node index values to map longitude j value
};
1. Using the above class map, write function void map::mapToGraph(graph &g){…} to createe a graph g that represents the legal moves in the map m. Each vertex should represent a cell, and each edge should represent a legal move between adjacent cells.
2. Writee a recursive function findPathRecursive(graph &g, stack<int> &moves) that looks for a path from the start island to the destination island. If a path from the start to the destination exists, your function should call the map::printPath() function that should print a sequence of correct moves (Go left, Go right, Go down, Go up, etc.). If no path from the start to the destination exists, the program should print, “No path exists”. If a solution exists the solver should also simulate the solution to each map by calling the map::print() function. Hint: consider recursive-DFS.
3. Writee a function findPathNonRecursive1(graph &g, stack<int> &moves) that does the same thing as in 2, but by using stack and without using recursion. If a path from the start to the destination exists, your function should call the map::printPath() function that should print a sequence of correct moves (Go left, Go right, Go down, Go up, etc.). If no path from the start to the destination exists, the program should print, “No path exists”. If a solution exists the solver should also simulate the solution to each map by calling the map::print() function. Hint: consider stack-based DFS.
4. Writee a function findPathNonRecursive2(graph &g, queue<int> &moves) that does the same thing as in 2, but by using queue and without using recursion. If a path from the start to the destination exists, your function should call the map::printPath() function that should print a sequence of correct moves (Go left, Go right, Go down, Go up, etc.). If no path from the start to the destination exists, the program should print, “No path exists”. If a solution exists the solver should also simulate the solution to each map by calling the map::print() function. Hint: consider queue-based BFS.
Part B
The shortest path on a map is a path from the start to the destination with the smallest number of intermediate islands, that is the path with the least number of intermediate “0”.
1. Write two functions findShortestPath1(graph &g, stack<int> &bestMoves) and findShortestPath2(graph &g, stack<int> &bestMoves) that each finds the shortest path on a map if a path from the start to the destination exists. The first algorithm should use Dijkstra algorithm and the second algorithm should use Bellman-Ford algorithm to find the shortest paths. In each case, if a solution exists the solver should call the map::printPath() function that should print a sequence of correct moves (Go left, Go right, Go down, Go up, etc.). If no path from the start to the destination exists, the program should print, “No path exists”. If a solution exists the solver should also simulate the solution to each map by calling the map::print() function. Each function should return true if any paths are found, and false otherwise.
