develop algorithms 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

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

develop algorithms

Project Solution

In this project, 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.

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.

You should have single main function that calls all the required functions for Part A, Part

B, and extra credit for all the 3 given input map files one by one.

Coded graph.h file for your reference and provided it for you to refer to and download

on canvas. You do not have to use this file mandatory, but if you are struggling to even

start the project then this should definitely make your life much easier.

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

create 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. Write 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. The map::print() function prints out a map visualization,

with the goal and current position of the car in the map at each move, marked to show

the progress. Hint: consider recursive-DFS.

3. Write 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. The map::print() function prints out a map visualization,

with the goal and current position of the car in the map at each move, marked to show

the progress. Hint: consider stack-based DFS.

4. Write 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. The map::print() function prints out a map visualization, 

with the goal and current position of the car in the map at each move, marked to show

the progress. Hint: consider queue-based BFS.

The code you submit should apply all three findPath functions to each map, one after the

other.

The map input files named map1.txt, map2.txt, and map3.txt can be downloaded from

the canvas. Example of a map input file:

7

10

Start - 0XXXXXXXXX

00000000XX

0X0X0X0XXX

0X0X0X0000

XX0XXX0XXX

X0000000XX

XXXXXXX000Z - Destination

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(g

raph &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. The map::print() function prints out a map visualization,

with the goal and current position of the car in the map at each move, marked to show

the progress. Each function should return true if any paths are found, and false

otherwise.

Note: The use of the additional functions of class map is optional but highly

recommended.

Extra Credit

1. Optimize Bellman-Ford algorithm to reduce the number of iterations and compare the

runtime of the unmodified and modified algorithm for three given input maps. Your 

optimized Bellman-Ford algorithm should call map::print() function. It should also print

the runtime of the unoptimized and optimized versions.

Thus, You should submit a single zip folder within which you need to have 4 files

including, 1) a single ".cpp" code file that includes all the above-required functions called

from a single main function, 2) a single ".h" header file, 3) README file with the compile

and execution instructions, and 4) your pre-compiled ".exe" executable file. On top of

your .cpp code file, .h header file, and README file, you need to mention your name as

comments. You may have an additional PDF file if you want to narrate your additional

observations about running the functions of this project, e.g., drawing the graph to

compare the runtime and explain the results. All submitted code files must be named as

"<your-name>.cpp". For example, it will be "jankibhimani.cpp", "jankibhimani_graph.h",

and "jankibhimani.exe". The zip folder containing all the files should be named as "<yourname>_code.zip". For example, it will be "jankibhimani_code.zip". Please follow the

“Guidelines for Software Engineering Techniques.pdf” and “Assignments and Project

Style and Documentation Guidelines.pdf” made available to you in your Student

Resources module for other document editing and code format guidelines.

Some header files you may need are following, that can be found in you header files zip

folder available to you to download on Canvas.

#include <iostream>

#include <limits.h>

#include "d_except.h"

#include <list>

#include <fstream>

#include "d_matrix.h"

#include <queue>

#include <vector>

 

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