ICT208 Algorithms and Data Structures Assessment 3: Recursion Case Study 2 Linked Lists- Case study 1 In this assessment, students will analyze a case and develop a solution by using recursive...

ICT208Algorithms and Data Structures

Assessment 3: Recursion Case Study 2

Part A: Maze exploration using recursive function (30%)

A Maze is given as N*N binary matrix of blocks where source block is the upper leftmost block i.e., maze[0][0] and destination block is lower rightmost block i.e., maze[N 1][N-1]. A rat starts from the source and has to reach the destination. The rat can move infour directions: left, right, up or down.

In the maze matrix, 0 means the block is a dead end and 1 means the block can beused in the path from source to destination. Backtracking is an algorithmic techniquefor solving problems recursively by trying to build a solution incrementally in mazeexploration.

Suggested Approach:Form a recursive function, which will follow a pathand check if the path reaches the destination or not. If the path does notreach the destination then backtrack and try other paths.

Algorithm:

1. Create a solution matrix, initially filled with 0’s.

2. Create a recursive function, which takes initial matrix, output matrixand position of rat (i, j).

3. if the position is out of the matrix or the position is not valid thenreturn.

4. Mark the position output[i][j] as 1 and check if the current position isdestination or not. If destination is reached print the output matrixand return.

5. Recursively call for position (i+1, j) and (i, j+1).

6. Unmark position (i, j), i.e output[i][j] = 0.

Your taskis to implement the given algorithm in C++ with recursive functions. Youneed to test the solution in a main function by creating a 2D array and print out themaze solution correspondingly if there is a path existing. Your main program should have an option that allows the program to find a solution using either 2 way movement or 4 way movement.

There are a few existing websites for reference on maze exploration using recursionfor you:

https://www.geeksforgeeks.org/rat-in-a-maze-backtracking-2/

https://learn.saylor.org/mod/book/view.php?id=33001&chapterid=12855

https://runestone.academy/ns/books/published//pythonds/Recursion/ExploringaMaze.html

Part B: Huffman decoding using recursive functions (10%)

We have discussed Huffman encoding for data compression in lecture and tutorial,now we can implement the Huffman decoding for data extraction to recover theoriginal data.

To decode the encoded data, we require the Huffman tree. We iterate through thebinary encoded data. To find character corresponding to current bits, we usefollowing simple steps.

1. We start from root and do following until a leaf is found.

2. If current bit is 0, we move to left node of the tree.

3. If the bit is 1, we move to right node of the tree.

4. If during traversal, we encounter a leaf node, we print character of thatparticular leaf node and then again continue the iteration of the encodeddata starting from step 1.

Your taskis to implement the Huffman decoding algorithm from the above steps in aC++ program with Huffman decoding function and a main function to decode acompressed string based on Huffman encoding and display the original string.

There are a few existing websites for reference on Huffman decoding algorithm foryou:

https://www.geeksforgeeks.org/huffman-decoding/

https://www.codespeedy.com/huffman-decoding-in-cpp/

https://www.programiz.com/dsa/huffman-coding

Submission requirement: upload the Mazz.cpp and Huffman.cpp to moodle by 5pm,June 3, 2022.

Marking rubric