Part $1$: Maze exploration using recursive function

A Maze is given as N$*$N binary matrix of blocks where source block is the upper left most 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 in four directions $($i$.$e$.,$ left,

right, up or down$).$

In the maze matrix, $0$ means the block is a dead end and non$-$zero means the block can be used in the path from source to destination, where non$-$zero value indicates the number of maximum jumps the rat can make from the cell $($maze$[$i$][$j$]).$ Also, a weight is applied to each cell in the path that is not dead$-$block, source or destination. The cell weight is set to be $1.$ Backtracking is an algorithmic technique for solving problems recursively by trying to build a solution incrementally in maze exploration.

Suggested Approach: Form a recursive function, which will follow a path and check if the path reaches the destination or not. If the path does not reach the destination, then backtrack and try other paths. Also, at any intermediate point along the longest path, make sure that you explore all the neighbours at that point to reach destination.

Objective:

Find the longest path from source to destination considering the cell weights in the path with multiple movement jumps.

Algorithm:

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

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

$3.$ if the position is out of the matrix or the position is not valid then return.

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

$5.$ Find all the neighbouring cells that are still open at the current position and recursively call for four movement directions.

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

Constraints:

$1.$ Jump value $($maze$[$i$][$j$])$ is in range $[1,5]$

Your task is to implement the given algorithm in C$++$ with recursive functions. You need to test the solution in a main function by creating a $2$D array and print out the maze solution correspondingly if there is a path existing. The output matrix contains $0$ and $1,$ where maze$[$i$][$j$]=1$ represents the cell is taken into the path and maze$[$i$][$j$]=0$ represents if any path exists.

Part $2$: Huffman decoding using recursive functions

To decode the encoded data, we require the Huffman tree. We iterate through the binary encoded data. To find character corresponding to current bits, we use following 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 that particular leaf node and then again continue the iteration of the encoded data starting from step $1.$

Your task is to implement the Huffman decoding algorithm from the above steps in a C$++$ program with Huffman decoding function and a main function to decode a compressed string based on Huffman encoding and display the original string.