$1.$ Tasks and Deliverables:

$1$ Binary Search Tree $($BST$)$

Tasks: Implement a Binary Search Tree with the following functionalities:

$1.$ Insert the values: $50,30,70,20,40,60,80$ sequentially.

$2.$ Delete the value $70$ from the BST$.$

$3.$ Search for the value $20$ in the BST$.$

$4.$ After each operation, provide the tree structure and show the

in$-$order traversal result.

Deliverables:

$1.$ Python file $($bst$.$py$)$ with the implementation of the BST and its functions.

$2.$ A brief report $($Word or PDF$)$ showing the tree structure and in$-$order

traversal after each operation.

$2$ Sorting Algorithms

Tasks:

$1.$ Sort the array $[64,34,25,12,22,11,90]$ using the following

algorithms:

i$.$ Insertion Sort

ii$.$ Bubble Sort

iii. Selection Sort

$2.$ Provide the time complexity for each algorithm, including best$-$case, worst$-$case, and average$-$case scenarios.

$3.$ Provide the space complexity for each algorithm, detailing the additional

space used.

Deliverables:

$1.$ Python file $($sortings$.$py$)$ with implementations of Insertion Sort, Bubble

Sort, and Selection Sort.

$2.$ Report with a detailed time and space complexity analysis for each

sorting algorithm.

$3$ Divide$-$and$-$Conquer Sorting

Tasks:

$1.$ Implement and sort the array $[38,27,43,3,9,82,10]$ using the

following algorithms:

i$.$ Merge Sort

ii$.$ Quick Sort

$2.$ Show intermediate steps of sorting for each algorithm.

$3.$ Test all implemented sorting algorithms $($Insertion$,$ Bubble, Selection, Merge, Quick Sort$)$ on an array of $1000$ randomly generated integers.

$4.$ Measure and record the time taken for each algorithm to sort the array. Deliverables:

$1.$ Python files $($divide$\_$conquer$\_$sorting.py and sorting$\_1000.$py$)$

with implementations for tasks $1$ and $3.$

$2.$ Report showing the array at each significant step of sorting.

$3.$ Report comparing the performance of each sorting algorithm, including

recorded times and observations