UnderGrad_CS_Projects

Under Graduate Computer Science Projects Refresher Made originally in Pascal, circa 1988. UPR RUM Mayaguez

Re coded in Python, for modern times. Oct-Nov 2024

1. Towers of Hanoi • Description: A classic recursive problem that involves moving a set of disks from one peg to another, following these rules: o Only one disk can be moved at a time. o A disk cannot be placed on top of a smaller disk. o The task is to move all disks from the source peg to the target peg using an auxiliary peg.

2. Binary Search • Description: An efficient searching algorithm that finds the position of a target value within a sorted list. It works by repeatedly dividing the search interval in half: o If the target value is less than the middle element, narrow the search to the lower half. o If greater, narrow to the upper half. o Repeat until the target is found or the interval is empty.

3. Merge Sort • Description: A divide-and-conquer sorting algorithm that: o Recursively splits the list into halves until each sublist has one element. o Merges sublists back together in sorted order. o It has a time complexity of O(nlog⁡n)O(nlogn), making it highly efficient.

4. Dijkstra's Algorithm • Description: A graph algorithm that finds the shortest path from a starting node to all other nodes in a weighted graph. It uses a priority queue to explore the shortest possible paths first, updating the shortest known distance to each node.

5. Breadth-First Search (BFS) • Description: A graph traversal algorithm that explores nodes level by level: o Starts at a given node and explores all its neighbors. o Moves to the neighbors' neighbors next, and so on. o Often used for finding the shortest path in an unweighted graph.

6. Depth-First Search (DFS) • Description: Another graph traversal algorithm that explores as far as possible along one branch before backtracking: o Uses a stack (either explicitly or via recursion). o Useful for tasks like topological sorting and detecting cycles.

7. Knapsack Problem (0/1 Knapsack) • Description: A dynamic programming problem where, given a set of items with weights and values, the goal is to determine the maximum value that can be obtained by selecting items such that their total weight does not exceed a given limit.

8. Floyd-Warshall Algorithm • Description: An algorithm used to find the shortest paths between all pairs of nodes in a weighted graph: o It’s a dynamic programming approach that updates the shortest path between nodes by considering all possible intermediate nodes. o The time complexity is O(n3).

9. Quicksort • Description: A highly efficient sorting algorithm that uses a divide-and-conquer approach: o Selects a "pivot" element and partitions the list into two sublists: elements less than the pivot and elements greater than the pivot. o Recursively sorts the sublists. o Has an average-case time complexity of O(nlog⁡n.

10. Prim's Algorithm • Description: A greedy algorithm that finds the minimum spanning tree of a weighted, undirected graph: o Starts with an arbitrary node and grows the tree by adding the smallest edge that connects a new node. o Useful for network design and ensuring minimal connection costs.