Design and Analysis of Algorithms

Explore the quicksort algorithm, a divide and conquer sorting method that uses a pivot to partition data, swaps, and recursively sorts subarrays to achieve a sorted sequence.

Explore how breadth-first search traverses a graph from a starting node by enqueueing unexplored neighbors and avoiding cycles until all vertices are visited.

learn how to identify articulation points in a connected component with a depth-first search and low values. explore constructing the dfs tree, back edges, and root and non-root conditions.

Explore how to compute the shortest paths from a single source to all vertices using Dijkstra's algorithm on weighted graphs.

Explore dynamic programming and the principle of optimality through a level-wise shortest-path example, comparing with greedy methods and showing how to build optimal solutions step by step.

Explore the travelling salesman problem: start at vertex 1, visit every vertex exactly once, return to 1, and minimize total cost using dynamic programming on a cost matrix.

Explore the 0/1 knapsack problem solved with lc branch and bound, using branching and bounding to maximize profit under capacity, with upper and lower bounds and an intelligent ranking function.