Dynamic Programming: Pascal's Triangle & Floyd's Algorithm

Description

This lecture covers dynamic programming with a focus on Pascal's Triangle and Floyd's Algorithm. It explains the calculation of coefficients using dynamic programming, the complexity of algorithms, and the optimization of operations. The lecture also delves into Floyd's Algorithm for finding the shortest path between nodes in a network, illustrating the concept with examples. Additionally, it discusses other algorithms like Dijkstra's Algorithm, A*, and Viterbi Algorithm for solving shortest path problems in different scenarios.

Official source

https://mediaspace.epfl.ch/media/0_0a0zrt39

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related lectures (53)

Explores dynamic programming strategies for finding shortest paths in networks with various algorithms and complexities.

Explores maximizing diversity in document selection, graph clique determination, theorems on negative type, and convex optimization.

Explores graph traversal methods, spanning trees, and shortest paths using BFS and DFS.

Explores dynamic programming for the Knapsack problem, discussing strategies, algorithms, NP-hardness, and time complexity analysis.

Introduces the concept of shortest path, discussing weighted paths, Hamiltonian paths, and path optimization algorithms.

Related concepts (40)

Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.

Glossary of graph theory

This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges.

Connectivity (graph theory)

In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network. In an undirected graph G, two vertices u and v are called connected if G contains a path from u to v.

Vertex (graph theory)

In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is represented by a line or arrow extending from one vertex to another.

Graph (discrete mathematics)

In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges.