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Mauricio Poppe | maurizzzio.com Reviews
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2 static
3 graphs
4 introduction
5 traversal
6 topological sorting
7 cut edges bridges
8 cut vertices articulation points
9 components
10 tree
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Mauricio Poppe | maurizzzio.com Reviews

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1

Introduction

http://www.maurizzzio.com/static/math/calculus/introduction.html

Single Source Shortest Path (SSSP). Taylor's Theorem and Infinite Series. Special factorial modulo p. Prime factors of a factorial. Calculus was created to solve some problems that other branches of math were not adequate to treat:. Determination of tangents to various curves (e.g. to determine the course of a light ray after it strikes the surface of a lens). Length of curves, areas and volumes of figures bounded by curves. To solve these problems the following concepts are needed:. Like the one below:.

2

Euclidean Algorithm

http://www.maurizzzio.com/static/math/number-theory/euclidean-algorithm.html

Single Source Shortest Path (SSSP). Taylor's Theorem and Infinite Series. Special factorial modulo p. Prime factors of a factorial. Euclid’s algorithm for finding the Greatest Common Divisor. Of two or more integers is based on the following observations:. If $x = y$ then. If $x y$ then. Suppose that $d$ is a divisor of $x$ and $y$ then $x$ and $y$ can be expressed as. Therefore $d$ is a divisor of $x - y$. By ensuring that $x geq y$ we can get rid of the. At this point `gcd(x, y) = gcd(x, 0) = x`.

3

Cut-edges (bridges)

http://www.maurizzzio.com/static/graphs/cut-edges.html

Single Source Shortest Path (SSSP). Taylor's Theorem and Infinite Series. Special factorial modulo p. Prime factors of a factorial. An edge $e = uv$ of a connected graph $G$ is called a bridge if $G - e$ is disconnected (obviously it increases the number of components). In the following undirected graph $G$ the edges $v 2v 3$ and $v 3v 4$ are bridges. An edge $e$ of an undirected graph $G$ is a bridge if and only if $e$ lies on no cycle. Every edge of an undirected tree is a bridge. Let $v$ be an adjacen...

4

Traversal

http://www.maurizzzio.com/static/graphs/traversal.html

Single Source Shortest Path (SSSP). Taylor's Theorem and Infinite Series. Special factorial modulo p. Prime factors of a factorial. Breadth First Search (BFS). Given a graph $G$ and a distinguished source vertex $s$, BFS explores the edges of $G$ to discover the vertices adjacent to $s$, as a consequence it also computes the distance of the path from $s$ to each reachable vertex. Depth First Search (DFS). Whenever a vertex $v$ is discovered by some vertex $u$, we say that $u$ is a predecesor. V {out}$ re...

5

Binary Exponentiation

http://www.maurizzzio.com/static/math/number-theory/binary-exponentiation.html

Single Source Shortest Path (SSSP). Taylor's Theorem and Infinite Series. Special factorial modulo p. Prime factors of a factorial. Finding $a n$ involves doing $n$ multiplications of $a$, the same operation can be done in $O(log(n) $ multiplications. For any number $a$ raised to an even. For any number $a$ rasied to an odd. Time complexity: $O(log(n) $. Computes * * a k * * Given the following facts: * * - if `k` is even then a (2k) = (a k) 2 * - if `k` is odd then a (2k 1) = (a k) 2 * a */.

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