pavly-gerges

Graph Algorithms I

Outline:

• Prerequisite Terminology.
• Mathematical Structures for representing graphs.
• Graph traversal algorithms.

Terminology:

• Directed graph (Or Digraph): a directed path that is composed of vertexes and edges; where edges are essentially represented by directed arcs from a vertex (known as initial vertex) to another vertex (known as terminating or end vertex).
• Undirected graph (or Multigraph): a non-directed path that is composed of vertexes and edges; where edges are represented by non-directed arcs from a vertex to another vertex (i.e., orientation of arcs are ignored).
• Adjacency Matrix Representation:

pavly-gerges

// The following code examines multiple routines of definining dynamic buffers in C.
// This file fires a runtime malloc() error due to a HEAP corruption error; because of buffer overflow.
// Two maneuvers are introduced to fix this 

#include <stdio.h>
#include <stdlib.h>

int main() {
    
    // buffers

pavly-gerges

A Mathematical Approach to coding in the C programming language: Scientific Coding

Preface:

This document is devoted to showing another perspective into programming, which in its surface is the scientific programming, but in its heart and core is really intricate. The complexity is imparted due to of the incorporation of mathematical models and their implementation to the syntatics of the programming language, unlike the practical OOP and Functional paradigms, the FSA model (Finite-Automata Model) is a theoretical model. However, in this short document, I am willing to show some caveats of using the FSM models in both low-level and high-level engineering and delivering a reliable software based on a true science.

Science behind the FSA models

The scientific basis is all emerged from the scientific modelling which is now a forked entity from the scientific philosophy models.

The Finite-State-Automata Models

pavly-gerges

Preface:

This document is devoted to derive the filter gates applied on the select lines of a multiplexer before entering the main AND circuit to produce the proper truth table. The document starts first by introducing the preliminaries using a miniaturized model, the 4-to-1 Multiplexer Model, the prototypical model of a MUX circuitry.

English:

For a 4-to-1 Multiplexer case. Let, $γ$ and $φ$ be symbols designating the select lines of the multiplexer And, $i$ be the symbols designating the input lines to the multiplexer, and $q$ designate the single output line from the MUX.

Lemma.01:

$$

pavly-gerges

In file included from /media/pavl-x86-machine/pavl-g/Projects/Electrostatic-Sandbox/electrostatic-sandbox-framework/electrostatic4j/serial4j/serial4j-native/src/lib/jni/com_serial4j_core_terminal_NativeTerminalDevice.cpp:40:
/media/pavl-x86-machine/pavl-g/Projects/Electrostatic-Sandbox/electrostatic-sandbox-framework/electrostatic4j/serial4j/serial4j-native/dependencies/include/electrostatic/util/errno/errno.h:14:16: error: expected identifier before ‘(’ token
   14 | typedef struct errno(errno);
      |                ^~~~~
/media/pavl-x86-machine/pavl-g/Projects/Electrostatic-Sandbox/electrostatic-sandbox-framework/electrostatic4j/serial4j/serial4j-native/dependencies/include/electrostatic/util/errno/errno.h:14:16: error: typedef ‘__errno_location’ is initialized (use ‘decltype’ instead)
   14 | typedef struct errno(errno);
      |                ^~~~~
/media/pavl-x86-machine/pavl-g/Projects/Electrostatic-Sandbox/electrostatic-sandbox-framework/electrostatic4j/serial4j/serial4j-native/dependencies/include/e

pavly-gerges

digraph G { rankdir = LR; a -> b }

pavly-gerges

flowchart LR

A[] 
B[]

flowchart LR

pavly-gerges

Diagrams

Markdown Preview Enhanced supports rendering flow charts, sequence diagrams, mermaid, PlantUML, WaveDrom, GraphViz, Vega & Vega-lite, Ditaa diagrams. You can also render TikZ, Python Matplotlib, Plotly and all sorts of other graphs and diagrams by using Code Chunk.

Please note that some diagrams don't work well with file exports such as PDF, pandoc, etc.

Flow Charts

This feature is powered by flowchart.js.

pavly-gerges

#include <electrostatic/algorithm/arithmos/algebra/switching.h>
#include <stdlib.h>

uint8_t switching_xor(SWITCHING_TYPE **inputs, SWITCHING_TYPE *output){
    if (inputs == NULL || output == NULL) {
        return 1;
    }
    for (int i = 0; inputs[i] != NULL; i++) {
        SWITCHING_TYPE prop0 = *output;
        SWITCHING_TYPE prop1 = *(inputs[i]);

pavly-gerges

#include <electrostatic/util/errno/errno.h>
#include <alloca.h>
#include <stdio.h>
#include <stdlib.h>
#include <electrostatic/algorithm/arithmos/adt/list.h>

void iterator(list *buffer, list_element *element) {
    uint64_t index = 0;
    buffer->function_table->indexof(buffer, element, &index);
    printf("Index at %llud = %d\n", index, *((int*) element->data));