ClecioJung/studying-c

A bunch of C code developed during my studies of programming

Overview

This is a set of simple C codes developed to study algorithms and concepts of computer science. It posseses the following characteristics:

• Developed with C11;
• This code uses some UNIX functions, so it is platform dependent (it was only tested on Linux);
• In this studies, I found this references to be very usefull:
  • Numerical Methods for Engineers;
  • C, the Complete Reference;
  • Numerical Linear Algebra;
  • Cálculo Numérico Computacional;
• Implemented data structures:
  • Linked list;
  • Doubly linked list;
  • XOR linked list;
  • Dynamic array;
  • Circular buffer;
  • Binary tree (In order to study binary trees, a simple expression parser was developed, as an example);
• Implemented sorting algorithms:
  • Bubble sort;
  • Select sort;
  • Insert sort;
  • Shell sort;
  • Merge sort;
  • Heap sort;
  • Quicksort;
• Implemented search algorithms:
  • Sequential search;
  • Binary search;
• Implemented approximations for constants:
  • Euler's constant;
  • Pi;
• Implemented scalar functions:
  • Exponentiation by a integer positive number;
  • Square root;
  • N-th root;
  • Exponential;
  • Trigonometric functions: sine, cosine, tangent and arctangent functions;
  • The atan2 function;
• Implemented operations with complex numbers:
  • Sum andsubtraction of complex numbers;
  • Multiplication and division of complex numbers;
  • Inversion of complex numbers;
  • Modulus and argument of complex numbers;
  • Construction of complex numbers by its polar form;
  • Complex conjugate;
  • Exponentiation by a integer positive number;
• Implemented operations with vectors:
  • Sum and subtraction of vectors;
  • Multiplication of vectors by scalars;
  • Dot product;
  • Cross product;
  • Euclidean norm;
• Implemented operations with polynomials:
  • Addidtion and multiplication of polynomials;
  • Differenctiation of polynomials;
  • Evaluation with Horner's method;
  • Division by a binomial using Ruffini's rule;
  • Computation of polynomial root bounds;
  • Polynomial root finding;
  • Legendre polynomials;
  • Chebyshev polynomials;
• Implemented operations with matrices:
  • Sum and subtraction of matrices;
  • Multiplication of matrices by scalars;
  • Multiplication between matrices;
  • Multiplication between matrices and vectors;
  • Trace;
  • Determinant;
  • Transpose matrix;
  • Symmetric matrix;
  • Skew-symmetric matrix;
  • LU decomposition;
  • LU Crout decomposition;
  • QR decomposition;
  • Householder matrix computation;
  • Hessenberg matrix computation;
  • Schur decomposition using the QR algorithm;
  • Eigenvalues computation;
  • Cholesky decomposition;
  • Greatest eigenvalue computation (and its eigenvector) using the power method;
  • Lowest eigenvalue computation (and its eigenvector) using the inverse power method;
  • Inverse matrix;
  • Pseudo-inverse matrix;
  • Jacobian matrix;
  • Vandermonde matrix;
• Implemented algorithm for solving systems of linear equations:
  • Gaussian elimination;
  • Gauss-Jordan elimination;
  • Solving linear equations using LU decomposition;
  • Jacobi method;
  • Gauss-Seidel method;
  • Algorithm for solving tridiagonal systems;
• Implemented algorithms for finding roots of equations:
  • Bisection method;
  • Fake-position method;
  • Newton-Raphson method;
  • Secant method;
  • Muller's method;
  • Newton-Raphson method for multivariable systems;
  • Broyden's method for multivariable systems;
• Implemented algorithms for curve-fitting:
  • Polynomial interpolation;
  • Lagrange interpolation;
  • Gregory-Newton intepolation;
  • Linear regression;
  • Polynomail regression;
  • Computation of Coefficient of determination for the polynomial regression;
  • Cubic spline interpolation;
• Implemented algorithms for numerical integration:
  • Trapezoidal rule;
  • Simpson's rule;
  • Simpson's 3/8 rule;
  • Gauss-Legendre quadrature;
• Implemented algorithms for solving Ordinary Differential Equations (ODE):
  • Euler method;
  • Heun's method;
  • Third order Runge-Kutta method;
  • Fourth order Runge-Kutta method;
  • Butcher’s (1964) fifth-order RK method;

Usage

Download this project and compile it by typing the command make in its folder. Next, just run one of the executables located in the bin folder. Here is an example:

$ make
$ ./bin/binary-tree

In order to check if there is any memory leak, use the valgrind command:

$ valgrind --tool=memcheck ./bin/binary-tree

To run all the tests, use the following command:

$ make test