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;

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