Rekurentní rovnice a algoritmy

Abstract

This bachelor’s thesis focuses on the use of recurrent equations to describe the complexity of al gorithms, especially those based on the "divide and conquer" principle. An important part of the thesis is the master theorem. The thesis aims to identify and clearly describe several practical prob lems, their recursive solutions and ways of influencing it’s complexity. It includes the mergesort algorithm, binary search and matrix search. An integral part is also the change of the coefficient of the recurrent equation. The effect of changing the coefficient on the time complexity is verified by measuring runtime of the algorithm. All described algorithms are implemented in the C# language. They are part of the algorithmic library, which is also the result of the bachelor’s thesis. The thesis will thus connect the theoretical basis of recurrent equations with the practical implementation and analysis of recursive algorithms.