N-ary Tree Data Structure API in Java

TreeDS4j is a Java (6+) API that allows handling n-ary tree data structure in such a flexible way. Indeed, the user is subject to enter structured and coherent data, and the latter would be stored in an hierarchy, accordingly. The link below contains two samples that show how to take advantage of the API.


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Logarithmic Summations and Discrete Loops - Ceiling and Floor Functions

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Reading the so called paper " Discrete Loops and Worst Case Performance " ( by Dr. Johann Blieberger ), I came across some interesting summations: Useful here: for ( i = 1; i <= n ; i ++ ) { for (j = 1; j <= i ; j *= 2) { // Some constant time C instructions. } } Because: Likewise: Applicable here: for ( i = 1; i <= n ; i ++ ) { for (j = 1; j < i ; j *= 2) { // Some constant time C instructions. } } Because: And more generally: for ( i = 1; i <= n ; i ++ ) { for (j = 1; j <= i ; j *= a) { // Some constant time C instructions. } } We can proceed like the following: Further: for ( i = 1; i <= n ; i ++ ) { for (j = 1; j < i ; j *= a) { // Some constant time C instructions. } } With: Thus, while I tried to refine the results of some nested loops running time analysis, I had to face a particul...
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Indirect Recursion - A Natural Phenomenon

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Triple Nested Loops - Two Linear Loops and One Logarithmic with a non-Constant Base - The Monster

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To obtain the function that tells the exact number of iterations a set of nested loops would perform didn't seem to be a tedious exercise. However, I came accross this interesting case: - Linear outer loop - Dependent first level linear inner loop - Dependent second level logarithmic inner loop with a general base. for ( i = 1 ; i <= n ; i ++ ) { for ( j = 1; j <= i ; j ++ ) { for ( k = 1 ; k <= j ; k *= a ) { // c } } } Ceilinged/Floored logarithmic functions within summations turned out to have very lengthy closed-forms (See my previous post). We will dissect the formulas above (for any a > 1 and n >= 1): Therefore, This link  points at a  plain   Java program that represents the above functions (f(), g () , h () , u () , v () , w () , respectively), and give the exact number of iterations performed by the covered algorithm mentioned earlier (receives two a...
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