Skip to main content

Analyzing Algorithms or Data Structures

 Algorithm 

step-by-step procedure for performing some task in a finite amount of time.

Data structure

systematic way of organizing and accessing data.

The running time of an algorithm or data structure operation typically depends on a number of factors. Its running time can be studied by executing it on various test, inputs and recording the actual time spent in each execution. The running time of an algorithm or data structure method increases with the input size.

The running time is also affected by

Hardware environment 

  • processor
  • clock rate
  • memory
  • disk, etc.

Software environment 

  • operating system
  • programming language
  • compiler
  • interpreter, etc

Limitations - Experimenting running time 

  • Limited set of test inputs
  • Running times to be performed in the same hardware and software environments.
  • Algorithm to be implemented and executed

Experimentation alone is not sufficient, an analytic framework is required to

  • take into account of all possible inputs
  • evaluate the relative efficiency of any two algorithms
  • perform studying a high-level description of the algorithm without implementing & executing.

Components of methodology for algorithm analysis

  • a language to describe algorithms
  • a computational model
  • a metric for measuring running time
  • an approach to characterize the running times

Pseudo Code

  • mixture of natural language and high-level programming
  • more structured code intended for human reader, not for computer.
  • describe the main ideas behind a generic implementation of a data structure or algorithm.

pseudo-code mixes natural language with standard programming language constructs such as 

  • Expressions 
  • Method declaration
  • Decision structures
  • Condition statements
  • Array Indexing
  • Method calls
  • Method returns

Popular posts from this blog

Gaussian Elimination - Row reduction Algorithm

 Gaussian elimination is a method for solving matrix equations of the form, Ax=b.  This method is also known as the row reduction algorithm. Back  Substitution Solving the last equation for the variable and then work backward into the first equation to solve it.  The fundamental idea is to add multiples of one equation to the others in order to eliminate a variable and to continue this process until only one variable is left. Pivot row The row that is used to perform elimination of a variable from other rows is called the pivot row. Example: Solving a linear equation The augmented matrix for the above equation shall be The equation shall be solved using back substitution. The eliminating the first variable (x1) in the first row (Pivot row) by carrying out the row operation. As the second row become zero, the row will be shifted to bottom by carrying out partial pivoting. Now, the second variable (x2)  shall be eliminated by carrying out the row operation again. ...

Decision Tree - Gini Index

The Gini index is used in CART. The Gini index measures the impurity of the data set, where p i - probability that data in the data set, D belong to class, C i  and pi = |C i,D |/|D| There are 2 v - 2 possible ways to form two partitions of the data set, D based on a binary split on a attribute. Each of the possible binary splits of the attribute is considered. The subset that gives the minimum Gini index is selected as the splitting subset for discrete valued attribute. The degree of Gini index varies between 0 and 1. The value 0 denotes that all elements belong to a certain class or if there exists only one class, and the value 1 denotes that the elements are randomly distributed across various classes. A Gini Index of 0.5 denotes equally distributed elements into some classes. The Gini index is biased toward multivalued attributes and has difficulty when the number of classes is large.

Data Cleaning Process

Data cleaning attempt to fill in missing values, smooth out noise while identifying  outliers, and correct inconsistencies in the data. Data cleaning is performed as an iterative two-step process consisting of discrepancy detection and data transformation. The missing values of the attribute can be addressed by Ignoring the value filling the value manually Using global constant to fill the value Using a measure of central tendency (mean or median) of value Using attribute mean or median belonging to same class Using the most probable value Noise is a random error or variance in a measured variable. The noisy data can be smoothened using following techniques. Binning methods smooth a sorted data value by consulting the nearby values around it. smoothing by bin means - each  value in a bin is replaced by the mean value of the bin. smoothing by bin medians - each bin value  is replaced by the bin median smoothing by bin boundaries - the minimum and maximum values in a ...