# Category Archives: Analysis

## Understanding Time Complexity with Simple ExamplesNovember 14, 2017

Lot of students get confused while understanding the concept of time-complexity, but in this article we will explain it with a very simple example: Imagine… Read More »

## Iterated Logarithm log*(n)November 7, 2017

Iterated Logarithm or Log*(n) is the number of times the logarithm function must be iteratively applied before the result is less than or equal to… Read More »

## Time complexity of recursive Fibonacci programOctober 20, 2017

The Fibonacci numbers are the numbers in the following integer sequence 0, 1, 1, 2, 3, 5, 8, 13… Mathematically Fibonacci numbers can be written… Read More »

## Regularity condition in the master theorem.October 6, 2017

Master theorem is a direct way to get the solution of a recurrence relation, provided that it is of the following type: T(n) = aT(n/b)… Read More »

## Online Algorithm

An online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to… Read More »

## Analysis of algorithems | little o and little omega notationsAugust 14, 2017

The main idea of asymptotic analysis is to have a measure of efficiency of algorithms that doesn’t depend on machine specific constants, mainly because this… Read More »

## Master Theorem For Subtract and Conquer RecurrencesJuly 12, 2017

Master theorem is used to determine the Big – O upper bound on functions which possess recurrence, i.e which can be broken into sub problems.… Read More »

## Analysis of Algorithms | Set 5 (Practice Problems)May 2, 2017

We have discussed Asymptotic Analysis, Worst, Average and Best Cases , Asymptotic Notations and Analysis of loops in previous posts.

## Auxiliary Space with Recursive FunctionsApril 23, 2017

Prerequisite : Recursion Memory used by a program is sometimes as important as running time, particularly in constrained environments such as mobile devices. For example… Read More »

## Asymptotic Analysis and comparison of sorting algorithmsDecember 28, 2016

It is a well established fact that merge sort runs faster than insertion sort. Using asymptotic analysis we can prove that merge sort runs in… Read More »

## Time Complexity of a Loop when Loop variable “Expands or Shrinks” exponentiallyNovember 22, 2016

For such cases, time complexity of the loop is O(log(log(n))).The following cases analyse different aspects of the problem. Case 1 : In this case, i… Read More »

## Pseudo-polynomial AlgorithmsFebruary 27, 2016

What is Pseudo-polynomial? An algorithm whose worst case time complexity depends on numeric value of input (not number of inputs) is called Pseudo-polynomial algorithm. For… Read More »

## Time Complexity where loop variable is incremented by 1, 2, 3, 4 ..September 1, 2015

What is the time complexity of below code?

## Time Complexity of Loop with PowersAugust 30, 2015

What is the time complexity of below function?

## Performance of loops (A caching question)

Consider below two C language functions to compute sum of elements in a 2D array. Ignoring the compiler optimizations, which of the two is better… Read More »