Advanced master theorem for divide and conquer recurrences
Master Theorem is used to determine running time of algorithms (divide and conquer algorithms) in terms of asymptotic notations. Consider a problem that be solved… Read More »
Category Archives: Analysis
Amortized analysis for increment in counter
Amortized analysis refers to determining the time-averaged running time for a sequence (not an individual) operation. It is different from average case analysis because here,… Read More »
Analysis of Algorithms | Big-O analysis
In our previous articles on Analysis of Algorithms, we had discussed asymptotic notations, their worst and best case performance etc. in brief. In this article,… Read More »
Time Complexity Analysis | Tower Of Hanoi (Recursion)
Tower of Hanoi is a mathematical puzzle where we have three rods and n disks. The objective of the puzzle is to move the entire… Read More »
Time taken by Loop unrolling vs Normal loop
We have discussed loop unrolling. The idea is to increase performance by grouping loop statements so that there are less number of loop control instruction… Read More »
Loop Invariant Condition with Examples of Sorting Algorithms
Loop Invariant Condition: Loop invariant condition is a condition about the relationship between the variables of our program which is definitely true immediately before and… Read More »
Analysis of different sorting techniques
In this article, we will discuss important properties of different sorting techniques including their complexity, stability and memory constraints. Before understanding this article, you should… Read More »
Different types of recurrence relations and their solutions
In this article, we will see how we can solve different types of recurrence relations using different approaches. Before understanding this article, you should have… Read More »
Complexity of different operations in Binary tree, Binary Search Tree and AVL tree
In this article, we will discuss complexity of different operations in binary trees including BST and AVL trees. Before understanding this article, you should have… Read More »
Practice Set for Recurrence Relations
Prerequisite – Analysis of Algorithms | Set 1, Set 2, Set 3, Set 4, Set 5 Que-1. Solve the following recurrence relation? T(n) = 7T(n/2)… Read More »
Practice Questions on Time Complexity Analysis
Prerequiste: Analysis of Algorithms 1. What is the time, space complexity of following code: Options: O(N * M) time, O(1) space O(N + M) time,… Read More »
Understanding Time Complexity with Simple Examples
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)
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 program
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.
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 »