mathematics on algonomics
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Mon, 02 Sep 2019 17:05:31 +0000

HashMap Hash Function
https://algonomics.io/blog/hashmaphashfunction/
Mon, 02 Sep 2019 17:05:31 +0000
https://algonomics.io/blog/hashmaphashfunction/
Assuming that you are already aware about the concept of hashing and hash functions in general, this post tries to look into the details of how the hash function is implemented in java8 HashMap.
Let’s take a quick look at the below mentioned snippet from java8 (1.8.0_221)  HashMap class:
// Computes key.hashCode() and spreads (XORs) higher bits of hash // to lower. Because the table uses poweroftwo masking, sets of // hashes that vary only in bits above the current mask will // always collide.

Fibonacci Numbers
https://algonomics.io/blog/fibonaccinumbers/
Tue, 30 Jul 2019 17:05:31 +0000
https://algonomics.io/blog/fibonaccinumbers/
Fibonacci Numbers, named after the great Italian mathematician of the same name, are so popular that theres even a mathematical journal (The FIbonacci Quarterly) dedicated to their theory and applications.
From golden ratio (also known as phi), to their appearance in various natural settings like branches of a tree, seed patterns of a sunflower, veins of leaves and many more, fibonacci numbers can be found almost everywhere.
Recurrence Relation Mathematically, the $n^{th}$ fibonacci number can be represented as the sum of two previous fibonacci numbers: $F_{n}=F_{n1}+F_{n2}$ with a set of given initial values:

Permutations and Combinations
https://algonomics.io/blog/permutationscombinations/
Thu, 06 Jun 2019 07:46:55 +0000
https://algonomics.io/blog/permutationscombinations/
Before we look into various mathematical formulas, the first thing is to understand the difference between permutation and combination. Consider the following two scenarios:
Selecting 2 students from a class of 30 students to collect notebooks from rest of the students. Entering the unlock code on your cell phone. As you notice, in the first case the order does not matter; i.e. the students (say a,b) can be selected in any order {a,b} or {b,a}, the end result remains same.

Bitwise Operations
https://algonomics.io/blog/bitwiseoperations/
Fri, 17 May 2019 03:48:01 +0000
https://algonomics.io/blog/bitwiseoperations/
Bitwise algorithms is a class of algorithms where instead of performing common operations like addition, comparisons etc on the decimal numbers, are performed on the individual bits that comprise those numbers.
The bitwise operations are considered very efficient as compared to their decimal counterparts.
Bitwise Operators Following is the list of bitwise operators:
Bitwise AND (&): Performs bitwise AND on the individual bits of the two operands.

Mathematical Progressions
https://algonomics.io/blog/mathematicalprogressions/
Mon, 06 May 2019 07:46:55 +0000
https://algonomics.io/blog/mathematicalprogressions/
A mathematical progression is a sequence of numbers such that all the members of the sequence are governed by certain rule, which defines the relation between consecutive terms. There are three types of mathematical progressions:
1. Arithmetic Progression An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
For an AP with common difference as d and first term as $a_1$, the terms of the progression can be represented as: $a_1, a_1+d, a_1+2d, a_1+3d … a_1+(n1)d$