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Articles by Vanshika Sood
Page 3 of 3
Pernicious Number
A number is considered to be pernicious if the number is a positive integer and the number of set bits in its binary expansion are prime. The first pernicious number is 3, as 3 = (11)2. It can be seen that the number of set bits in the binary representation of 3 are 2, which is a prime number. The first 10 pernicious numbers are 3, 5, 6, 7, 9, 10, 11, 12, 13, 14. Interestingly, powers of 2 can never be pernicious since they always have only 1 set bit. 1 is not a prime number. On the other ...
Read MoreOdious Number
A number is considered to be an odious number if it has an odd number of 1s in its binary expansion. The first 10 odious numbers are 1, 2, 4, 7, 10, 11, 13, 14, 16, 19, 21. Interestingly, all powers of 2 are odious since they have only 1 set bit. The following article discusses 2 approaches in detail to find whether a number is an odious number or not. Problem Statement This problem aims to check whether the given number is an odious number i.e. it is a positive number with an odd number of set bits in ...
Read MorePythagorean Quadruple
A group of four positive integers (a, b, c, and d) that satisfy the Pythagorean equation are called Pythagorean quadruples. The equation can be written as: a2 + b2 + c2 = d2 , with ‘d’ being the largest value out of the given numbers. In other words, the square of the fourth integer should be equal to the sum obtained by adding the squares of the previous three numbers. (1, 2, 2, 3) is a Pythagorean quadruplet as (12 + 22 + 22) = (1 + 4 + 4) = (9) = (32). Due to the requirement ...
Read MorePalindromic Selfie Numbers
A number is considered to be a “Selfie Number” if it can be represented using only its own digits and certain mathematical operations. For example, 936 is a selfie number. $$\mathrm{936\:=\:(\sqrt{9})!^{3} \:+\:6!\:=\:216\:+\:720\:=\:936}$$ Here it can be observed that a series of operations are performed on the digits of the original number and the resultant is equal to the original number. Palindromic Selfie Numbers are a special kind of selfie number. They satisfy the selfie multiplicative rule. Consider a number x. Let the number formed by reversing the digits of x be $\mathrm{x^\prime}$. Let y be a ...
Read MoreClosest Numbers from a List of Unsorted Integers
In the following article, we discuss two approaches to find the closest numbers from a list of unsorted integers. Let us first understand what is meant by the term ‘closest numbers’. Closest numbers are the pair(s) of numbers which have the least difference between them. Problem Statement Given a list of distinct unsorted integers, we need to find the pair of elements that have the least difference between them. If there are multiple pairs, we need to find all of them. Furthermore, in the article wherever there is a mention of difference, it means absolute difference. Examples Input: [44, 42, ...
Read MoreDelete a Linked List Using Recursion
Linked List A linked list is a linear data structure in which the elements are stored at non-contiguous memory locations. Each element consists of a node. A node is composed of a data field, which holds the value of the element, and an address field, which points to the location of the next node in the series. The first node of the linked list is referred to as the ‘head’ of the list. The last element of the linked list can be defined as the element which points to NULL. A diagrammatic representation of a linked list is shown below. ...
Read MoreTo Check if a Number is a Munchhausen Number
Munchhausen Numbers are peculiar numbers which possess a unique property. A number is considered to be munchhausen if the sum of the digits of the number, raised to their own power, is equal to the original number. These numbers are uncommon and not many of them are known. If the definition 00 = 0 is used, then 0 can also be considered a munchhausen number. The following article provides a method to determine whether a number is munchhausen or not while keeping in mind these characteristics of munchhausen numbers. Problem Statement The task at hand is to check whether a ...
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