Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
In mathematics, a Stella Octangula number is a figurate number based on the Stella Octangula, of the form n(2n2 − 1). Stella Octangula numbers which are perfect squares are 1 and 9653449. Problem Statement Given a number n, check whether it is the Stella Octangula number or not. The sequence of Stella Octangula numbers is 0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990 Example1 Input x = 14 Output Yes Explanation $$\mathrm{For\: n = 2, expression \:n\lgroup 2n^2 – 1\rgroup is\: 14}$$ Example2 Input n = 22 Output No Explanation $$\mathrm{There \:is\: no\: ... Read More
According to Nicomachus’ Theorem, the sum of the cubes of the first n integers is equal to the square of the nth triangular number. Or, we can also say − The sum of cubes of first n natural numbers is equal to square of sum of first natural numbers. Putting it algebraically, $$\mathrm{\displaystyle\sum\limits_{i=0}^n i^3=\lgroup \frac{n^2+n}{2}\rgroup^2}$$ Theorem $$1^3 = 1$$ $$2^3 = 3 + 5$$ $$3^3 = 7 + 9 + 11$$ $$4^3 = 13 + 15 + 17 + 19\vdots$$ Generalizing $$n^3 =\lgroup n^2−n+1\rgroup+\lgroup n^2−n+3\rgroup+⋯+\lgroup n^2+n−1\rgroup$$ Proof By Induction For all n Ε Natural ... Read More
In this problem, we will learn to implement the unrolled linked list. The unrolled linked list is a specialized version of the linked list. The normal linked list contains a single element in a single node, but the unrolled linked list contains a group of elements in each node. Also, insertion, deletion, and traversal in the unrolled linked list work the same as the typical linked list. The linear search is faster in the array than in the linked list. So, we can add elements in the array and an array in each node of the linked list. Also, ... Read More
In this problem, we need to implement Vizing's Theorem. Vizing's Theorem is used with graphs. Theorem statement - For any undirected graph G, the value of the Chromatic index is equal to the d or d + 1, where d is the maximum degree of the graph. The degree for any vertex is the total number of incoming or outgoing edges. Problem statement - We have given a graph and need to implement Vizing's Theorem to find the Chromatic index of the graph. Note - The chromatic index is a positive integer, requiring a ... Read More
The Schonhage-Strassen algorithm is useful when we need to multiply large decimal numbers. As Java supports the 1018 size of integers, and if we need to multiply the digits of more than 1018, we need to use the Schonhage-Strassen algorithm, as it is one of the fastest multiplication algorithms. It uses the basic rules for the multiplication of two numbers. It first performs the linear convolution and then performs the carry to get the final result. Problem statement - We have given mul1 and mul2 large decimal numbers and need to implement the Schonhage-Strassen algorithm to multiply both ... Read More
Problem Statement For an index and an arr[]. Check if the array[] can be partitioned into two disjoint sets, excluding arr[index] such that the sum of both sets has equal value. Example 1 Input arr[] = {4, 3, 1, 2}, Index = 1 Output No Explanation We have to exclude arr[1] = 3 All possible sets are − Set 1: (4), Set 2: (2, 1), sum = 4≠3 Set 1: (4, 1), Set 2: (2), sum = 5≠2 Set 1: (4, 2), Set 2: (1), sum = 6≠1 No combination satisfies the conditions. Example 2Input arr[] ... Read More
A square triangular number, also referred to as a triangular square number, is a number that is both a triangular number and a perfect square. Square triangular numbers have an unlimited number of possible values; the first few are − 0, 1, 36, 1225, 41616... A triangular number or triangle number counts objects arranged in an equilateral triangle. The nth triangular number is the number of dots in the triangular arrangement with n dots on each side and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers, ... Read More
In this problem, we need to find the index of the pattern in the string. Implementing an efficient text search is very important to allow users to search large text databases easily. For example, you are writing a blog in Microsoft Word or code in VSCode, containing 1 lakh+ word. If the search algorithm is inefficient, it can take time to show you search results when searching for any word or sentence. We will learn two different approaches to implementing the string search algorithm. One is the naïve approach, and another is the KMP algorithm. Problem statement - ... Read More
Introduction Pygame is the module used for game development in Python; it is considered to be one of the most effective modules for this purpose. The development of video games can not only be profitable in today's market but also serve as a medium for educational and promotional purposes. Creating games requires knowledge of mathematics, logic, physics, artificial intelligence, and a lot of other subjects, yet it can be really enjoyable. We will discuss in detail what is Pygame, how to implement a normal PyGame window and how to allow users to resize the window with a working example. ... Read More
In this problem, we need to find the sum of all prefixes of the given string. The best solution approach is that traverse through each prefix of the string and add them to get the answer. Problem statement - We have given a string named num_Str containing N digits. We need to find the sum of all prefixes of the given string. Sample examples Input num_str = "1123" Output 1247 Explanation - All prefixes of the given strings are 1, 11, 112, and 1123. The sum of all prefixes is 1247. Input num_str = ... Read More