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C++ Articles
Page 391 of 597
Centered Heptagonal Number
What do you understand by the term centered hepatgonal number? Let’s decode in this article. First of all, what is a heptagonal number? A heptagonal number is a figurate number representing the number of dots that can be arranged to form a regular heptagon (a seven−sided polygon). The formula for the nth heptagonal number is: n(5n−3)/2, where n must be a positive integer. The first few heptagonal numbers, for example, are: 1 is the first heptagonal number (corresponding to a heptagon with one dot). 7 is the second heptagonal number (corresponding to a heptagon with 7 dots). 18 is ...
Read MoreCake Number
What do you understand by the term `Cake Number`? Let's decode it in this article. The term "cake number" describes a concept of discrete geometry and combinatorics−related mathematical idea. It is built on the concept of the Lazy caterer's sequence. What is the Lazy Caterer's Sequence? The maximum number of pieces a disk (cake or pizza) can be sliced into using a specific number of straight slices is known as the Lazy caterer's sequence. Although it mentions a disk, we will consider a cake in our example. One straight cut can divide a cake into two pieces, two straight cuts ...
Read MoreAdvantages and Disadvantages of Three-tier Architecture
A 3−tier application architecture is a modular client−server architecture that consists of a presentation tier, an application tier, and a data tier. The presentation tier is a graphical user interface (GUI) that interacts with the other two tiers; the data tier stores information; the application tier manages logic. A 3−tier architecture has pros in terms of better horizontal scalability, performance, and availability. When there are three layers, each component can be produced concurrently by a separate team of programmers using a different programming language than the developers of the other levels. The 3−tier paradigm makes it simpler for an organization ...
Read MoreLargest Component Size in a Graph Formed by Connecting Non-Co-Prime Nodes
Introduction In this tutorial, we discuss the problem of finding the largest component size in a graph generated by connecting non-co-prime nodes through C++. Graphs are formed by nodes connected by edges. The components of the graph are a subset of values that form nodes. There is an array a[] which forms graph G. The components of the graph are a subset of values that form nodes. The non-coprime numbers are the numbers that have a HCF (Highest Common Factor) other than 1, that means they have some other common factors. We solve the problem statement in this tutorial using ...
Read MoreCorollaries of Binomial Theorem
The Binomial Theorem describes how to expand an expression raised to any finite power. A binomial theorem is a powerful expansion tool that has applications in algebra, probability, and other fields. Assume we have an expression $\mathrm{(x\:+\:y)^n}$and we need to expand the expression, we can do this using the generalised equation of binomial theorem. The binomial theorem defines a binomial expression for two different terms. The general equation of binomial theorem is: $$\mathrm{(a+b)^{n}=^n{C_{r=0}}a^{n-r}b^{0}\:+\:^n{C_{r=1}}a^{n-1}b^{1\:}+\:........\:+\:^n{C_{r=n-1}}a^{1}b^{n-1}+^n{C_{r=n}}a^{0}b^{n}}$$ $$\mathrm{=n_{\sum_{r=0}}^n{C_{r}}a^{n-r}b^{r}}$$ Where we can get the value of $\mathrm{^n{C_{r}}}$ using the formula, $$\mathrm{^n{C_{r}}=\frac{n!}{(n-r)!r!}}$$[0! is always equals to 1] NOTE There ...
Read MoreWays to choose three points with distance between the most distant points <= L
The problem states that we need to figure out the number of ways to choose three points with distance between the most distant points less than or equal to L, a positive integer that will be given as an input. In the problem we will be given an array of different points which lies on the x-axis and an integer L greater than 0. The task involves finding the number of sets of three points where the distance between the most distant points is less than or equal to that integer L. NOTE : The set of points ...
Read MoreTwo Odd Occurring Elements in an Array where all Other Occur Even Times
The problem includes finding two odd occurring elements in an array where all other elements occur even times in C++. An array is a data structure in C++ which is used to store a list of elements in it of similar data types. We will be given an array of any size greater than or equal to 2 in input. The array will contain integers in it. Every integer in the array will occur even times except two integers which will be occurring odd times in the array. In this problem, we need to find out those two elements ...
Read MoreSum of Product of r and rth Binomial Coefficient (r * nCr)
The problem states that we must determine the sum of the product of r and the rth binomial coefficient (r*nCr). Positive numbers that are coefficients in the binomial theorem are called binomial coefficients. Both Pascal's triangle and a straightforward formula can be used to determine the binomial coefficients. The formula for binomial coefficient is: $$\mathrm{n_{c_{r}}=\frac{n!}{(n-r)!r!}}$$ NOTE : The value of 0! is always equal to 1. In this equation n and r can be any non-negative integers and r should never be greater than n. The objective at hand in this problem entails computing the ...
Read MoreSet the Rightmost Unset Bit
The problem statement includes setting the rightmost unset bit of any positive integer N in C++. A bit is simply a binary digit of any number when represented in the form of a binary number. A binary number is the numerical representation of any data in the form of 0 and 1 where every bit(digit) of the number represents the power of 2 starting with 2^0 from the unit digit. Let's represent an integer 7 in the form of a binary number. The binary representation of 7 will be 111. These numbers can either be represented ...
Read MoreSubtract 1 Without Arithmetic Operators
This problem includes that we need to subtract 1 without using arithmetic operators. We will be given any integer N as input in the problem and we need to subtract 1 from the number or simply we need to print N-1. Our task is to perform the operation without using any arithmetic operators. The arithmetic operations involves variety of operations on numbers like addition(+), subtraction(-), multiplication(*), division(/), modulo(%), etc. These operations are supported by every programming language on numbers. Despite using this we need to subtract 1 from the number. For example, Input 7 Output 6 Explanation ...
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