In this article, we will describe every possible approach to find the number of quadruples in which the first 3 terms are in A.P., and the last 3 are in G.P. First, we will explain the basic definition of arithmetic progression(A.P.) and geometric progression (G.P.).Arithmetic progression(A.P.) − It is a sequence of numbers in which the common difference (d) is the same or constant that means a difference of two consecutive numbers is constant. For example: 1, 3, 5, 7, 9 | d = 2Geometric Progression(G.P.) − It is a sequence of numbers in which the common ratios (r) are ... Read More

A quadrilateral forms a polygon with four vertices and four edges in Euclidean plane geometry. The name 4-gon etc. Included in other names of quadrilaterals and sometimes they are also known as a square, display style, etc.In this article, we will explain the approaches to finding the number of quadrilaterals possible from the given points. In this problem, we need to find out how many possible quadrilaterals are possible to create with the provided four points ( x, y ) in the cartesian plane. So here is the example for the given problem −Input : A( -2, 8 ), B( ... Read More

In this article we will describe the ways to find the number of primes in a subarray. We have an array of positive numbers arr[] and q queries having two integers that denote our range {l, R} we need to find the number of primes in the given range. So below is an example of the given problem −Input : arr[] = {1, 2, 3, 4, 5, 6}, q = 1, L = 0, R = 3 Output : 2 In the given range the primes are {2, 3}. Input : arr[] = {2, 3, 5, 8 ... Read More

In this article, we will explain everything about finding the number of prime pairs in an array using C++. We have an array arr[] of integers, and we need to find all the possible prime pairs present in it. So here is the example for the problem −Input : arr[ ] = { 1, 2, 3, 5, 7, 9 } Output : 6 From the given array, prime pairs are (2, 3), (2, 5), (2, 7), (3, 5), (3, 7), (5, 7) Input : arr[] = {1, 4, 5, 9, 11} Output : 1Approaches to Find ... Read More

In this article, we need to find a number of prefix sum which are prime numbers in a given array arr[ ] of positive integers and range query L, R, where L is the initial index value arr[ L ] for prefixsum[ ] array and R is the number of prefix sum we need to find.To fill the prefix sum array, we start with index L to index R and add the present value with the last element in the given array. So here is the Example for the problem −Input : arr[ ] = { 3, 5, 6, 2, ... Read More

In this article, we will explain how to solve the number of possible pairs of hypotenuse and area form a right-angled triangle in C++.We need to determine the number of all possible pairs of a hypotenuse and the area ( H, A ) to form a right-angled triangle with H as hypotenuse and A as Area.In this example −         x = Base of Right Angled Triangle         y = Height of Right Angled Triangle         H = hypotenuse of Right Angled TriangleWe know Area of right angled triangle, A = ( x * ... Read More

In an array, A pair a[i], a[j] is known as an inversion if a[i] > a[j] and i < j. We have two numbers N and k, and need to figure out how many possible permutations of the first N numbers end in a perfect K inversion. So here is the example −Input: N = 4, K = 1 Output: 3 Explanation: Permutation of the first N numbers in total : 1234, 1243, 1324 and 2134. With 1 inversion we have 1243, 1324 and 2134. Input : N = 3, K = 2 Output : 3 Explanation: Permutation of ... Read More

As we all know, pentagons and hexagons are equally essential parts of football. These shapes fit together like a puzzle for forming a perfectly spherical shape. So here we have a football, in which we have to find the hexagons and pentagons.We will use the Euler characteristic to solve the problem easily. Euler characteristic is a number that works to describe a specific shape or structure of any topological space. So we can use it for calculating the number of Pentagons and Hexagons on the football.In Euler characteristics −chi(S) − Integer for a specific surface SF − facesG − GraphV ... Read More

In this article, we'll use C++ to calculate the number of weight W paths in a K-ary tree in this article. We've given a K-ary tree, which is a tree in which each node has K children and each edge has a weight assigned to it, with weights descending from 1 to K from one node to all of its children.We need to count the cumulative number of paths beginning from the root that have a weight of W and at least one edge with a weight of M. So, here's example −Input : W = 4, K = 3, ... Read More

C++ has a huge list of functions to solve mathematical issues. One of the mathematical functions is to find Nth odd digits using codes. This article will describe the complete approach of finding the odd Nth number and understand what odd numbers are and what numbers are made up of odd digits.Finding the Nth Number Made up of Odd Digits OnlyOdd numbers give remainder on dividing by two, so the first few odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19...To find the required number, we have two approaches here −Approach 1 − Check every natural ... Read More