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Must do Math for Competitive Programming

Last Updated: 19 February 2023

Competitive Programming (CP) doesn’t typically require one to know high-level calculus or some rocket science. But there are some concepts and tricks which are sufficient ...read more

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Total number of BSTs using array elements

Last Updated: 30 June 2022

Prerequisite: Total number of possible Binary Search Trees with n keysGiven an array arr[] of N integers. The task is to count the number of Binary Search Tree can be made ...read more

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Total number of possible Binary Search Trees using Catalan Number

Last Updated: 16 June 2022

Given an integer N, the task is to count the number of possible Binary Search Trees with N keys.Examples: Input: N = 2Output: 2For N = 2, there are 2 unique BSTs 1 ...read more

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Dyck Words of given length

Last Updated: 31 May 2021

Given an integer n, the task is to count Dyck words possible of length n. A DYCK word is a word containing only characters 'X' and 'Y' such that in every prefix of the wor...read more

Competitive Programming

Number of ways a convex polygon of n+2 sides can split into triangles by connecting vertices

Last Updated: 01 September 2022

Given a convex polygon with n+2 sides. The task is to calculate the number of ways in which triangles can be formed by connecting vertices with non-crossing line segments....read more

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Number of Binary Trees for given Preorder Sequence length

Last Updated: 23 June 2022

Count the number of Binary Tree possible for a given Preorder Sequence length n.Examples:Input : n = 1Output : 1Input : n = 2Output : 2Input : n = 3Output : 5Background :I...read more

Non-crossing lines to connect points in a circle

Last Updated: 02 May 2022

Consider a circle with n points on circumference of it where n is even. Count number of ways we can connect these points such that no two connecting lines to cross each ot ...read more

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Last Updated: 11 April 2023

Consider a n x n grid with indexes of top left corner as (0, 0). Dyck path is a staircase walk from bottom left, i.e., (n-1, 0) to top right, i.e., (0, n-1) that lies abov...read more

Applications of Catalan Numbers

Last Updated: 01 February 2023

Background :Catalan numbers are defined using below formula:[Tex]C_{n} = (2n)!/(n+1)!n! = \prod^{n}_{k=2} \frac{n+k}{k} for_ n = 0[/Tex]Catalan numbers can also be defined...read more

Technical Scripter

Find all possible binary trees with given Inorder Traversal

Last Updated: 25 December 2022

Given an array that represents Inorder Traversal, find all possible Binary Trees with the given Inorder traversal and print their preorder traversals.Examples:Input: in[ ...read more

Succinct Encoding of Binary Tree

Last Updated: 22 December 2022

A succinct encoding of Binary Tree takes close to minimum possible space. The number of structurally different binary trees on n nodes is n'th Catalan number. For large n, ...read more

Construct all possible BSTs for keys 1 to N

Last Updated: 28 December 2022

In this article, first count of possible BST (Binary Search Trees)s is discussed, then the construction of all possible BSTs.How many structurally unique BSTs for keys fro ...read more

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Find the number of valid parentheses expressions of given length

Last Updated: 15 March 2023

Given a number n find the number of valid parentheses expressions of that length.Examples :Input: 2Output: 1 There is only possible valid expression of length 2, "()"Input ...read more

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Program for nth Catalan Number

Last Updated: 22 November 2023

Catalan numbers are defined as a mathematical sequence that consists of positive integers, which can be used to find the number of possibilities of various combinations.Th...read more

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Total number of possible Binary Search Trees and Binary Trees with n keys

Last Updated: 30 December 2022

Total number of possible Binary Search Trees with n different keys (countBST(n)) = Catalan number Cn = (2n)! / ((n + 1)! * n!)For n = 0, 1, 2, 3, … values of Catalan numbe ...read more

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