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Get StartedEuclid’s algorithm (or Euclidean algorithm) is a method for efficiently finding the greatest common divisor (GCD) of two numbers. The GCD of two integers, X and Y, is the largest number that divides both X and Y without leaving a remainder.
The extended Euclidean algorithm is an extension to the Euclidean algorithm, which computes, besides the greatest common divisor of integers a and b, the coefficients of Bézout’s identity, i.e., integers x and y such that ax + by = gcd(a, b).
The Vigenère cipher is a form of polyalphabetic substitution to encrypt alphabetic text by using a keyword. The Vigenère cipher is easy to understand and implement. It consists of several Caesar ciphers in sequence with different shift values.
The Diffie-Hellman algorithm is used to establish a shared secret between two parties that can be used for secret communication to exchange data over a public network.
An Eulerian trail (or Eulerian path) is a path in a graph that visits every edge exactly once. Given a directed graph, check whether it has an Eulerian path or not.
An independent set is a set of nodes in a binary tree, no two of which are adjacent. The maximum independent set problem is finding an independent set of the largest possible size for a given binary tree.
Find the total number of ways in which n hats can be returned to n people such that no hat makes it back to its owner.
Given a directed graph, check if it is possible to construct a cycle that visits each edge exactly once, i.e., check whether the graph has an Eulerian cycle or not.
Given a binary tree, write an efficient algorithm to find the maximum path sum between any two nodes in it. The path can start and end at any node in the tree and need not go through the root.
A triangulation of a convex polygon results in a set of non-intersecting diagonals between non-adjacent vertices, which completely partition the interior of the convex hull of the polygon into triangles.
Given an undirected graph, check whether it has an Eulerian path or not. In other words, check if it is possible to construct a path that visits each edge exactly once.
Suppose you are given n red and n blue water jugs, all of different shapes and sizes. All red jugs hold different amounts of water, as do the blue ones. Moreover, there is a blue jug for every red jug that holds the same amount of water and vice versa.