### Finding the Eulerian path in $O(M)$

A Eulerian path is a path in a graph that passes through all of its edges exactly once. A Eulerian cycle is a Eulerian path […]

A Eulerian path is a path in a graph that passes through all of its edges exactly once. A Eulerian cycle is a Eulerian path […]

You are given a directed weighted graph $G$ with $N$ vertices and $M$ edges. Find any cycle of negative weight in it, if such a […]

Problem: You are given a connected undirected graph (with possible multiple edges) represented using an adjacency matrix. Find the number of different spanning trees of […]

Given a directed or an undirected weighted graph $G$ with $n$ vertices. The task is to find the length of the shortest path $d_{ij}$ between […]

We are given an undirected graph. An articulation point (or cut vertex) is defined as a vertex which, when removed along with associated edges, makes […]

1. Overview We are given an undirected graph. A bridge is an edge whose removal makes the graph disconnected (or, more precisely, increases the number […]

We are given an undirected graph. A bridge is defined as an edge which, when removed, makes the graph disconnected (or more precisely, increases the […]

1. Problem statement Given $n$ points on the plane. Each point $p_i$ is defined by its coordinates $(x_i,y_i)$. It is required to find among them […]

Let a simple polygon (i.e. without self intersection, not necessarily convex) be given. It is required to calculate its area given its vertices. 1. Method […]

Given two circles. It is required to find all their common tangents, i.e. all such lines that touch both circles simultaneously. The described algorithm will […]

The task is: given the coordinates of the ends of a segment, construct a line passing through it. We assume that the segment is non-degenerate, […]

You are given two numbers $n$ and $k$. Find the largest power of $k$ $x$ such that $n!$ is divisible by $k^x$. 1. Prime $k$ […]

The rank of a matrix is the largest number of linearly independent rows/columns of the matrix. The rank is not only defined for square matrices. The […]

Given a string $s$ of length $n$. A repetition is two occurrences of a string in a row. In other words a repetition can be described by […]

You are given a matrix with n rows and m columns. Find the largest submatrix consisting of only zeros (a submatrix is a rectangular area of the matrix). 1. […]

1. Introduction A quick intro on how to find the min/max value from a given list/collection with the powerful Stream API in Java8. 2. Find Max in […]

1. Overview Finding differences between collections of objects of the same data type is a common programming task. As an example, imagine we have a […]