The max flow problem is a classic optimization problem in graph theory that involves finding the maximum amount of flow that can be sent through a network of pipes, channels, or other pathways, subject to capacity constraints. The problem can be used to model a wide variety of real-world situations,…

There are M transmitter and N receiver stations. Given a matrix that keeps track of the number of packets to be transmitted from a given transmitter to a receiver. If the (i; j)-th entry of the matrix is k, it means at that time the station i has k packets for transmission to station j. During a…

Try it on GfG Practice Given an undirected graph, the task is to check if the graph contains a cycle or not, using DSU. Examples: Input: The following is the graph Output: Yes Explanation: There is a cycle of vertices {0, 1, 2}. Recommended Practice Detect Cycle using DSU Try It! We already have…

Try it on GfG Practice Given a directed graph, determine if a vertex j is reachable from another vertex i for all vertex pairs (i, j) in the given graph. Here reachable means that there is a path from vertex i to j. The reach-ability matrix is called the transitive closure of a graph. Example:…

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An Adjacency List is used for representing graphs. Here, for every vertex in the graph, we have a list of all the other vertices which the particular vertex has an edge to. Problem: Given the adjacency list and number of vertices and edges of a graph, the task is to represent the adjacency list for…

Try it on GfG Practice Given two integers n and k, your task is to find a string of minimum length to contain all possible strings of size n as a substring. The characters of the string should be integers ranging from 0 to k - 1. Examples: Input: n = 2, k = 2 Output: 00110 Explanation: Allowed…

Try it on GfG Practice Given a 2D binary matrix of size N * M, where 0 represents an empty space while 1 represents a wall you cannot walk through. You are also given an integer K. You can walk up, down, left, or right. Given that you can remove up to K walls, return the minimum number of steps to…

Try it on GfG Practice Given a binary matrix mat[][] of dimensions NxM such that 1 denotes the island and 0 denotes the water. The task is to find the number of closed islands in the given matrix. A closed island is known as the group of 1s that is surrounded by only 0s on all the four sides…

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Try it on GfG Practice Given an undirected graph with V vertices and E edges (edges[][]), Your task is to return all the articulation points in the graph. If no such point exists, return {-1}. Note: An articulation point is a vertex whose removal, along with all its connected edges, increases the…

Try it on GfG Practice A directed graph is strongly connected if there is a path between all pairs of vertices. A strongly connected component (SCC) of a directed graph is a maximal strongly connected subgraph. For example, there are 3 SCCs in the following graph: We have discussed Kosaraju's…

Try it on GfG Practice Given a 2D grid of size n*n, where each cell represents the cost to traverse through that cell, the task is to find the minimum cost to move from the top left cell to the bottom right cell. From a given cell, we can move in 4 directions: left, right, up, down. Note: It is…

Try it on GfG Practice Given n and k, Construct a palindrome of size n using a binary number of size k repeating itself to wrap into the palindrome. The palindrome must always begin with 1 and contains maximum number of zeros. Examples : Input : n = 5, k = 3 Output : 11011 Explanation : the 3 sized…

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Try it on GfG Practice Flood Fill is a classic algorithm used to change the color of an area in a 2D image where all pixels are connected and have the same initial color. Think of it like the paint bucket tool in graphic design software like MS Paint or Photoshop—when you click on a spot, it…

Try it on GfG Practice Given an array arr[] of distinct elements, find the minimum number of swaps required to sort the array. Examples: Input: arr[] = [2, 8, 5, 4] Output: 1 Explanation: Swap 8 with 4 to get the sorted array. Input: arr[] = [10, 19, 6, 3, 5] Output: 2 Explanation: Swap 10 with 3…

Try it on GfG Practice Strongly Connected Components (SCCs) are a fundamental concept in graph theory and algorithms. In a directed graph, a Strongly Connected Component is a subset of vertices where every vertex in the subset is reachable from every other vertex in the same subset by traversing the…

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Try it on GfG Practice Given a Directed Graph with n vertices represented as a list of directed edges represented by a 2D array edgeList[][], where each edge is defined as (u, v) meaning there is a directed edge from u to v. Additionally, you are given two vertices: source and destination. The task…

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Try it on GfG Practice Given a binary grid of n*m. Find the distance of the nearest 1 in the grid for each cell. The distance is calculated as |i1 - i2| + |j1 - j2|, where i1, j1 are the row number and column number of the current cell, and i2, j2 are the row number and column number of the nearest…

Try it on GfG Practice Given a grid of size N * M consisting of O's and X's. The task is to find the number of 'X' total shapes. Note: 'X' shape consists of one or more adjacents X's (diagonals not included). Examples: Input: grid = {{X, O, X}, {O, X, O}, {X, X, X}} Output: 3 Explanation: The grid…

Try it on GfG Practice What is Hamiltonian Cycle? Hamiltonian Cycle or Circuit in a graph G is a cycle that visits every vertex of G exactly once and returns to the starting vertex. If graph contains a Hamiltonian cycle, it is called Hamiltonian graph otherwise it is non-Hamiltonian.Finding a…

Try it on GfG Practice A matching in a Bipartite Graph is a set of the edges chosen in such a way that no two edges share an endpoint. A maximum matching is a matching of maximum size (maximum number of edges). In a maximum matching, if any edge is added to it, it is no longer a matching. There can…

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Try it on GfG Practice Given an undirected graph, the task is to return all the connected components in any order. Examples: Input: Consider the following graph Example of an undirected graph Output: [[0, 1, 2], [3, 4]] Explanation: There are 2 different connected components. They are {0, 1, 2} and…

Try it on GfG Practice Given a 2-D grid of characters mat[][] and a string word, the task is to check if that word exist in the grid mat[][] or not. A word can be matched in 4 directions at any point. The 4 directions are horizontally left and right, vertically up and down. Examples: Input: mat[][]…

Given a text string and a pattern string, check if a pattern exists in text or not. Few pattern searching algorithms (KMP, Rabin-Karp, Naive Algorithm, Finite Automata) are already discussed, which can be used for this check. Here we will discuss suffix tree based algorithm. As a prerequisite, we…

Try it on GfG Practice Given a 2D grid m*n of characters and a word, the task is to find all occurrences of the given word in the grid. A word can be matched in all 8 directions at any point. Word is said to be found in a direction if all characters match in this direction (not in zig-zag form). The…

Given two strings s and t. The task is to find maximum length of some prefix of the string S which occur in string t as subsequence. Examples : Input : s = "digger" t = "biggerdiagram" Output : 3 digger biggerdiagram Prefix "dig" of s is longest subsequence in t. Input : s = "geeksforgeeks" t =…

Given a text txt and a wildcard pattern pat, implement a wildcard pattern matching algorithm that finds if the wildcard pattern is matched with the text. The matching should cover the entire text. The wildcard pattern can include the characters ‘?’ and ‘*’ which denote: ‘?’ – matches any single…

Try it on GfG Practice Given a string s, the task is to find the length of the longest proper prefix which is also a suffix. A proper prefix is a prefix that doesn’t include whole string. For example, prefixes of "abc" are "", "a", "ab" and "abc" but proper prefixes are "", "a" and "ab" only.…

Given a text t and a pattern p where t consists of only lowercase English alphabets while p consists of lowercase English alphabets as well as special characters '.' and '*', the task is to implement a function to test regular expression such that: '.' Matches any single character.​​​​'*' Matches…

Try it on GfG Practice A string contains patterns of the form 1(0+)1 where (0+) represents any non-empty consecutive sequence of 0's. Count all such patterns. The patterns are allowed to overlap. Note : It contains digits and lowercase characters only. The string is not necessarily a binary. 100201…

Try it on GfG Practice Given a 2-dimensional character array and a string, we need to find the given string in a 2-dimensional character array, such that individual characters can be present left to right, right to left, top to down or down to top. Examples: Input : a ={ {D,D,D,G,D,D},…

Problem Statement: Given a text txt[0..n-1] and a pattern pat[0..m-1], write a function search(char pat[], char txt[]) that prints all occurrences of pat[] in txt[]. You may assume that n > m.As discussed in the previous post, we discussed that there are two ways efficiently solve the above problem.…