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Algorithms Articles
Page 28 of 39
How to find if a graph is Bipartite?
A graph is said to be a bipartite graph, when vertices of that graph can be divided into two independent sets such that every edge in the graph is either start from the first set and ended in the second set, or starts from the second set, connected to the first set, in other words, we can say that no edge can found in the same set.Checking of a bipartite graph is possible by using the vertex coloring. When a vertex is in the same set, it has the same color, for another set, the color will change.Input and OutputInput: ...
Read MoreShortest path with exactly k Edges
One directed graph is provided with the weight between each pair of vertices, and two vertices u and v are also provided. Our task is to find the shortest distance from vertex u to vertex v, with exactly k number of edges. To solve this problem, we will start from vertex u and go to all adjacent vertices and recur for adjacent vertices using the k value as k - 1.Input and OutputInput: The cost matrix of the graph. 0 10 3 2 ∞ 0 ∞ 7 ∞ ∞ 0 6 ∞ ∞ ∞ 0 Output: Weight of the shortest ...
Read MoreCheck if a given graph is tree or not
In this problem, one undirected graph is given, we have to check the graph is tree or not. We can simply find it by checking the criteria of a tree. A tree will not contain a cycle, so if there is any cycle in the graph, it is not a tree.We can check it using another approach, if the graph is connected and it has V-1 edges, it could be a tree. Here V is the number of vertices in the graph.Input and OutputInput: The adjacency matrix. 0 0 0 0 1 0 0 0 0 1 0 0 0 ...
Read MoreConnectivity in a directed graph
To check connectivity of a graph, we will try to traverse all nodes using any traversal algorithm. After completing the traversal, if there is any node, which is not visited, then the graph is not connected.For the directed graph, we will start traversing from all nodes to check connectivity. Sometimes one edge can have the only outward edge but no inward edge, so that node will be unvisited from any other starting node.In this case, the traversal algorithm is recursive DFS traversal.Input and OutputInput: Adjacency matrix of a graph 0 1 0 0 0 0 0 1 0 ...
Read MoreDetect Cycle in a an Undirected Graph
To detect if there is any cycle in the undirected graph or not, we will use the DFS traversal for the given graph. For every visited vertex v, when we have found any adjacent vertex u, such that u is already visited, and u is not the parent of vertex v. Then one cycle is detected. We will assume that there are no parallel edges for any pair of vertices.Input and Output: Adjacency matrix 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 ...
Read MoreBridges in a Graph
An edge in an undirected graph is said to be a bridge, if and only if by removing it, disconnects the graph, or make different components of the graph. In a practical approach, if some bridges are present in a network when the connection of bridges is broken, it can break the whole network.Input and OutputInput: The adjacency matrix of the graph. 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 Output: Bridges in given graph: Bridge 3--4 Bridge 0--3AlgorithmbridgeFind(start, visited, disc, low, ...
Read MoreWord Break Problem
In the input of this problem, one sentence is given without spaces, another dictionary is also provided of some valid English words. We have to find the possible ways to break the sentence in individual dictionary words.We will try to search from the left of the string to find a valid word when a valid word is found, we will search for words in the next part of that string.Input and OutputInput: A set of valid words as dictionary, and a string where different words are placed without spaces. Dictionary: {mobile, sam, sung, man, mango, icecream, and, go, i, love, ...
Read MoreClosest Pair of Points Problem
In this problem, a set of n points are given on the 2D plane. In this problem, we have to find the pair of points, whose distance is minimum.To solve this problem, we have to divide points into two halves, after that smallest distance between two points is calculated in a recursive way. Using distances from the middle line, the points are separated into some strips. We will find the smallest distance from the strip array. At first two lists are created with data points, one list will hold points which are sorted on x values, another will hold data ...
Read MorePeak Element in 2D array
An item is said to be a peak element when it is greater than or equal with all four neighbor of that element. The neighbor elements are the top, bottom, left and right elements. For this problem, we will consider some bounds. The diagonal elements are not checked as neighbor elements. More than one peak element may present in a matrix, and the peak element is not necessarily the largest element in the matrix.Input and OutputInput: A matrix of different numbers. 10 8 10 10 14 13 12 11 15 9 11 11 15 9 11 21 16 17 19 ...
Read MoreCount Inversions in an array
The inversions of an array indicate; how many changes are required to convert the array into its sorted form. When an array is already sorted, it needs 0 inversions, and in another case, the number of inversions will be maximum, if the array is reversed.To solve this problem, we will follow the Merge sort approach to reduce the time complexity, and make it in Divide and Conquer algorithm.Input and OutputInput: A sequence of numbers. (1, 5, 6, 4, 20). Output: The number of inversions required to arrange the numbers into ascending order. Here the number of inversions are 2. First ...
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