Algorithms Articles - Page 39 of 41

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 More

An undirected graph is said to be a biconnected graph, if there are two vertex-disjoint paths between any two vertices are present. In other words, we can say that there is a cycle between any two vertices.We can say that a graph G is a bi-connected graph if it is connected, and there are no articulation points or cut vertex are present in the graph.To solve this problem, we will use the DFS traversal. Using DFS, we will try to find if there is any articulation point is present or not. We also check whether all vertices are visited by ... Read More

Medians are the middle numbers, in other words, the median value is the middle observation in an ordered list. It corresponds to the cumulative percentage of 50%.The size of two arrays must be same, we will find the median of two separate arrays at first, then compare the separate medians to get an actual median of two lists.Input and OutputInput: Two sorted array are given. Array 1: {1, 2, 3, 6, 7} Array 2: {4, 6, 8, 10, 11} Output: The median from two array. Here the median value is 6. Merge the given lists into one. {1, 2, 3, ... Read More

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 ... Read More

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 More

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 More

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 More

In this section, we will try to solve the famous number maze problem called Sudoku. Sudoku is a 9 x 9 number grid, and the whole grid are also divided into 3 x 3 boxes There are some rules to solve the Sudoku.We have to use digits 1 to 9 for solving this problem.One digit cannot be repeated in one row, one column or in one 3 x 3 box.Using the backtracking algorithm, we will try to solve the Sudoku problem. When some cell is filled with a digit, it checks whether it is valid or not. When it is ... Read More

In this problem, there is a given maze of size N x N. The source and the destination location is top-left cell and bottom right cell respectively. Some cells are valid to move and some cells are blocked. If one rat starts moving from start vertex to destination vertex, we have to find that is there any way to complete the path, if it is possible then mark the correct path for the rat.The maze is given using a binary matrix, where it is marked with 1, it is a valid path, otherwise 0 for a blocked cell.NOTE: The rat can ... Read More

This algorithm is named Z Algorithm because, in this algorithm, we need to create a Z array. The size of the Z array is the same as the text size. This array is used to store the length of longest possible substring starting from the current character of the main string. At first, the pattern and the main text are concatenated with a special symbol which is not present in the text and pattern. If the P is pattern and T is the main text, then after concatenation, it would be P$T (Assuming $ is not present in the P ... Read More