Algorithms Articles - Page 38 of 39

From the text, we can generate all suffixes to make a tree structure. We know that every pattern that presents in the text, must be a prefix of one of the possible suffix in the text. By building Trie of all suffixes, we can find any substring in linear time. Every suffix is ending with string terminating symbol. From each node if there is any path, it moves forward, otherwise returns that pattern is not found.For this algorithm, the time complexity is O(m+k), where the m is the length of string and k is the frequency of the pattern in ... Read More

From a given string, we can get all possible suffixes. After sorting the suffixes in lexicographical order, we can get the suffix array. Suffix arrays can also be formed using suffix trees. By using the DFS traversal of suffix trees, we can get suffix arrays. Suffix arrays are helpful to find suffixes in linear time. We can also find substrings using suffix array by using binary search type procedure.The time complexity is O(m log n)Input and OutputInput: Main String: “BANANA”, Pattern: “NAN” Output: Pattern found at position: 2AlgorithmfillSuffixArray (text, suffArray)Input: The main stringOutput: The array of suffixesBegin    n := text Length ... Read More

The bad character heuristic method is one of the approaches of Boyer Moore Algorithm. Another approach is Good Suffix Heuristic. In this method we will try to find a bad character, that means a character of the main string, which is not matching with the pattern. When the mismatch has occurred, we will shift the entire pattern until the mismatch becomes a match, otherwise, pattern moves past the bad character.Here the time complexity is O(m/n) for best case and O(mn)for the worst case, where n is the length of the text and m is the length of the pattern.Input and ... Read More

Anagrams are basically all permutations of a given string or pattern. This pattern searching algorithm is slightly different. In this case, not only the exact pattern is searched, it searches all possible arrangements of the given pattern in the text.To solve this problem, we will divide the whole texts into several windows of length same as patterns. Then count on each character of the pattern is found and stored in an array. For each window, we also try to find the count array, then check whether they are matching or not.The time Complexity of Anagram Pattern Search Algorithm is O(n).Input ... Read More

It is similar to the previous algorithm. Here the only difference is, the Graph G(V, E) is represented by an adjacency list.Time complexity adjacency list representation is O(E log V).Input and OutputInput: The cost matrix: Output: Edge: A--B And Cost: 1 Edge: B--E And Cost: 2 Edge: A--C And Cost: 3 Edge: A--D And Cost: 4 Edge: E--F And Cost: 2 Edge: F--G And Cost: 3 Total Cost: 15Algorithmprims(g: Graph, start)Input −  The graph g and the seed vertex named ‘start’Output − The Tree after adding edges.Begin    create two set B, N    add the start node in B ... Read More

A list of arrival and departure time is given. Now the problem is to find the minimum number of platforms are required for the railway as no train waits.By sorting all timings in sorted order, we can find the solution easily, it will be easy to track when the train has arrived but not left the station.The time complexity of this problem is O(n Log n).Input and OutputInput: Lists of arrival time and departure time. Arrival: {900, 940, 950, 1100, 1500, 1800} Departure: {910, 1200, 1120, 1130, 1900, 2000} Output: Minimum Number of Platforms Required: 3AlgorithmminPlatform(arrival, departure, int n)Input − The ... Read More

There is a list of coin C(c1, c2, ……Cn) is given and a value V is also given. Now the problem is to use the minimum number of coins to make the chance V.Note − Assume there are an infinite number of coins CIn this problem, we will consider a set of different coins C{1, 2, 5, 10} are given, There is an infinite number of coins of each type. To make change the requested value we will try to take the minimum number of coins of any type.As an example, for value 22 − we will choose {10, 10, 2}, ... Read More

In the previous Huffman code problem, the frequency was not sorted. If the frequency list is given in sorted order, the task of assigning code is being more efficient.In this problem, we will use two empty queues. Then create a leaf node for each unique character and insert it into the queue in increasing order of frequency.In this approach, the complexity of the algorithm is O(n).Input and OutputInput: Different letters and their frequency in sorted order Letters: {L, K, X, C, E, B, A, F} Frequency: {1, 1, 2, 2, 2, 2, 3, 4} Output: Codes for the letters L: ... Read More

There is a given graph G(V, E) with its adjacency list representation, and a source vertex is also provided. Dijkstra’s algorithm to find the minimum shortest path between source vertex to any other vertex of the graph G.To Solve this problem, we will use two lists. One is to store vertices which have been considered as the shortest path tree, and another will hold the vertices which are not considered yet. In each phase of the algorithm, we find the unconsidered vertex and which has the minimum distance from the source.Another list is used to hold the predecessor node. Using ... Read More

Activity Selection Problem The activity selection problem is an example of a greedy algorithm where the maximum number of non-overlapping activities are selected from the given activity set. A person can complete one activity at a time. The activities are given in the form of their starting and completion times. In this article, we have an array of integers that stores the starting and completion time of each activity. Our task is to select the maximum number of non-overlapping activities from the given activity array. Scenario An example of the maximum activity ... Read More