There is a connected graph G(V, E) and the weight or cost for every edge is given. Prim’s Algorithm will find the minimum spanning tree from the graph G. It is a growing tree approach. This algorithm needs a seed value to start the tree. The seed vertex is grown to form the whole tree.The problem will be solved using two sets. One set holds the nodes that are already selected, and another set holds the item those are not considered yet. From the seed vertex, it takes adjacent vertices, based on minimum edge cost, thus it grows the tree by ... 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

Huffman coding is a lossless data compression algorithm. In this algorithm, a variable-length code is assigned to input different characters. The code length is related to how frequently characters are used. Most frequent characters have the smallest codes and longer codes for least frequent characters.There are mainly two parts. First one to create a Huffman tree, and another one to traverse the tree to find codes.For an example, consider some strings “YYYZXXYYX”, the frequency of character Y is larger than X and the character Z has the least frequency. So the length of the code for Y is smaller than ... 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

This is an example of the non-comparison sorting technique. It is used where the number of items and the range of possible key values is approximately the same.To perform this sort, we need to make some holes. The number of holes needed is decided by the range of numbers. In each hole, items are inserted. Finally deleted from the hole and stored into an array for sorted order.The complexity of Pigeon-Hole Sort TechniqueTime Complexity: O(n+2^k)Space Complexity: O(2^k)Input and OutputInput: The unsorted list: 802 630 20 745 52 300 612 932 78 187 Output: Data before Sorting: 802 630 20 745 ... Read More

Cycle Sort is an in-place sorting algorithm. It is also a comparison based sort and efficient for any other in-place sorting technique. It finds the minimum number of memory write to perform the sorting tasks.The complexity of Cycle Sort TechniqueTime Complexity: O(n^2)Space Complexity: O(1)Input and OutputInput: A list of unsorted data: 23 63 98 74 20 14 36 45 99 78 Output: Array before Sorting: 23 63 98 74 20 14 36 45 99 78 Array after Sorting: 14 20 23 36 45 63 74 78 98 99AlgorithmcycleSort(array, size)Input − An array of data, and the total number in the ... Read More

The basic idea of comb sort and the bubble sort is same. In other words, comb sort is an improvement on the bubble sort. In the bubble sorting technique, the items are compared with the next item in each phase. But for the comb sort, the items are sorted in a specific gap. After completing each phase, the gap is decreased. The decreasing factor or the shrink factor for this sort is 1.3. It means that after completing each phase the gap is divided by 1.3.The complexity of Comb Sort TechniqueTime Complexity: O(n log n) for the best case. O(n^2/2^p) (p ... Read More