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Analysis of Algorithms Articles
Page 3 of 17
Yen's k-Shortest Path Algorithm in Data Structure
Instead of giving a single shortest path, Yen’s k-shortest path algorithm gives k shortest paths so that we can get the second shortest path and the third shortest path and so on.Let us consider a scenario that we have to travel from place A to place B and there are multiple routes available between place A and place B, but we have to find the shortest path and neglect all the paths that are less considered in terms of its time complexity in order to reach the destination.Let us understand with an example-Consider the given example as the bridge which ...
Read MoreFloyd Cycle Detection Algorithm to detect the cycle in a linear Data Structure
Floyd Cycle is one of the cycle detection algorithms to detect the cycle in a given singly linked list.In the Floyd Cycle algorithm, we have two pointers that initially point at the head. In Hare and Tortoise’s story, Hare moves twice as fast as Tortoise, and whenever the hare reaches the end of the path, the tortoise reaches the middle of the path.AlgorithmInitialize Hare and Tortoise at the head node of the List.Initially, the hare moves twice as fast as the tortoise.Move the hare and tortoise both and find if the hare reaches the end of the Linked List, return ...
Read MoreAuto-complete feature using Trie
We have a Trie, and when a user enters a character, we have to show the matching string the Trie. This feature we call it as auto-completion. For example, if a Trie contains "xyzzzz, ""xyz, " "xxxyyxzzz" and when the user enter xy, then we have to show them xyzzzz, xyz, etc.., Steps to achieve the result.Search for the string using the standard Trie algorithm.If the string is not present, then return -1.If the string is present and is the end of a word in Trie, then print the string.If the matching string doesn't have any node, then return.Else print ...
Read MoreSegment Trees in Data Structure
In this section we will see what is the segment tree. Before discussing that, let us see one problem.Suppose we have an array arr[0, …, n-1], We can do following operations −Find the sum of elements from index l to r, where 0 ≤ l ≤ r ≤ n-1Change the value of a specified element of the array to a new value x. We need to do arr[i] = x. The i in range 0 to n – 1.We can solve this problem by using the Segment tree. The segment tree can help us to get the sum and query ...
Read MoreInterval Trees in Data Structure
In this section we will see what is the interval tree. As the name suggests, that the interval trees are the trees which are associated with the intervals. So before discussing about the interval trees, let us see the elementary intervals.An interval is basically a range. So if one interval is written as [a, b] it indicates that the range is starting from a, and ending at b.Now suppose there is an interval [10, 20]. So there are three range values. First one is -∞ to 10, 10 to 20 and finally 20 to ∞Now, suppose we will create second ...
Read MoreB-tree Deletion in Data Structure
Here we will see, how to perform the deletion of a node from B-Tree. Suppose we have a BTree like below −Example of B-Tree −Deletion has two parts. At first we have to find the element. That strategy is like the querying. Now for deletion, we have to care about some rules. One node must have at-least m/2 elements. So if we delete, one element, and it has less than m-1 elements remaining, then it will adjust itself. If the entire node is deleted, then its children will be merged, and if their size issame as m, then split them ...
Read MoreB-tree Query in Data Structure
Here we will see, how to perform the searching in B-Tree. The B-Tree searching is also known as B-Tree Querying. Suppose we have a B-tree like below −Example of B-Tree −The searching technique is very similar to the binary search tree. Suppose we want to search 66 from the above tree. So we will start from root, now 66 is larger than root element 46. So we will move to the right child of the root. Then the right child has more than one element. The elements are sorted, they are [56, 81]. Our target key is larger than 56, ...
Read MoreB-tree Insertion in Data Structure
Here we will see, how to perform the insertion into a B-Tree. Suppose we have a B-Tree like below −Example of B-Tree −To insert an element, the idea is very similar to the BST, but we have to follow some rules. Each node has m children, and m-1 elements. If we insert an element into one node, there are two situations. If the node has elements less than m-1, then the new element will be inserted directly into the node. If it has m-1 elements, then by taking all elements, and the element which will be inserted, then take the ...
Read MoreInterval Heaps in Data Structure
Here we will see what is the interval heaps. The interval heaps are complete binary tree, in which, each node except possibly the last one contains two elements. Let the priorities of two elements in node P are ‘a’ and ‘b’. Here we are considering a ≤ b. We say that the node P represents the closed interval [a, b]. Here a is the left endpoint of the interval of P, and b is the right endpoint. The [c, d] is contained in the interval [a, b] if and only if a ≤ c ≤ d ≤ b. In an ...
Read MoreMax WBLT Operations in Data Structure
Here we will see what are the different Max-WBLT operations. The HBLT has different operations like insert, delete, and initializations. They are quite similar to the WBLT also. However, the meld operation can be done in a single top-to-bottom pass.A single pass meld operation is possible for WBLT. Because we can find the w values, on the way down. We can update the w values and swap subtrees as necessary. For HBLT, we cannot find the s values on the way down to the tree.As the meld can be done in a single top-to-bottom pass, then the insert and delete ...
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