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Linear Probing in Data Structure
In this section we will see what is linear probing technique in open addressing scheme. There is an ordinary hash function h´(x) : U → {0, 1, . . ., m – 1}. In open addressing scheme, the actual hash function h(x) is taking the ordinary hash function h’(x) and attach some another part with it to make one linear equation.h´(𝑥) = 𝑥 𝑚𝑜𝑑 𝑚ℎ(𝑥, 𝑖) = (ℎ´(𝑥) + 𝑖)𝑚𝑜𝑑 𝑚The value of i| = 0, 1, . . ., m – 1. So we start from i = 0, and increase this until we get one freespace. So initially ...
Read MoreHashing with Open Addressing in Data Structure
In this section we will see what is the hashing by open addressing. The open addressing is another technique for collision resolution. Unlike chaining, it does not insert elements to some other data-structures. It inserts the data into the hash table itself. The size of the hash table should be larger than the number of keys.There are three different popular methods for open addressing techniques. These methods are −Linear ProbingQuadratic ProbingDouble HashingIn this technique, we use a hash function like other hash techniques. If the place is free, then insert the element into that location. Now if that place is ...
Read MoreUniversal Hashing in Data Structure
For any hash function we can say that if the table size m is much smaller than universe size u, then for any hash function h, there is some large subset of U that has the same hash value.To get rid of this problem, we need a set of hash functions, from which we can choose any one that works well for S. If most of the hash functions are better for S, we can choose random hash functionSuppose ℌ be a set of hash functions. We can say ℌ is universal if, for each x, y ∈ U, the ...
Read MoreHashing by Division in Data Structure
Here we will discuss about the hashing with division. For this we use the hash function −ℎ(𝑥) = 𝑥 𝑚𝑜𝑑 𝑚To use this hash function we maintain an array A[0, … m – 1]. Where each element of the array is a pointer to the head of the linked list. The linked list Li is pointed to array element A[i] holds all elements x such that h(x) = i. This technique is known as hashing by chaining.In such hash table, if we want to increase an element x, this will take O(1) time. we compute the index i = h(x). ...
Read MoreHash Tables for Integer Keys in Data Structure
Here we will discuss about the Hash tables with the integer keys. Here the key values 𝑥 comes from universe 𝑈 such that 𝑈 = {0, 1, … , 𝑢 – 2, 𝑢 – 1}. A hash function is ℎ. The domain of this hash function is 𝑈. The range is in the set {0, 1, … , 𝑚 – 1}, and 𝑚 ≤ 𝑢.A hash function h is said to be a perfect hash function for a set 𝑆 ⊆ 𝑈 if for every 𝑥 ∈ 𝑆, ℎ(𝑥) is unique. A perfect hash function ℎ for 𝑆 is minimal ...
Read MoreDeletion from a Max Heap in Data Structure
Here we will see how to delete elements from binary max heap data structures. Suppose the initial tree is like below −Deletion Algorithmdelete(heap, n) − Begin if heap is empty, then exit else item := heap[1] last := heap[n] n := n – 1 for i := 1, j := 2, j = heap[j], then break heap[i] := heap[j] done end if heap[i] := last EndExampleSuppose we want to delete 30 from the final heap −
Read MoreInsertion into a Max Heap in Data Structure
Here we will see how to insert and elements from binary max heap data structures. Suppose the initial tree is like below −Insertion Algorithminsert(heap, n, item) − Begin if heap is full, then exit else n := n + 1 for i := n, i > 1, set i := i / 2 in each iteration, do if item
Read MoreEulerian and Hamiltonian Graphs in Data Structure
In this section we will see the Eulerian and Hamiltonian Graphs. But before diving into that, at first we have to see what are trails in graph. Suppose we have one graph like below −The trail is a path, which is a sequence of edges (v1, v2), (v2, v3), …, (vk - 1, vk) in which all vertices (v1, v2, … , vk) may not be distinct, but all edges are distinct. In this example one trail is {(B, A), (A, C), (C, D), (D, A), (A, F)} This is a trail. But this will not be considered as simple ...
Read MoreDepth-First Search on a Digraph in Data Structure
The Depth first search for graphs are similar. But for Digraphs or directed graphs, we can find some few types of edges. The DFS algorithm forms a tree called DFS tree. There are four types of edges called −Tree Edge (T) − Those edges which are present in the DFS treeForward Edge (F) − Parallel to a set of tree edges. (From smaller DFS number to larger DFS number, and Larger DFS completion number to Smaller DFS completion number)Backward Edge (B) − From larger DFS number to Smaller DFS number and Smaller DFS completion number to Larger DFS completion number.Cross ...
Read MoreSearching a Graph in Data Structure
We know that the graph is one non-linear data structure. In this data structure, we put some values into nodes, and the nodes are connected though different edges. As we can store data into the graph structure, we also need to search elements from the graph to use them.For searching in graphs, there are two different methods. The Breadth First Search and the Depth First searching techniques.Breadth First Search (BFS)The Breadth First Search (BFS) traversal is an algorithm, which is used to visit all of the nodes of a given graph. In this traversal algorithm one node is selected and ...
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