A utility function used for Inorder Walk

Adds an edge to an Adjacency List element

Replaces the value of an edge (u -->) v to (u --> v') newNodes the entire list of adjacencyList[u] => O(|E|) operation Here, "v" is stored as "oldVert

Inserts Node to the Linked List by Head Insertion - O(1) Returns address of head which is the newly created node.

Returns the element with Minimum Priority and deletes it

Returns (n! % PRIME)

Applies the heapify procedure - O(log N)

Applies the heapify procedure - O(log N)

In-Order Walk of Segment Tree

Prints the 'trieTree' in a Pre-Order or a DFS manner which automatically results in a Lexicographical Order

Prints the Adjacency List

Adds a new edge into the Adjacency List Follows Head Insertion for O(1) Insertion

Follows head insertion to give O(1) insertion

Follows head insertion to give O(1) insertion

Adds a new edge, u --> v, to adjacencyList[u]

Adds a new node in the linked list. Follows head insertion for O(1) performance. @param oldHead head of the linked list to which new node is to be ad

Appends a new Edge to the linked list

Adds an element to the heap and returns the size - O(log N)

Bellman-Ford Algorithm which takes the Graph (adjacencyList[]), starting vertex (startVertex), and an empty array shortestDistances[] as input. It app

Main Binary Search logic

This makes the neccessary adjustments after insertion to ensure the validity of Heap Property in the Binary Heap

Build Heap Procedure - O(N)

Build Heap Procedure - O(N)

The recursive procedure which actually constructs the Segment Tre

Searches for a node in the Heap in O(1) time and decreases its value Then calls Heapify() on it's parent to adjust heap -> totally takes O(log N) time

Deletes and entry in the Priority Queue

Deletes the vertex and returns the size - O(log N)

Dijkstra's Algorithm function

Dijkstra's Algorithm function