dequeued (or removedfrom the front howeverunlike regular queuein priority queue the logical order of elements is determined by their priority while the higher priorities max priority elements are added at the front of the queuein priority out elements with lower priority are added at the rear conceptuallywe can think of priority queue as bag of priorities shown in fig in this bag you figure priority queue visualization can insert any priority but you can take out one with the highest value though we can easily implement priority queues using linear arraybut we should first consider the time required to insert an element in the array and then sort it we need (ntime to insert an element and at least ( log ntime to sort the array thereforea better way to implement priority queue is by using binary heap which allows both enqueue and dequeue of elements in (log ntime binomial heaps binomial heap is set of binomial trees that satisfy the binomial heap properties firstlet us discuss what binomial tree is binomial tree is an ordered tree that can be recursively defined as followsa binomial tree of order has single node binomial tree of order has root node whose children are the root nodes of binomial trees of order - - and binomial tree bi has nodes the height of binomial tree bi is look at fig which shows few binomial trees of different orders we can construct binomial tree bi from two binomial trees of order bi- by linking them together in such way that the root of one is the leftmost child of the root of another bi- bi- ( binomial tree bi is collection of binomial trees of order - - (binomial treeb (binomial treeb (binomial treeb (binomial treeb figure binomial trees binomial heap is collection of binomial trees that satisfy the following propertiesevery binomial tree in satisfies the minimum heap property ( the key of node is either greater than or equal to the key of its parentthere can be one or zero binomial trees for each order including zero order