Queues Queue API Application: Radix Sort Implementation: Using Deque Circular Array

1. Lecture 8 Queues and Priority Queues • Queues • Queue API • Application: Radix Sort • Implementation: • Using Deque • Circular Array • Priority Queue • Priority Queue API • Implementation Glimpse: Heaps

2. Queues • Three container adapters • stack: LIFO discipline • queue: FIFO • priority_queue: HPFO • Queue • <queue> • Remove from front, insert at back • Underlying sequence container: deque • Priority_queue • <queue> • top () yields HP element • Underlying SC: vector

3. Queue Example string s1, s2; // Modify s1, leave s2==“” queue<char> q; size_t n = s1.length (); for (size_t i = 0; i < n; ++i) q.push (s1[n – i – 1]); while (! q.empty ()) { s2 += q.front (); q.pop (); } cout << boolalpha << (s1 == s2) << endl;

4. queue (); Create an empty queue. CLASS queue CLASS queue <queue> <queue> Constructor Operations bool empty () const; Check whether the queue is empty. Return true if it is empty and false otherwise. T& front (); Return a reference to the value of the item at the front of the queue. Precondition: The queue is not empty.

5. CLASS queue <queue> Operations const T& front () const; Constant version of front(). T& back (); const T& back () const; void pop (); Remove the item from the front of the queue. Precondition: The queue is not empty. Postcondition: The element at the front of the queue is the element that was added immediately after the element just popped or the queue is empty.

6. void push (const T& item); Insert the argument item at the back of the queue. Postcondition: The queue has a new item at the back CLASS queue <queue> Operations size_t size () const; Return the number of elements in the queue. 6

7. Radix Sort Order ten 2 digit numbers in 10 bins from smallest to largest. Requires d = 2 passes, generally d = max (digits in an element) passes. Initial Sequence: 91 06 85 15 92 35 30 22 39 Pass 0: Distribute the #’s into bins according to the 1's digit (100).

8. The Radix Sort New Sequence: 30 91 92 22 85 15 35 06 39 Pass 1: Take new sequence and distribute the #’s into bins determined by the 10's digit (101). Complexity? O (d*N)

9. Implementing a Queue typedef Employee* value_type; class Queue { deque<value_type> d; public: Queue () : d () { } // Initially empty value_type &front () { ?? } value_type &back () { ?? } // Const versions too void push (const value_type& v) { d.push_back (v); } void pop () { ?? } bool empty () const { return d.empty (); } size_t size () const { return d.size (); } };

10. Implementing a Queue (Alternative) typedef Employee* value_type; class Queue { value_type A[CAP]; size_t qFront, qBack, count; // [qFront, qBack) size_t decr (size_t index) { index += CAP - 1; return index % CAP; } size_t incr (size_t index) { ++index; return index % CAP; } public: Queue () : qFront (0), qBack (0), count (0) { } value_type& front () { return (A[qFront]); } value_type& back () { size_t last = decr (qBack); return (A[last]); } void push (const value_type& v) // Check overflow? { A[qBack] = v; qBack = incr (qBack); ++count; } void pop () // Underflow? { qFront = incr (qFront); --count; } bool empty () const { return (count == 0); } };

11. Circular Array Impl.

12. Priority Queue Form of queue in which values are removed according to their designated priority 3 2 6 1 Items entered the queue in sequential order but will be removed in the order Job #2, #1, #4, #3.

13. Priority Queue Example string s1 = “Bjarne”, s2; priority_queue <char> pq; size_t n = s1.length (); for (size_t i = 0; i < n; i++) pq.push (s1[i]); while (! pq.empty ()) { s2 += q.top (); q.pop (); } cout << s2 << endl;

14. priority_queue (); Create an empty priority queue. Type T must implement operator < (or provide comparator). CLASS priority_queue CLASS priority_queue <queue> <queue> Constructor Operations bool empty () const; Check whether the priority queue is empty. Return true if it is empty, and false otherwise. void pop (); Remove the item of highest priority from the queue. Precondition: The priority queue is not empty. Postcondition: The priority queue has 1 less element

15. CLASS priority_queue <queue> Operations void push (const T& item); Insert the argument item into the priority queue. Postcondition: The priority queue contains a new element. size_t size () const; Return the number of items in the priority queue. T& top ();  NO! Why? Return a reference to the item having the highest priority. Precondition: The priority queue is not empty. const T& top () const; Constant version of top().

16. Implementing a Priority Queue (Partial) typedef timer value_type; class PriorityQueue { vector<value_type> v; // v is maintained as a heap public: PriorityQueue () { } // initially empty const value_type& top () const { return v.front (); } void push (const value_type& i) { v.push_back (i); upHeap (); } void pop () { v[0] = v.back (); v.pop_back (); downHeap (); } bool empty () const { return v.empty (); } size_t size () const { return v.size (); } };

17. Popping From a Heap v[0] = v.back ();