In this blog post, I will provide the F# implementation for max priority queue. First the java based implementation taken from Algorithms 4th Edition by Robert Sedgewick and Kevin Wayne. You can find the complete priority queue implementation here : http://algs4.cs.princeton.edu/24pq/MaxPQ.java.html

Priority Queue

public class MaxPQ implements Iterable {
    private Key[] pq;                    // store items at indices 1 to N
    private int N;                       // number of items on priority queue
    private Comparator comparator;  // optional Comparator

    public MaxPQ(int initCapacity) {
        pq = (Key[]) new Object[initCapacity + 1];
        N = 0;
    }

    public boolean isEmpty() {
        return N == 0;
    }

    public int size() {
        return N;
    }

    public Key max() {
        if (isEmpty()) throw new NoSuchElementException("Priority queue underflow");
        return pq[1];
    }

    public void insert(Key x) {
        pq[++N] = x;
        swim(N);
    }

    public Key delMax() {
        Key max = pq[1];
        exch(1, N--);
        sink(1);
        pq[N+1] = null;  
        return max;
    }

    private void swim(int k) {
        while (k > 1 && less(k/2, k)) {
            exch(k, k/2);
            k = k/2;
        }
    }

    private void sink(int k) {
        while (2*k <= N) {
            int j = 2*k;
            if (j < N && less(j, j+1)) j++;
            if (!less(k, j)) break;
            exch(k, j);
            k = j;
        }
    }

    private boolean less(int i, int j) {
        if (comparator == null) {
            return ((Comparable) pq[i]).compareTo(pq[j]) < 0;
        }
        else {
            return comparator.compare(pq[i], pq[j]) < 0;
        }
    }

    private void exch(int i, int j) {
        Key swap = pq[i];
        pq[i] = pq[j];
        pq[j] = swap;
    }
}

Java based implementation is fairly straight forward. The crux of the code lies in the Swim & Sink method. Lets take a look at the F# based implementation :

module PriorityQueue

type PriorityQueue<'T when 'T :> System.IComparable<'T>> (maxN : int) =
    let pq : 'T array = Array.zeroCreate (maxN + 1)
    let mutable N = 0
    
    let Less i j = pq.[i].CompareTo(pq.[j]) < 0
    let Exchange i j = 
        let temp = pq.[i]
        pq.[i] <- pq.[j]
        pq.[j] <- temp
        i

    let rec Swim k =
        match (k > 1 && Less (k/2) k) with
        | true -> Exchange (k/2) k |> Swim;
        | false -> ()
    
    let rec Sink k =
        match 2*k <= N, 2*k with
        | true, j when j < N && Less j (j + 1) -> match Less k (j+1), j+1 with
                                                    | true, x -> Exchange k x |> ignore; Sink x;
                                                    | false, _ -> ()
        | true, j -> Exchange k j |> ignore; Sink j;
        | false, _ -> ()

    member x.IsEmpty with get() = N = 0
    member x.Size with get() = N

    member x.Insert (item:'T) = N <- N + 1; pq.[N] <- item; Swim N;

    member x.DelMax() =
        let max = pq.[1]
        Exchange 1 N |> ignore
        N <- N - 1
        pq.[N+1] <- Unchecked.defaultof<'T>
        Sink 1
        max

Lets break down the above code and try to understand the individual pieces:

• In the beginning I have declared a module. Modules are like namespaces with a constraint that their definition cannot span to multiple files. Modules can be used to logically group functionality within a file.
• Next I have declared a generic class with constraint on the type parameter. Also note that, just after the class definition I have declared what is called as primary constructor in F#.
• After the class definition, we have multiple “let” statements. All of those let statements are either doing some sort of initialization or are used for declaring internal helper functions. “let” based functions aren’t exposed outside the type definition.
• Followed by the “let” based declarations, we see member definitions which are nothing but methods in F#. Within the various member definitions, IsEmpty & Size are basically read-only properties. Once again we are seeing the power of F#’s pattern matching & overall succinctness in play here.

In next blog post, we will move on to Graphs.

Thanks.