import javax.annotation.Nonnull;
import gov.nasa.jpf.annotation.*;
import gov.nasa.jpf.aprop.*;

@Invariant({"numElems >= 0", "elems satisfies Heap$IsSorted(numElems)"})
public class Heap implements PriorityQueue {
    private @Nonnull Comparable[] elems;
    private int numElems;


    static class IsSorted implements Predicate {
	@SandBox
        public String evaluate (Object testObj, Object[] args) {
            Comparable[] elems = (Comparable[]) testObj;
            int numElems = (Integer) args[0];
            for (int i = 0; i < numElems; i++) {
                if (2*i+1 < numElems
                    && elems[i].compareTo(elems[2*i+1]) > 0)
                    return "not sorted "+i+":"+elems[i]+" > "+(2*i+1)+":"+elems[2*i+1];
                if (2*i+2 < numElems
                    && elems[i].compareTo(elems[2*i+2]) > 0)
                    return "not sorted "+i+":"+elems[i]+" > "+(2*i+2)+":"+elems[2*i+2];
            }
            return null;
        }
    }

    public Heap() {
	elems = new Comparable[5];
	numElems = 0;
    }

    private void grow() {
	Comparable[] newElems = new Comparable[elems.length*2];
	System.arraycopy(elems, 0, newElems, 0, elems.length);
	elems = newElems;
    }

    public void enqueue(Comparable o) {
	if (numElems >= elems.length)
	    grow();
	int pos = numElems++;
	int parent = (pos) / 2;
	while (pos > 0 && elems[parent].compareTo(o) > 0) {
	    elems[pos] = elems[parent];
	    pos = parent;
	    parent = (pos) / 2;
	}
	elems[pos] = o;
    }

    public Comparable removeFirst() {
	Comparable first = elems[0];
	Comparable last = elems[--numElems];
	int pos = 0;
	int child = 2*pos+1;
	while (child < numElems) {
	    if (child + 1 < numElems
		&& elems[child].compareTo(elems[child+1]) > 0) {
		child++;
	    }

	    if (elems[child].compareTo(last) > 0)
		break;

	    elems[pos] = elems[child];
	    pos = child;
	    child = 2*pos+1;
	}
	elems[pos] = last;
	return first;
    }

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

    public String toString() {
	StringBuffer sb = new StringBuffer("Heap[");
	String comma = "";
	for (int i = 0; i < numElems; i++) {
	    sb.append(comma).append(elems[i]);
	    comma=",";
	}
	return sb.append("]").toString();
    }
}