fibonacciheap.java

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    }

    // size

    /**
     * Joins two Fibonacci heaps into a new one. No heap consolidation is
     * performed at this time. The two root lists are simply joined together.
     *
     * <p>Running time: O(1) actual</p>
     *
     * @param h1 first heap
     * @param h2 second heap
     *
     * @return new heap containing h1 and h2
     */
    public static <T> FibonacciHeap<T> union(
        FibonacciHeap<T> h1,
        FibonacciHeap<T> h2)
    {
        FibonacciHeap<T> h = new FibonacciHeap<T>();

        if ((h1 != null) && (h2 != null)) {
            h.minNode = h1.minNode;

            if (h.minNode != null) {
                if (h2.minNode != null) {
                    h.minNode.right.left = h2.minNode.left;
                    h2.minNode.left.right = h.minNode.right;
                    h.minNode.right = h2.minNode;
                    h2.minNode.left = h.minNode;

                    if (h2.minNode.key < h1.minNode.key) {
                        h.minNode = h2.minNode;
                    }
                }
            } else {
                h.minNode = h2.minNode;
            }

            h.nNodes = h1.nNodes + h2.nNodes;
        }

        return h;
    }

    // union

    /**
     * Creates a String representation of this Fibonacci heap.
     *
     * @return String of this.
     */
    public String toString()
    {
        if (minNode == null) {
            return "FibonacciHeap=[]";
        }

        // create a new stack and put root on it
        Stack<FibonacciHeapNode<T>> stack = new Stack<FibonacciHeapNode<T>>();
        stack.push(minNode);

        StringBuffer buf = new StringBuffer(512);
        buf.append("FibonacciHeap=[");

        // do a simple breadth-first traversal on the tree
        while (!stack.empty()) {
            FibonacciHeapNode<T> curr = stack.pop();
            buf.append(curr);
            buf.append(", ");

            if (curr.child != null) {
                stack.push(curr.child);
            }

            FibonacciHeapNode<T> start = curr;
            curr = curr.right;

            while (curr != start) {
                buf.append(curr);
                buf.append(", ");

                if (curr.child != null) {
                    stack.push(curr.child);
                }

                curr = curr.right;
            }
        }

        buf.append(']');

        return buf.toString();
    }

    // toString

    /**
     * Performs a cascading cut operation. This cuts y from its parent and then
     * does the same for its parent, and so on up the tree.
     *
     * <p>Running time: O(log n); O(1) excluding the recursion</p>
     *
     * @param y node to perform cascading cut on
     */
    protected void cascadingCut(FibonacciHeapNode<T> y)
    {
        FibonacciHeapNode<T> z = y.parent;

        // if there's a parent...
        if (z != null) {
            // if y is unmarked, set it marked
            if (!y.mark) {
                y.mark = true;
            } else {
                // it's marked, cut it from parent
                cut(y, z);

                // cut its parent as well
                cascadingCut(z);
            }
        }
    }

    // cascadingCut

    protected void consolidate()
    {
        int arraySize =
            ((int) Math.floor(Math.log(nNodes) * oneOverLogPhi)) + 1;

        List<FibonacciHeapNode<T>> array =
            new ArrayList<FibonacciHeapNode<T>>(arraySize);

        // Initialize degree array
        for (int i = 0; i < arraySize; i++) {
            array.add(null);
        }

        // Find the number of root nodes.
        int numRoots = 0;
        FibonacciHeapNode<T> x = minNode;

        if (x != null) {
            numRoots++;
            x = x.right;

            while (x != minNode) {
                numRoots++;
                x = x.right;
            }
        }

        // For each node in root list do...
        while (numRoots > 0) {
            // Access this node's degree..
            int d = x.degree;
            FibonacciHeapNode<T> next = x.right;

            // ..and see if there's another of the same degree.
            for (;;) {
                FibonacciHeapNode<T> y = array.get(d);
                if (y == null) {
                    // Nope.
                    break;
                }

                // There is, make one of the nodes a child of the other.
                // Do this based on the key value.
                if (x.key > y.key) {
                    FibonacciHeapNode<T> temp = y;
                    y = x;
                    x = temp;
                }

                // FibonacciHeapNode<T> y disappears from root list.
                link(y, x);

                // We've handled this degree, go to next one.
                array.set(d, null);
                d++;
            }

            // Save this node for later when we might encounter another
            // of the same degree.
            array.set(d, x);

            // Move forward through list.
            x = next;
            numRoots--;
        }

        // Set min to null (effectively losing the root list) and
        // reconstruct the root list from the array entries in array[].
        minNode = null;

        for (int i = 0; i < arraySize; i++) {
            FibonacciHeapNode<T> y = array.get(i);
            if (y == null) {
                continue;
            }

            // We've got a live one, add it to root list.
            if (minNode != null) {
                // First remove node from root list.
                y.left.right = y.right;
                y.right.left = y.left;

                // Now add to root list, again.
                y.left = minNode;
                y.right = minNode.right;
                minNode.right = y;
                y.right.left = y;

                // Check if this is a new min.
                if (y.key < minNode.key) {
                    minNode = y;
                }
            } else {
                minNode = y;
            }
        }
    }

    // consolidate

    /**
     * The reverse of the link operation: removes x from the child list of y.
     * This method assumes that min is non-null.
     *
     * <p>Running time: O(1)</p>
     *
     * @param x child of y to be removed from y's child list
     * @param y parent of x about to lose a child
     */
    protected void cut(FibonacciHeapNode<T> x, FibonacciHeapNode<T> y)
    {
        // remove x from childlist of y and decrement degree[y]
        x.left.right = x.right;
        x.right.left = x.left;
        y.degree--;

        // reset y.child if necessary
        if (y.child == x) {
            y.child = x.right;
        }

        if (y.degree == 0) {
            y.child = null;
        }

        // add x to root list of heap
        x.left = minNode;
        x.right = minNode.right;
        minNode.right = x;
        x.right.left = x;

        // set parent[x] to nil
        x.parent = null;

        // set mark[x] to false
        x.mark = false;
    }

    // cut

    /**
     * Make node y a child of node x.
     *
     * <p>Running time: O(1) actual</p>
     *
     * @param y node to become child
     * @param x node to become parent
     */
    protected void link(FibonacciHeapNode<T> y, FibonacciHeapNode<T> x)
    {
        // remove y from root list of heap
        y.left.right = y.right;
        y.right.left = y.left;

        // make y a child of x
        y.parent = x;

        if (x.child == null) {
            x.child = y;
            y.right = y;
            y.left = y;
        } else {
            y.left = x.child;
            y.right = x.child.right;
            x.child.right = y;
            y.right.left = y;
        }

        // increase degree[x]
        x.degree++;

        // set mark[y] false
        y.mark = false;
    }

    // link
}

// FibonacciHeap