COMP 310 Fall 2010	Lec22: Extended Visitors Example, continued...

Let's finish our discussion from last lecture...

Deletion algorithm for self-balancing trees.

Below is the code for the deletion algorithm.   Things to note:

•  How the "candidate data" technique is used progressively isolate the item to delete.
• How the algorithm for an arbitrary order tree boils down to only 3 distinct cases: empty, order 1, and everything else.

/**
 * DeleteNAlgo  -  deletes the supplied parameter from a TreeN
 *  preserving balance with a maximum number of elements per node.
 */
public class DeleteNAlgo implements ITreeNAlgo {

	/**
	 * Splits child upwards if its state > order and splices it into
	 * its parent.  The supplied param is an ISpliceCmd used to do the
	 * splicing.
	 */
	private SplitUpAndApply splitUpAndSplice;

	/**
	 * Constructor for the class
	 * @param order -- the max possible number of elements in a node
	 */
	public DeleteNAlgo(int order) {
		splitUpAndSplice = new SplitUpAndApply(order);
	}

	public Object caseAt(int s, final TreeN host, Object... keys) {
		final Object key = keys[0];

		switch(s) {
		case 0: {
			return key;  // no-op for empty case
		}

		case 1: {
			collapse2Node(host);
		}// fall through to default case

		default: {
			return host.execute(new ITreeNAlgo() {
				public Object caseAt(int s_help, final TreeN h, Object... cmds) {
					switch(s_help) {
					case 0: {
						return key;
					}
					case 1: {
						if (h.getDat(0).equals(key)) {
							//System.out.println("Found data element!");
							Object d = h.getDat(0); // get key
							h.splitDownAt(0); //transition to empty
							return d;
						}
						else {
							//System.err.println("Element "+ key +" not in tree!");
							((ILambda)cmds[0]).apply(h);
							return h.getDat(0);
						}
					}
					default : {
						final int x = findX(h, s_help, ((Integer)key).intValue());
						TreeN newChild = collapse2Node(h.splitDownAt(x).getChild(x)); // push data down
						Object result = newChild.execute(this,
								new ILambda() {
							/**
							 * @param child a TreeN subtree of h.
							 */
							public Object apply(Object... children) {
								return h.spliceAt(x, (TreeN)children[0]);
							}
						});
						h.execute(splitUpAndSplice, cmds[0]);
						return result;
					}
					}
				}
			}
			, new ILambda() {  // Top-level no-op lambda
				public Object apply(Object... nu) {
					return host;
				}
			});
		}
		}
	}

	//------ Utility methods ------------------------------------------------------

	/**
	 * Utility method to collapses a 2-node tree by splicing it with
	 * its two children.
	 * @param t -- must be a 2-node tree!
	 */
	private final TreeN collapse2Node(TreeN t) {
		t.spliceAt(1,t.getChild(1));
		t.spliceAt(0,t.getChild(0));
		return t;
	}

	/**
	 * Utility method that finds the index of the data element that
	 * either matches the supplied key or is the first element bigger
	 * than the key.
	 * @param t - an TreeN
	 * @param state - the state of the tree
	 * @param k - the key to locate
	 * @return - the index of the data element such that if k exists in the
	 * tree, it is guaranteed to be in the 2-node tree
	 * defined by the data at the index and its left and right children.
	 */
	private final int findX(TreeN t, int state, int k) {
		for(int i = 0;i< state; i++) if(t.getDat(i).intValue()>=k) return i;
		return state-1;
	}
}

© 2010 by Stephen Wong and Scott Rixner