LogNArray v2 [based on TreeMap, dev.] [1024412]

// see: https://en.wikipedia.org/wiki/Order_statistic_tree
sclass LogNArray<A> extends RandomAccessAbstractList<A> {

  private transient Entry<A> root;

  /**
   * The number of entries in the tree
   */
  //private transient int size = 0;

  /**
   * The number of structural modifications to the tree.
   */
  private transient int modCount = 0;

  // Query Operations

  public int size() {
    ret root == null ? 0 : root.size;
  }

  public bool contains(Object value) {
    for (Entry<A> e = getFirstEntry(); e != null; e = successor(e))
      if (eq(value, e.value))
        true;
    false;
  }

  public A get(int idx) {
    Entry<A> p = getEntry(idx);
    return p == null ? null : p.value;
  }

  int subTreeSize(Entry<A> e) { ret e == null ? 0 : e.size; }

  final Entry<A> getEntry(int idx) {
    if (idx < 0 || idx >= size())
      throw new IndexOutOfBoundsException(idx + " / " + size());
    Entry<A> p = root;
    while true {
      int sizeLeft = subTreeSize(p.left);
      if (idx < sizeLeft)
        continue with p = p.left;
      idx -= sizeLeft;
      if (idx == 0) ret p;
      idx--;
      p = p.right;
    }
  }

  /*public A put(Int key, A value) {
      Entry<A> t = root;
      if (t == null) {
          compare(key, key); // type (and possibly null) check

          root = new Entry<>(key, value, null);
          //size = 1;
          modCount++;
          return null;
      }
      int cmp;
      Entry<A> parent;
      // split comparator and comparable paths
      Comparator<? super Int> cpr = comparator;
      if (cpr != null) {
          do {
              parent = t;
              cmp = cpr.compare(key, t.key);
              if (cmp < 0)
                  t = t.left;
              else if (cmp > 0)
                  t = t.right;
              else
                  return t.setValue(value);
          } while (t != null);
      }
      else {
          if (key == null)
              throw new NullPointerException();
          @SuppressWarnings("unchecked")
              Comparable<? super Int> k = (Comparable<? super Int>) key;
          do {
              parent = t;
              cmp = k.compareTo(t.key);
              if (cmp < 0)
                  t = t.left;
              else if (cmp > 0)
                  t = t.right;
              else
                  return t.setValue(value);
          } while (t != null);
      }
      Entry<A> e = new Entry<>(key, value, parent);
      if (cmp < 0)
          parent.left = e;
      else
          parent.right = e;
      fixAfterInsertion(e);
      //size++;
      modCount++;
      return null;
  }*/

  /*public A remove(int idx) {
    Entry<A> p = getEntry(key);
    if (p == null)
        return null;

    A oldValue = p.value;
    deleteEntry(p);
    return oldValue;
  }*/

  public void clear() {
      modCount++;
      //size = 0;
      root = null;
  }

  // Red-black mechanics

  private static final boolean RED   = false;
  private static final boolean BLACK = true;

  /**
   * Node in the Tree.  Doubles as a means to pass key-value pairs back to
   * user (see Map.Entry).
   */

  static final class Entry<A> {
      int size = 1; // entry count of subtree
      //Int key;
      A value;
      Entry<A> left;
      Entry<A> right;
      Entry<A> parent;
      boolean color = BLACK;

      /**
       * Make a new cell with given value and parent, and with
       * {@code null} child links, size 1, and BLACK color.
       */
      Entry(A value, Entry<A> parent) {
          this.value = value;
          this.parent = parent;
      }
  }

  final Entry<A> getFirstEntry() {
      Entry<A> p = root;
      if (p != null)
          while (p.left != null)
              p = p.left;
      return p;
  }

  final Entry<A> getLastEntry() {
      Entry<A> p = root;
      if (p != null)
          while (p.right != null)
              p = p.right;
      return p;
  }

  static <Int,A> LogNArray.Entry<A> successor(Entry<A> t) {
      if (t == null)
          return null;
      else if (t.right != null) {
          Entry<A> p = t.right;
          while (p.left != null)
              p = p.left;
          return p;
      } else {
          Entry<A> p = t.parent;
          Entry<A> ch = t;
          while (p != null && ch == p.right) {
              ch = p;
              p = p.parent;
          }
          return p;
      }
  }

  static <Int,A> Entry<A> predecessor(Entry<A> t) {
      if (t == null)
          return null;
      else if (t.left != null) {
          Entry<A> p = t.left;
          while (p.right != null)
              p = p.right;
          return p;
      } else {
          Entry<A> p = t.parent;
          Entry<A> ch = t;
          while (p != null && ch == p.left) {
              ch = p;
              p = p.parent;
          }
          return p;
      }
  }

  /**
   * Balancing operations.
   *
   * Implementations of rebalancings during insertion and deletion are
   * slightly different than the CLR version.  Rather than using dummy
   * nilnodes, we use a set of accessors that deal properly with null.  They
   * are used to avoid messiness surrounding nullness checks in the main
   * algorithms.
   */

  private static <Int,A> boolean colorOf(Entry<A> p) {
      return (p == null ? BLACK : p.color);
  }

  private static <Int,A> Entry<A> parentOf(Entry<A> p) {
      return (p == null ? null: p.parent);
  }

  private static <Int,A> void setColor(Entry<A> p, boolean c) {
      if (p != null)
          p.color = c;
  }

  private static <Int,A> Entry<A> leftOf(Entry<A> p) {
      return (p == null) ? null: p.left;
  }

  private static <Int,A> Entry<A> rightOf(Entry<A> p) {
      return (p == null) ? null: p.right;
  }

  /** From CLR */
  private void rotateLeft(Entry<A> p) {
      if (p != null) {
          Entry<A> r = p.right;
          p.right = r.left;
          if (r.left != null)
              r.left.parent = p;
          r.parent = p.parent;
          if (p.parent == null)
              root = r;
          else if (p.parent.left == p)
              p.parent.left = r;
          else
              p.parent.right = r;
          r.left = p;
          p.parent = r;
      }
  }

  /** From CLR */
  private void rotateRight(Entry<A> p) {
      if (p != null) {
          Entry<A> l = p.left;
          p.left = l.right;
          if (l.right != null) l.right.parent = p;
          l.parent = p.parent;
          if (p.parent == null)
              root = l;
          else if (p.parent.right == p)
              p.parent.right = l;
          else p.parent.left = l;
          l.right = p;
          p.parent = l;
      }
  }

  /** From CLR */
  private void fixAfterInsertion(Entry<A> x) {
      x.color = RED;

      while (x != null && x != root && x.parent.color == RED) {
          if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {
              Entry<A> y = rightOf(parentOf(parentOf(x)));
              if (colorOf(y) == RED) {
                  setColor(parentOf(x), BLACK);
                  setColor(y, BLACK);
                  setColor(parentOf(parentOf(x)), RED);
                  x = parentOf(parentOf(x));
              } else {
                  if (x == rightOf(parentOf(x))) {
                      x = parentOf(x);
                      rotateLeft(x);
                  }
                  setColor(parentOf(x), BLACK);
                  setColor(parentOf(parentOf(x)), RED);
                  rotateRight(parentOf(parentOf(x)));
              }
          } else {
              Entry<A> y = leftOf(parentOf(parentOf(x)));
              if (colorOf(y) == RED) {
                  setColor(parentOf(x), BLACK);
                  setColor(y, BLACK);
                  setColor(parentOf(parentOf(x)), RED);
                  x = parentOf(parentOf(x));
              } else {
                  if (x == leftOf(parentOf(x))) {
                      x = parentOf(x);
                      rotateRight(x);
                  }
                  setColor(parentOf(x), BLACK);
                  setColor(parentOf(parentOf(x)), RED);
                  rotateLeft(parentOf(parentOf(x)));
              }
          }
      }
      root.color = BLACK;
  }

  /**
   * Delete node p, and then rebalance the tree.
   */
  private void deleteEntry(Entry<A> p) {
      modCount++;
      //size--;

      // If strictly internal, copy successor's element to p and then make p
      // point to successor.
      if (p.left != null && p.right != null) {
          Entry<A> s = successor(p);
          p.value = s.value;
          p = s;
      } // p has 2 children

      // Start fixup at replacement node, if it exists.
      Entry<A> replacement = (p.left != null ? p.left : p.right);

      if (replacement != null) {
          // Link replacement to parent
          replacement.parent = p.parent;
          if (p.parent == null)
              root = replacement;
          else if (p == p.parent.left)
              p.parent.left  = replacement;
          else
              p.parent.right = replacement;

          // Null out links so they are OK to use by fixAfterDeletion.
          p.left = p.right = p.parent = null;

          // Fix replacement
          if (p.color == BLACK)
              fixAfterDeletion(replacement);
      } else if (p.parent == null) { // return if we are the only node.
          root = null;
      } else { //  No children. Use self as phantom replacement and unlink.
          if (p.color == BLACK)
              fixAfterDeletion(p);

          if (p.parent != null) {
              if (p == p.parent.left)
                  p.parent.left = null;
              else if (p == p.parent.right)
                  p.parent.right = null;
              p.parent = null;
          }
      }
  }

  /** From CLR */
  private void fixAfterDeletion(Entry<A> x) {
      while (x != root && colorOf(x) == BLACK) {
          if (x == leftOf(parentOf(x))) {
              Entry<A> sib = rightOf(parentOf(x));

              if (colorOf(sib) == RED) {
                  setColor(sib, BLACK);
                  setColor(parentOf(x), RED);
                  rotateLeft(parentOf(x));
                  sib = rightOf(parentOf(x));
              }

              if (colorOf(leftOf(sib))  == BLACK &&
                  colorOf(rightOf(sib)) == BLACK) {
                  setColor(sib, RED);
                  x = parentOf(x);
              } else {
                  if (colorOf(rightOf(sib)) == BLACK) {
                      setColor(leftOf(sib), BLACK);
                      setColor(sib, RED);
                      rotateRight(sib);
                      sib = rightOf(parentOf(x));
                  }
                  setColor(sib, colorOf(parentOf(x)));
                  setColor(parentOf(x), BLACK);
                  setColor(rightOf(sib), BLACK);
                  rotateLeft(parentOf(x));
                  x = root;
              }
          } else { // symmetric
              Entry<A> sib = leftOf(parentOf(x));

              if (colorOf(sib) == RED) {
                  setColor(sib, BLACK);
                  setColor(parentOf(x), RED);
                  rotateRight(parentOf(x));
                  sib = leftOf(parentOf(x));
              }

              if (colorOf(rightOf(sib)) == BLACK &&
                  colorOf(leftOf(sib)) == BLACK) {
                  setColor(sib, RED);
                  x = parentOf(x);
              } else {
                  if (colorOf(leftOf(sib)) == BLACK) {
                      setColor(rightOf(sib), BLACK);
                      setColor(sib, RED);
                      rotateLeft(sib);
                      sib = leftOf(parentOf(x));
                  }
                  setColor(sib, colorOf(parentOf(x)));
                  setColor(parentOf(x), BLACK);
                  setColor(leftOf(sib), BLACK);
                  rotateRight(parentOf(x));
                  x = root;
              }
          }
      }

      setColor(x, BLACK);
  }

  /**
   * Finds the level down to which to assign all nodes BLACK.  This is the
   * last `full' level of the complete binary tree produced by buildTree.
   * The remaining nodes are colored RED. (This makes a `nice' set of
   * color assignments wrt future insertions.) This level number is
   * computed by finding the number of splits needed to reach the zeroeth
   * node.
   *
   * @param size the (non-negative) number of keys in the tree to be built
   */
  private static int computeRedLevel(int size) {
      return 31 - Integer.numberOfLeadingZeros(size + 1);
  }
}

Travelled to 6 computer(s): bhatertpkbcr, mqqgnosmbjvj, pyentgdyhuwx, pzhvpgtvlbxg, tvejysmllsmz, vouqrxazstgt

Snippet ID:	#1024412
Snippet name:	LogNArray v2 [based on TreeMap, dev.]
Eternal ID of this version:	#1024412/12
Text MD5:	e218fba96a516a2cc9c23442a664817e
Transpilation MD5:	ba1ee5307ba902cc8076a7b714b727b9
Author:	stefan
Category:	javax
Type:	JavaX fragment (include)
Public (visible to everyone):	Yes
Archived (hidden from active list):	No
Created/modified:	2019-08-11 11:38:26
Source code size:	12931 bytes / 438 lines
Pitched / IR pitched:	No / No
Views / Downloads:	205 / 298
Version history:	11 change(s)
Referenced in:	[show references]

< > BotCompany Repo | #1024412 // LogNArray v2 [based on TreeMap, dev.]

JavaX fragment (include) [tags: use-pretranspiled]

Author comment

1	// see: https://en.wikipedia.org/wiki/Order_statistic_tree
2	sclass LogNArray<A> extends RandomAccessAbstractList<A> {
3
4	private transient Entry<A> root;
5
6	/**
7	* The number of entries in the tree
8	*/
9	//private transient int size = 0;
10
11	/**
12	* The number of structural modifications to the tree.
13	*/
14	private transient int modCount = 0;
15
16	// Query Operations
17
18	public int size() {
19	ret root == null ? 0 : root.size;
20	}
21
22	public bool contains(Object value) {
23	for (Entry<A> e = getFirstEntry(); e != null; e = successor(e))
24	if (eq(value, e.value))
25	true;
26	false;
27	}
28
29	public A get(int idx) {
30	Entry<A> p = getEntry(idx);
31	return p == null ? null : p.value;
32	}
33
34	int subTreeSize(Entry<A> e) { ret e == null ? 0 : e.size; }
35
36	final Entry<A> getEntry(int idx) {
37	if (idx < 0 \|\| idx >= size())
38	throw new IndexOutOfBoundsException(idx + " / " + size());
39	Entry<A> p = root;
40	while true {
41	int sizeLeft = subTreeSize(p.left);
42	if (idx < sizeLeft)
43	continue with p = p.left;
44	idx -= sizeLeft;
45	if (idx == 0) ret p;
46	idx--;
47	p = p.right;
48	}
49	}
50
51	/*public A put(Int key, A value) {
52	Entry<A> t = root;
53	if (t == null) {
54	compare(key, key); // type (and possibly null) check
55
56	root = new Entry<>(key, value, null);
57	//size = 1;
58	modCount++;
59	return null;
60	}
61	int cmp;
62	Entry<A> parent;
63	// split comparator and comparable paths
64	Comparator<? super Int> cpr = comparator;
65	if (cpr != null) {
66	do {
67	parent = t;
68	cmp = cpr.compare(key, t.key);
69	if (cmp < 0)
70	t = t.left;
71	else if (cmp > 0)
72	t = t.right;
73	else
74	return t.setValue(value);
75	} while (t != null);
76	}
77	else {
78	if (key == null)
79	throw new NullPointerException();
80	@SuppressWarnings("unchecked")
81	Comparable<? super Int> k = (Comparable<? super Int>) key;
82	do {
83	parent = t;
84	cmp = k.compareTo(t.key);
85	if (cmp < 0)
86	t = t.left;
87	else if (cmp > 0)
88	t = t.right;
89	else
90	return t.setValue(value);
91	} while (t != null);
92	}
93	Entry<A> e = new Entry<>(key, value, parent);
94	if (cmp < 0)
95	parent.left = e;
96	else
97	parent.right = e;
98	fixAfterInsertion(e);
99	//size++;
100	modCount++;
101	return null;
102	}*/
103
104	/*public A remove(int idx) {
105	Entry<A> p = getEntry(key);
106	if (p == null)
107	return null;
108
109	A oldValue = p.value;
110	deleteEntry(p);
111	return oldValue;
112	}*/
113
114	public void clear() {
115	modCount++;
116	//size = 0;
117	root = null;
118	}
119
120	// Red-black mechanics
121
122	private static final boolean RED = false;
123	private static final boolean BLACK = true;
124
125	/**
126	* Node in the Tree. Doubles as a means to pass key-value pairs back to
127	* user (see Map.Entry).
128	*/
129
130	static final class Entry<A> {
131	int size = 1; // entry count of subtree
132	//Int key;
133	A value;
134	Entry<A> left;
135	Entry<A> right;
136	Entry<A> parent;
137	boolean color = BLACK;
138
139	/**
140	* Make a new cell with given value and parent, and with
141	* {@code null} child links, size 1, and BLACK color.
142	*/
143	Entry(A value, Entry<A> parent) {
144	this.value = value;
145	this.parent = parent;
146	}
147	}
148
149	final Entry<A> getFirstEntry() {
150	Entry<A> p = root;
151	if (p != null)
152	while (p.left != null)
153	p = p.left;
154	return p;
155	}
156
157	final Entry<A> getLastEntry() {
158	Entry<A> p = root;
159	if (p != null)
160	while (p.right != null)
161	p = p.right;
162	return p;
163	}
164
165	static <Int,A> LogNArray.Entry<A> successor(Entry<A> t) {
166	if (t == null)
167	return null;
168	else if (t.right != null) {
169	Entry<A> p = t.right;
170	while (p.left != null)
171	p = p.left;
172	return p;
173	} else {
174	Entry<A> p = t.parent;
175	Entry<A> ch = t;
176	while (p != null && ch == p.right) {
177	ch = p;
178	p = p.parent;
179	}
180	return p;
181	}
182	}
183
184	static <Int,A> Entry<A> predecessor(Entry<A> t) {
185	if (t == null)
186	return null;
187	else if (t.left != null) {
188	Entry<A> p = t.left;
189	while (p.right != null)
190	p = p.right;
191	return p;
192	} else {
193	Entry<A> p = t.parent;
194	Entry<A> ch = t;
195	while (p != null && ch == p.left) {
196	ch = p;
197	p = p.parent;
198	}
199	return p;
200	}
201	}
202
203	/**
204	* Balancing operations.
205	*
206	* Implementations of rebalancings during insertion and deletion are
207	* slightly different than the CLR version. Rather than using dummy
208	* nilnodes, we use a set of accessors that deal properly with null. They
209	* are used to avoid messiness surrounding nullness checks in the main
210	* algorithms.
211	*/
212
213	private static <Int,A> boolean colorOf(Entry<A> p) {
214	return (p == null ? BLACK : p.color);
215	}
216
217	private static <Int,A> Entry<A> parentOf(Entry<A> p) {
218	return (p == null ? null: p.parent);
219	}
220
221	private static <Int,A> void setColor(Entry<A> p, boolean c) {
222	if (p != null)
223	p.color = c;
224	}
225
226	private static <Int,A> Entry<A> leftOf(Entry<A> p) {
227	return (p == null) ? null: p.left;
228	}
229
230	private static <Int,A> Entry<A> rightOf(Entry<A> p) {
231	return (p == null) ? null: p.right;
232	}
233
234	/** From CLR */
235	private void rotateLeft(Entry<A> p) {
236	if (p != null) {
237	Entry<A> r = p.right;
238	p.right = r.left;
239	if (r.left != null)
240	r.left.parent = p;
241	r.parent = p.parent;
242	if (p.parent == null)
243	root = r;
244	else if (p.parent.left == p)
245	p.parent.left = r;
246	else
247	p.parent.right = r;
248	r.left = p;
249	p.parent = r;
250	}
251	}
252
253	/** From CLR */
254	private void rotateRight(Entry<A> p) {
255	if (p != null) {
256	Entry<A> l = p.left;
257	p.left = l.right;
258	if (l.right != null) l.right.parent = p;
259	l.parent = p.parent;
260	if (p.parent == null)
261	root = l;
262	else if (p.parent.right == p)
263	p.parent.right = l;
264	else p.parent.left = l;
265	l.right = p;
266	p.parent = l;
267	}
268	}
269
270	/** From CLR */
271	private void fixAfterInsertion(Entry<A> x) {
272	x.color = RED;
273
274	while (x != null && x != root && x.parent.color == RED) {
275	if (parentOf(x) == leftOf(parentOf(parentOf(x)))) {
276	Entry<A> y = rightOf(parentOf(parentOf(x)));
277	if (colorOf(y) == RED) {
278	setColor(parentOf(x), BLACK);
279	setColor(y, BLACK);
280	setColor(parentOf(parentOf(x)), RED);
281	x = parentOf(parentOf(x));
282	} else {
283	if (x == rightOf(parentOf(x))) {
284	x = parentOf(x);
285	rotateLeft(x);
286	}
287	setColor(parentOf(x), BLACK);
288	setColor(parentOf(parentOf(x)), RED);
289	rotateRight(parentOf(parentOf(x)));
290	}
291	} else {
292	Entry<A> y = leftOf(parentOf(parentOf(x)));
293	if (colorOf(y) == RED) {
294	setColor(parentOf(x), BLACK);
295	setColor(y, BLACK);
296	setColor(parentOf(parentOf(x)), RED);
297	x = parentOf(parentOf(x));
298	} else {
299	if (x == leftOf(parentOf(x))) {
300	x = parentOf(x);
301	rotateRight(x);
302	}
303	setColor(parentOf(x), BLACK);
304	setColor(parentOf(parentOf(x)), RED);
305	rotateLeft(parentOf(parentOf(x)));
306	}
307	}
308	}
309	root.color = BLACK;
310	}
311
312	/**
313	* Delete node p, and then rebalance the tree.
314	*/
315	private void deleteEntry(Entry<A> p) {
316	modCount++;
317	//size--;
318
319	// If strictly internal, copy successor's element to p and then make p
320	// point to successor.
321	if (p.left != null && p.right != null) {
322	Entry<A> s = successor(p);
323	p.value = s.value;
324	p = s;
325	} // p has 2 children
326
327	// Start fixup at replacement node, if it exists.
328	Entry<A> replacement = (p.left != null ? p.left : p.right);
329
330	if (replacement != null) {
331	// Link replacement to parent
332	replacement.parent = p.parent;
333	if (p.parent == null)
334	root = replacement;
335	else if (p == p.parent.left)
336	p.parent.left = replacement;
337	else
338	p.parent.right = replacement;
339
340	// Null out links so they are OK to use by fixAfterDeletion.
341	p.left = p.right = p.parent = null;
342
343	// Fix replacement
344	if (p.color == BLACK)
345	fixAfterDeletion(replacement);
346	} else if (p.parent == null) { // return if we are the only node.
347	root = null;
348	} else { // No children. Use self as phantom replacement and unlink.
349	if (p.color == BLACK)
350	fixAfterDeletion(p);
351
352	if (p.parent != null) {
353	if (p == p.parent.left)
354	p.parent.left = null;
355	else if (p == p.parent.right)
356	p.parent.right = null;
357	p.parent = null;
358	}
359	}
360	}
361
362	/** From CLR */
363	private void fixAfterDeletion(Entry<A> x) {
364	while (x != root && colorOf(x) == BLACK) {
365	if (x == leftOf(parentOf(x))) {
366	Entry<A> sib = rightOf(parentOf(x));
367
368	if (colorOf(sib) == RED) {
369	setColor(sib, BLACK);
370	setColor(parentOf(x), RED);
371	rotateLeft(parentOf(x));
372	sib = rightOf(parentOf(x));
373	}
374
375	if (colorOf(leftOf(sib)) == BLACK &&
376	colorOf(rightOf(sib)) == BLACK) {
377	setColor(sib, RED);
378	x = parentOf(x);
379	} else {
380	if (colorOf(rightOf(sib)) == BLACK) {
381	setColor(leftOf(sib), BLACK);
382	setColor(sib, RED);
383	rotateRight(sib);
384	sib = rightOf(parentOf(x));
385	}
386	setColor(sib, colorOf(parentOf(x)));
387	setColor(parentOf(x), BLACK);
388	setColor(rightOf(sib), BLACK);
389	rotateLeft(parentOf(x));
390	x = root;
391	}
392	} else { // symmetric
393	Entry<A> sib = leftOf(parentOf(x));
394
395	if (colorOf(sib) == RED) {
396	setColor(sib, BLACK);
397	setColor(parentOf(x), RED);
398	rotateRight(parentOf(x));
399	sib = leftOf(parentOf(x));
400	}
401
402	if (colorOf(rightOf(sib)) == BLACK &&
403	colorOf(leftOf(sib)) == BLACK) {
404	setColor(sib, RED);
405	x = parentOf(x);
406	} else {
407	if (colorOf(leftOf(sib)) == BLACK) {
408	setColor(rightOf(sib), BLACK);
409	setColor(sib, RED);
410	rotateLeft(sib);
411	sib = leftOf(parentOf(x));
412	}
413	setColor(sib, colorOf(parentOf(x)));
414	setColor(parentOf(x), BLACK);
415	setColor(leftOf(sib), BLACK);
416	rotateRight(parentOf(x));
417	x = root;
418	}
419	}
420	}
421
422	setColor(x, BLACK);
423	}
424
425	/**
426	* Finds the level down to which to assign all nodes BLACK. This is the
427	* last `full' level of the complete binary tree produced by buildTree.
428	* The remaining nodes are colored RED. (This makes a `nice' set of
429	* color assignments wrt future insertions.) This level number is
430	* computed by finding the number of splits needed to reach the zeroeth
431	* node.
432	*
433	* @param size the (non-negative) number of keys in the tree to be built
434	*/
435	private static int computeRedLevel(int size) {
436	return 31 - Integer.numberOfLeadingZeros(size + 1);
437	}
438	}