LogNArray v4 [more compact version hiding color flag in size field, OK, makes a difference only without CompressedOOPS] [1024427]

// see: https://en.wikipedia.org/wiki/Order_statistic_tree
// based on: https://algs4.cs.princeton.edu/33balanced/RedBlackBST.java.html
final sclass LogNArray<Value> extends RandomAccessAbstractList<Value> {

 // A symbol table implemented using a left-leaning red-black BST.
 // This is the 2-3 version.
 
  private static final boolean RED   = true;
  private static final boolean BLACK = false;

  private Node<Value> root;     // root of the BST

  // BST helper node data type
  private final sclass Node<Value> {
    private Value val;         // associated data
    private Node<Value> left, right;  // links to left and right subtrees
    private int sizeAndColor; // subtree count + color (highest bit)
    
    *() {}

    *(Value val, boolean color, int size) {
      this.val = val;
      sizeAndColor = size | (color ? 0x80000000 : 0);
    }
    
    int size() { ret sizeAndColor & 0x7FFFFFFF; }
    bool color() { ret sizeAndColor < 0; }
    
    void setSize(int size) { sizeAndColor = sizeAndColor & 0x80000000 | size; }
    void setColor(bool color) { sizeAndColor = size() | (color ? 0x80000000 : 0); }
  }

  // is node x red; false if x is null ?
  private boolean isRed(Node<Value> x) {
      if (x == null) return false;
      return x.color() == RED;
  }

  // number of node in subtree rooted at x; 0 if x is null
  private int size(Node<Value> x) {
      if (x == null) return 0;
      return x.size();
  } 


  public int size() {
      return size(root);
  }

  public boolean isEmpty() {
      return root == null;
  }


  public void add(int idx, Value val) {
    if (idx < 0 || idx > size()) throw new IndexOutOfBoundsException(idx + " / " + size());
    
    root = add(root, idx, val);
    root.setColor(BLACK);
    ifdef LogNArray_debug assertTrue(check()); endifdef
  }

  // insert the value pair in index k of subtree rooted at h
  private Node<Value> add(Node<Value> h, int k, Value val) { 
    if (h == null) ret new Node(val, RED, 1);

    int t = size(h.left);
    if (k < t)
      // replace / fit in left child
      h.left = add(h.left, k, val);
    else if (k == t) {
      // move value to right child, replace value
      h.right = add(h.right, 0, h.val);
      h.val = val;
    } else
      // replace / fit in right child
      h.right = add(h.right, k-t-1, val); 

    // fix-up any right-leaning links
    if (isRed(h.right) && !isRed(h.left))      h = rotateLeft(h);
    if (isRed(h.left)  &&  isRed(h.left.left)) h = rotateRight(h);
    if (isRed(h.left)  &&  isRed(h.right))     flipColors(h);
    h.setSize(size(h.left) + size(h.right) + 1);
    
    ifdef LogNArray_debug
      print("LogNArray.add: Node " + h.val + " new size: " + h.size());
    endifdef

    ret h;
  }

  public Value remove(int idx) { 
    Value oldValue = get(idx);
    
    // if both children of root are black, set root to red
    if (!isRed(root.left) && !isRed(root.right))
      root.setColor(RED);

    root = remove(root, idx);
    if (root != null) root.setColor(BLACK);
    
    ifdef LogNArray_debug assertTrue(check()); endifdef
    
    ret oldValue;
  }

  private Node<Value> remove(Node<Value> h, int k) { 
    int t = size(h.left);
    if (k < t) { // remove from left child
      if (!isRed(h.left) && !isRed(h.left.left))
        h = moveRedLeft(h);
      h.left = remove(h.left, k);
    } else { // remove from center or right child
      if (isRed(h.left)) {
        h = rotateRight(h);
        t = size(h.left);
      }
      if (h.right == null) null; // drop whole node
      if (!isRed(h.right) && !isRed(h.right.left)) {
        h = moveRedRight(h);
        t = size(h.left);
      }
      if (k == t) { // replace center value with min of right child
        h.val = nodeAtIndex(h.right, 0).val;
        h.right = remove(h.right, 0);
      }
      else h.right = remove(h.right, k-t-1);
    }
    ret balance(h);
  }

  // make a left-leaning link lean to the right
  private Node<Value> rotateRight(Node<Value> h) {
      // assert (h != null) && isRed(h.left);
      Node<Value> x = h.left;
      h.left = x.right;
      x.right = h;
      x.setColor(x.right.color());
      x.right.setColor(RED);
      x.setSize(h.size());
      h.setSize(size(h.left) + size(h.right) + 1);
      return x;
  }

  // make a right-leaning link lean to the left
  private Node<Value> rotateLeft(Node<Value> h) {
      // assert (h != null) && isRed(h.right);
      Node<Value> x = h.right;
      h.right = x.left;
      x.left = h;
      x.setColor(x.left.color());
      x.left.setColor(RED);
      x.setSize(h.size());
      h.setSize(size(h.left) + size(h.right) + 1);
      return x;
  }

  // flip the colors of a node and its two children
  private void flipColors(Node<Value> h) {
      // h must have opposite color of its two children
      // assert (h != null) && (h.left != null) && (h.right != null);
      // assert (!isRed(h) &&  isRed(h.left) &&  isRed(h.right))
      //    || (isRed(h)  && !isRed(h.left) && !isRed(h.right));
      h.setColor(!h.color());
      h.left.setColor(!h.left.color());
      h.right.setColor(!h.right.color());
  }

  // Assuming that h is red and both h.left and h.left.left
  // are black, make h.left or one of its children red.
  private Node<Value> moveRedLeft(Node<Value> h) {
      // assert (h != null);
      // assert isRed(h) && !isRed(h.left) && !isRed(h.left.left);

      flipColors(h);
      if (isRed(h.right.left)) { 
          h.right = rotateRight(h.right);
          h = rotateLeft(h);
          flipColors(h);
      }
      return h;
  }

  // Assuming that h is red and both h.right and h.right.left
  // are black, make h.right or one of its children red.
  private Node<Value> moveRedRight(Node<Value> h) {
      // assert (h != null);
      // assert isRed(h) && !isRed(h.right) && !isRed(h.right.left);
      flipColors(h);
      if (isRed(h.left.left)) { 
          h = rotateRight(h);
          flipColors(h);
      }
      return h;
  }

  // restore red-black tree invariant
  private Node<Value> balance(Node<Value> h) {
      // assert (h != null);

      if (isRed(h.right))                      h = rotateLeft(h);
      if (isRed(h.left) && isRed(h.left.left)) h = rotateRight(h);
      if (isRed(h.left) && isRed(h.right))     flipColors(h);

      h.setSize(size(h.left) + size(h.right) + 1);
      return h;
  }


  /**
   * Returns the height of the BST (for debugging).
   * @return the height of the BST (a 1-node tree has height 0)
   */
  public int height() {
      return height(root);
  }
  
  private int height(Node<Value> x) {
      if (x == null) return -1;
      return 1 + Math.max(height(x.left), height(x.right));
  }
  
  public Value get(int k) {
    ret nodeAtIndex(k).val;
  }

  public Value set(int k, Value val) {
    Node<Value> n = nodeAtIndex(k);
    Value oldValue = n.val;
    n.val = val;
    ret oldValue;
  }

  public Node<Value> nodeAtIndex(int k) {
      if (k < 0 || k >= size()) {
          throw new IndexOutOfBoundsException(k + " / " + size());
      }
      ret nodeAtIndex(root, k);
  }

  // the key of rank k in the subtree rooted at x
  private Node<Value> nodeAtIndex(Node<Value> x, int k) {
      // assert x != null;
      // assert k >= 0 && k < size(x);
      int t = size(x.left); 
      if      (t > k) return nodeAtIndex(x.left,  k); 
      else if (t < k) return nodeAtIndex(x.right, k-t-1); 
      else            return x; 
  } 
  
  private boolean check() {
      if (!isSizeConsistent()) println("Subtree counts not consistent");
      if (!is23())             println("Not a 2-3 tree");
      if (!isBalanced())       println("Not balanced");
      return isSizeConsistent() && is23() && isBalanced();
  }

  // are the size fields correct?
  private boolean isSizeConsistent() { return isSizeConsistent(root); }
  private boolean isSizeConsistent(Node<Value> x) {
      if (x == null) return true;
      if (x.size() != size(x.left) + size(x.right) + 1) return false;
      return isSizeConsistent(x.left) && isSizeConsistent(x.right);
  } 

  // Does the tree have no red right links, and at most one (left)
  // red links in a row on any path?
  private boolean is23() { return is23(root); }
  private boolean is23(Node<Value> x) {
      if (x == null) return true;
      if (isRed(x.right)) return false;
      if (x != root && isRed(x) && isRed(x.left))
          return false;
      return is23(x.left) && is23(x.right);
  } 

  // do all paths from root to leaf have same number of black edges?
  private boolean isBalanced() { 
      int black = 0;     // number of black links on path from root to min
      Node<Value> x = root;
      while (x != null) {
          if (!isRed(x)) black++;
          x = x.left;
      }
      return isBalanced(root, black);
  }

  // does every path from the root to a leaf have the given number of black links?
  private boolean isBalanced(Node<Value> x, int black) {
      if (x == null) return black == 0;
      if (!isRed(x)) black--;
      return isBalanced(x.left, black) && isBalanced(x.right, black);
  }
  
  public void clear() { root = null; }
}

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Snippet ID:	#1024427
Snippet name:	LogNArray v4 [more compact version hiding color flag in size field, OK, makes a difference only without CompressedOOPS]
Eternal ID of this version:	#1024427/5
Text MD5:	7a6bd3c6c460a8f6ee733c7d57945723
Transpilation MD5:	aa4975d0aa40ab6ea6ebe05193febd96
Author:	stefan
Category:	javax
Type:	JavaX fragment (include)
Public (visible to everyone):	Yes
Archived (hidden from active list):	No
Created/modified:	2019-08-12 14:36:36
Source code size:	9376 bytes / 296 lines
Pitched / IR pitched:	No / No
Views / Downloads:	205 / 461
Version history:	4 change(s)
Referenced in:	[show references]

< > BotCompany Repo | #1024427 // LogNArray v4 [more compact version hiding color flag in size field, OK, makes a difference only without CompressedOOPS]

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

Author comment

1	// see: https://en.wikipedia.org/wiki/Order_statistic_tree
2	// based on: https://algs4.cs.princeton.edu/33balanced/RedBlackBST.java.html
3	final sclass LogNArray<Value> extends RandomAccessAbstractList<Value> {
4
5	// A symbol table implemented using a left-leaning red-black BST.
6	// This is the 2-3 version.
7
8	private static final boolean RED = true;
9	private static final boolean BLACK = false;
10
11	private Node<Value> root; // root of the BST
12
13	// BST helper node data type
14	private final sclass Node<Value> {
15	private Value val; // associated data
16	private Node<Value> left, right; // links to left and right subtrees
17	private int sizeAndColor; // subtree count + color (highest bit)
18
19	*() {}
20
21	*(Value val, boolean color, int size) {
22	this.val = val;
23	sizeAndColor = size \| (color ? 0x80000000 : 0);
24	}
25
26	int size() { ret sizeAndColor & 0x7FFFFFFF; }
27	bool color() { ret sizeAndColor < 0; }
28
29	void setSize(int size) { sizeAndColor = sizeAndColor & 0x80000000 \| size; }
30	void setColor(bool color) { sizeAndColor = size() \| (color ? 0x80000000 : 0); }
31	}
32
33	// is node x red; false if x is null ?
34	private boolean isRed(Node<Value> x) {
35	if (x == null) return false;
36	return x.color() == RED;
37	}
38
39	// number of node in subtree rooted at x; 0 if x is null
40	private int size(Node<Value> x) {
41	if (x == null) return 0;
42	return x.size();
43	}
44
45
46	public int size() {
47	return size(root);
48	}
49
50	public boolean isEmpty() {
51	return root == null;
52	}
53
54
55	public void add(int idx, Value val) {
56	if (idx < 0 \|\| idx > size()) throw new IndexOutOfBoundsException(idx + " / " + size());
57
58	root = add(root, idx, val);
59	root.setColor(BLACK);
60	ifdef LogNArray_debug assertTrue(check()); endifdef
61	}
62
63	// insert the value pair in index k of subtree rooted at h
64	private Node<Value> add(Node<Value> h, int k, Value val) {
65	if (h == null) ret new Node(val, RED, 1);
66
67	int t = size(h.left);
68	if (k < t)
69	// replace / fit in left child
70	h.left = add(h.left, k, val);
71	else if (k == t) {
72	// move value to right child, replace value
73	h.right = add(h.right, 0, h.val);
74	h.val = val;
75	} else
76	// replace / fit in right child
77	h.right = add(h.right, k-t-1, val);
78
79	// fix-up any right-leaning links
80	if (isRed(h.right) && !isRed(h.left)) h = rotateLeft(h);
81	if (isRed(h.left) && isRed(h.left.left)) h = rotateRight(h);
82	if (isRed(h.left) && isRed(h.right)) flipColors(h);
83	h.setSize(size(h.left) + size(h.right) + 1);
84
85	ifdef LogNArray_debug
86	print("LogNArray.add: Node " + h.val + " new size: " + h.size());
87	endifdef
88
89	ret h;
90	}
91
92	public Value remove(int idx) {
93	Value oldValue = get(idx);
94
95	// if both children of root are black, set root to red
96	if (!isRed(root.left) && !isRed(root.right))
97	root.setColor(RED);
98
99	root = remove(root, idx);
100	if (root != null) root.setColor(BLACK);
101
102	ifdef LogNArray_debug assertTrue(check()); endifdef
103
104	ret oldValue;
105	}
106
107	private Node<Value> remove(Node<Value> h, int k) {
108	int t = size(h.left);
109	if (k < t) { // remove from left child
110	if (!isRed(h.left) && !isRed(h.left.left))
111	h = moveRedLeft(h);
112	h.left = remove(h.left, k);
113	} else { // remove from center or right child
114	if (isRed(h.left)) {
115	h = rotateRight(h);
116	t = size(h.left);
117	}
118	if (h.right == null) null; // drop whole node
119	if (!isRed(h.right) && !isRed(h.right.left)) {
120	h = moveRedRight(h);
121	t = size(h.left);
122	}
123	if (k == t) { // replace center value with min of right child
124	h.val = nodeAtIndex(h.right, 0).val;
125	h.right = remove(h.right, 0);
126	}
127	else h.right = remove(h.right, k-t-1);
128	}
129	ret balance(h);
130	}
131
132	// make a left-leaning link lean to the right
133	private Node<Value> rotateRight(Node<Value> h) {
134	// assert (h != null) && isRed(h.left);
135	Node<Value> x = h.left;
136	h.left = x.right;
137	x.right = h;
138	x.setColor(x.right.color());
139	x.right.setColor(RED);
140	x.setSize(h.size());
141	h.setSize(size(h.left) + size(h.right) + 1);
142	return x;
143	}
144
145	// make a right-leaning link lean to the left
146	private Node<Value> rotateLeft(Node<Value> h) {
147	// assert (h != null) && isRed(h.right);
148	Node<Value> x = h.right;
149	h.right = x.left;
150	x.left = h;
151	x.setColor(x.left.color());
152	x.left.setColor(RED);
153	x.setSize(h.size());
154	h.setSize(size(h.left) + size(h.right) + 1);
155	return x;
156	}
157
158	// flip the colors of a node and its two children
159	private void flipColors(Node<Value> h) {
160	// h must have opposite color of its two children
161	// assert (h != null) && (h.left != null) && (h.right != null);
162	// assert (!isRed(h) && isRed(h.left) && isRed(h.right))
163	// \|\| (isRed(h) && !isRed(h.left) && !isRed(h.right));
164	h.setColor(!h.color());
165	h.left.setColor(!h.left.color());
166	h.right.setColor(!h.right.color());
167	}
168
169	// Assuming that h is red and both h.left and h.left.left
170	// are black, make h.left or one of its children red.
171	private Node<Value> moveRedLeft(Node<Value> h) {
172	// assert (h != null);
173	// assert isRed(h) && !isRed(h.left) && !isRed(h.left.left);
174
175	flipColors(h);
176	if (isRed(h.right.left)) {
177	h.right = rotateRight(h.right);
178	h = rotateLeft(h);
179	flipColors(h);
180	}
181	return h;
182	}
183
184	// Assuming that h is red and both h.right and h.right.left
185	// are black, make h.right or one of its children red.
186	private Node<Value> moveRedRight(Node<Value> h) {
187	// assert (h != null);
188	// assert isRed(h) && !isRed(h.right) && !isRed(h.right.left);
189	flipColors(h);
190	if (isRed(h.left.left)) {
191	h = rotateRight(h);
192	flipColors(h);
193	}
194	return h;
195	}
196
197	// restore red-black tree invariant
198	private Node<Value> balance(Node<Value> h) {
199	// assert (h != null);
200
201	if (isRed(h.right)) h = rotateLeft(h);
202	if (isRed(h.left) && isRed(h.left.left)) h = rotateRight(h);
203	if (isRed(h.left) && isRed(h.right)) flipColors(h);
204
205	h.setSize(size(h.left) + size(h.right) + 1);
206	return h;
207	}
208
209
210	/**
211	* Returns the height of the BST (for debugging).
212	* @return the height of the BST (a 1-node tree has height 0)
213	*/
214	public int height() {
215	return height(root);
216	}
217
218	private int height(Node<Value> x) {
219	if (x == null) return -1;
220	return 1 + Math.max(height(x.left), height(x.right));
221	}
222
223	public Value get(int k) {
224	ret nodeAtIndex(k).val;
225	}
226
227	public Value set(int k, Value val) {
228	Node<Value> n = nodeAtIndex(k);
229	Value oldValue = n.val;
230	n.val = val;
231	ret oldValue;
232	}
233
234	public Node<Value> nodeAtIndex(int k) {
235	if (k < 0 \|\| k >= size()) {
236	throw new IndexOutOfBoundsException(k + " / " + size());
237	}
238	ret nodeAtIndex(root, k);
239	}
240
241	// the key of rank k in the subtree rooted at x
242	private Node<Value> nodeAtIndex(Node<Value> x, int k) {
243	// assert x != null;
244	// assert k >= 0 && k < size(x);
245	int t = size(x.left);
246	if (t > k) return nodeAtIndex(x.left, k);
247	else if (t < k) return nodeAtIndex(x.right, k-t-1);
248	else return x;
249	}
250
251	private boolean check() {
252	if (!isSizeConsistent()) println("Subtree counts not consistent");
253	if (!is23()) println("Not a 2-3 tree");
254	if (!isBalanced()) println("Not balanced");
255	return isSizeConsistent() && is23() && isBalanced();
256	}
257
258	// are the size fields correct?
259	private boolean isSizeConsistent() { return isSizeConsistent(root); }
260	private boolean isSizeConsistent(Node<Value> x) {
261	if (x == null) return true;
262	if (x.size() != size(x.left) + size(x.right) + 1) return false;
263	return isSizeConsistent(x.left) && isSizeConsistent(x.right);
264	}
265
266	// Does the tree have no red right links, and at most one (left)
267	// red links in a row on any path?
268	private boolean is23() { return is23(root); }
269	private boolean is23(Node<Value> x) {
270	if (x == null) return true;
271	if (isRed(x.right)) return false;
272	if (x != root && isRed(x) && isRed(x.left))
273	return false;
274	return is23(x.left) && is23(x.right);
275	}
276
277	// do all paths from root to leaf have same number of black edges?
278	private boolean isBalanced() {
279	int black = 0; // number of black links on path from root to min
280	Node<Value> x = root;
281	while (x != null) {
282	if (!isRed(x)) black++;
283	x = x.left;
284	}
285	return isBalanced(root, black);
286	}
287
288	// does every path from the root to a leaf have the given number of black links?
289	private boolean isBalanced(Node<Value> x, int black) {
290	if (x == null) return black == 0;
291	if (!isRed(x)) black--;
292	return isBalanced(x.left, black) && isBalanced(x.right, black);
293	}
294
295	public void clear() { root = null; }
296	}