private void keys(Node x, Queue<Key> queue, Key lo, Key hi) {
if (x == null) return;
int compLo = lo.compareTo(x.key);
int compHi = hi.compareTo(x.key);
if (compLo < 0) keys(x.left, queue, lo, hi);
if (compLo <= 0 && compHi >= 0) queue.enqueue(x.key);
if (compHi > 0) keys(x.right, queue, lo, hi);
}
private Node delete(Node x, Key key) {
if (x == null) return null;
int comp = key.compareTo(x.key);
if (comp < 0) x.left = delete(x.left, key);
else if (comp > 0) x.right = delete(x.right, key);
else {
if (x.left == null) {
if (x.pred != null) x.pred.succ = x.succ;
if (x.succ != null) x.succ.pred = x.pred;
return x.right;
}
if (x.right == null) {
if (x.pred != null) x.pred.succ = x.succ;
if (x.succ != null) x.succ.pred = x.pred;
return x.left;
}
Node t = max(x.left);
t.left = deleteMaxWithOutDeleteThread(x.left);
t.right = x.right;
if (x.pred != null) x.pred.succ = x.succ;
if (x.succ != null) x.succ.pred = x.pred;
x = t;
}
x.N = size(x.left) + size(x.right) + 1;
x.height = Math.max(height(x.left), height(x.right)) + 1;
x.avgCompares =
(avgCompares(x.left) * size(x.left) + avgCompares(x.right) * size(x.right) + size(x))
/ size(x);
return x;
}
private int rank(Node x, Key key) {
if (x == null) return 0;
int comp = key.compareTo(x.key);
if (comp == 0) return size(x.left);
else if (comp < 0) return rank(x.left, key);
else return size(x.left) + 1 + rank(x.right, key);
}
private Node put(Node x, Key key, Value val) {
if (x == null) {
Node pre = floor(root, key);
Node nex = ceiling(root, key);
lastest = new Node(key, val, 1, 1, 1);
if (pre != null) pre.succ = lastest;
if (nex != null) nex.pred = lastest;
lastest.succ = nex;
lastest.pred = pre;
return lastest;
}
int comp = key.compareTo(x.key);
if (comp < 0) x.left = put(x.left, key, val);
else if (comp > 0) x.right = put(x.right, key, val);
else {
lastest = x;
x.value = val;
}
x.N = size(x.right) + size(x.left) + 1;
x.height = Math.max(height(x.left), height(x.right)) + 1;
x.avgCompares =
(avgCompares(x.left) * size(x.left) + avgCompares(x.right) * size(x.right) + size(x))
/ size(x);
return x;
}
/* private Node get(Node x, Key key) //recursive implementation
{
if(x == null)
return null;
int com = key.compareTo(x.key);
if(com < 0) return get(x.left, key);
else if(com > 0) return get(x.right, key);
else return x;
}*/
private Node get(Node x, Key key) {
while (x != null) {
int comp = key.compareTo(x.key);
if (comp < 0) x = x.left;
else if (comp > 0) x = x.right;
else return x;
}
return null;
}
private Node floor(Node x, Key key) {
if (x == null) return null;
int comp = key.compareTo(x.key);
if (comp < 0) return floor(x.left, key);
else if (comp > 0) {
Node res = floor(x.right, key);
if (res != null) return res;
else return x;
} else return x;
}
private Node ceiling(Node x, Key key) {
if (x == null) return null;
int comp = key.compareTo(x.key);
if (comp > 0) return ceiling(x.right, key);
else if (comp == 0) return x;
else {
Node res = ceiling(x.left, key);
if (res == null) return x;
else return res;
}
}
public boolean checkSelectRank() {
for (Key k : keys()) {
if (k.compareTo(select(rank(k))) != 0) return false;
}
return true;
}