红黑树是一种自平衡二叉查找树,它通过对节点进行着色和旋转操作保持树的平衡,从而保证了查找、插入和删除操作的时间复杂度均为$O(logn)$,其中$n$为树中节点的数量。
下面是红黑树的Java实现:
public class RedBlackTree<K extends Comparable<K>, V> {
private static final boolean RED = true;
private static final boolean BLACK = false;
private Node root;
private class Node {
K key;
V value;
Node left, right;
boolean color;
int size;
public Node(K key, V value, boolean color, int size) {
this.key = key;
this.value = value;
this.color = color;
this.size = size;
}
}
private boolean isRed(Node x) {
if (x == null) {
return false;
}
return x.color == RED;
}
private int size(Node x) {
if (x == null) {
return 0;
}
return x.size;
}
public int size() {
return size(root);
}
public V get(K key) {
Node x = root;
while (x != null) {
int cmp = key.compareTo(x.key);
if (cmp < 0) {
x = x.left;
} else if (cmp > 0) {
x = x.right;
} else {
return x.value;
}
}
return null;
}
public void put(K key, V value) {
root = put(root, key, value);
root.color = BLACK;
}
private Node put(Node h, K key, V value) {
if (h == null) {
return new Node(key, value, RED, 1);
}
int cmp = key.compareTo(h.key);
if (cmp < 0) {
h.left = put(h.left, key, value);
} else if (cmp > 0) {
h.right = put(h.right, key, value);
} else {
h.value = value;
}
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.size = size(h.left) + size(h.right) + 1;
return h;
}
private Node rotateLeft(Node h) {
Node x = h.right;
h.right = x.left;
x.left = h;
x.color = h.color;
h.color = RED;
x.size = h.size;
h.size = size(h.left) + size(h.right) + 1;
return x;
}
private Node rotateRight(Node h) {
Node x = h.left;
h.left = x.right;
x.right = h;
x.color = h.color;
h.color = RED;
x.size = h.size;
h.size = size(h.left) + size(h.right) + 1;
return x;
}
private void flipColors(Node h) {
h.color = RED;
h.left.color = BLACK;
h.right.color = BLACK;
}
}