Java数据结构与算法(红黑树)

前言

红黑树是一种自平衡二叉搜索树，确保在插入和删除操作后，树的高度保持平衡，从而保证基本操作（插入、删除、查找）的时间复杂度为O(log n)。

实现原理

红黑树具有以下性质：

1. 每个节点要么是红色，要么是黑色。
2. 根节点是黑色的。
3. 每个叶子节点（NIL节点，通常是空节点）是黑色的。
4. 如果一个节点是红色的，则它的两个子节点都是黑色的。
5. 从任一节点到其每个叶子的所有路径都包含相同数目的黑色节点。

动画过程

Red/Black Tree Visualization

具体代码实现

public class RedBlackTree {
    private static final boolean RED = false;
    private static final boolean BLACK = true;

    private class Node {
        int key;
        Node left, right, parent;
        boolean color;

        Node(int key, boolean color, Node parent) {
            this.key = key;
            this.color = color;
            this.parent = parent;
        }
    }

    private Node root;
    private Node TNULL;

    public RedBlackTree() {
        TNULL = new Node(0, BLACK, null);
        root = TNULL;
    }

    private void rotateLeft(Node x) {
        Node y = x.right;
        x.right = y.left;
        if (y.left != TNULL) {
            y.left.parent = x;
        }
        y.parent = x.parent;
        if (x.parent == null) {
            this.root = y;
        } else if (x == x.parent.left) {
            x.parent.left = y;
        } else {
            x.parent.right = y;
        }
        y.left = x;
        x.parent = y;
    }

    private void rotateRight(Node x) {
        Node y = x.left;
        x.left = y.right;
        if (y.right != TNULL) {
            y.right.parent = x;
        }
        y.parent = x.parent;
        if (x.parent == null) {
            this.root = y;
        } else if (x == x.parent.right) {
            x.parent.right = y;
        }
        y.right = x;
        x.parent = y;
    }

    private void insertFix(Node k) {
        Node u;
        while (k.parent.color == RED) {
            if (k.parent == k.parent.parent.left) {
                u = k.parent.parent.right;
                if (u.color == RED) {
                    u.color = BLACK;
                    k.parent.color = BLACK;
                    k.parent.parent.color = RED;
                    k = k.parent.parent;
                } else {
                    if (k == k.parent.right) {
                        k = k.parent;
                        rotateLeft(k);
                    }
                    k.parent.color = BLACK;
                    k.parent.parent.color = RED;
                    rotateRight(k.parent.parent);
                }
            } else {
                u = k.parent.parent.left;
                if (u.color == RED) {
                    u.color = BLACK;
                    k.parent.color = BLACK;
                    k.parent.parent.color = RED;
                    k = k.parent.parent;
                } else {
                    if (k == k.parent.left) {
                        k = k.parent;
                        rotateRight(k);
                    }
                    k.parent.color = BLACK;
                    k.parent.parent.color = RED;
                    rotateLeft(k.parent.parent);
                }
            }
            if (k == root) {
                break;
            }
        }
        root.color = BLACK;
    }

    public void insert(int key) {
        Node node = new Node(key, RED, null);
        node.left = TNULL;
        node.right = TNULL;

        Node y = null;
        Node x = this.root;

        while (x != TNULL) {
            y = x;
            if (node.key < x.key) {
                x = x.left;
            } else {
                x = x.right;
            }
        }

        node.parent = y;
        if (y == null) {
            root = node;
        } else if (node.key < y.key) {
            y.left = node;
        } else {
            y.right = node;
        }

        if (node.parent == null) {
            node.color = BLACK;
            return;
        }

        if (node.parent.parent == null) {
            return;
        }

        insertFix(node);
    }

    public Node search(int key) {
        return searchTreeHelper(this.root, key);
    }

    private Node searchTreeHelper(Node node, int key) {
        if (node == TNULL || key == node.key) {
            return node;
        }

        if (key < node.key) {
            return searchTreeHelper(node.left, key);
        }
        return searchTreeHelper(node.right, key);
    }

    public void printTree() {
        printHelper(this.root, "", true);
    }

    private void printHelper(Node root, String indent, boolean last) {
        if (root != TNULL) {
            System.out.print(indent);
            if (last) {
                System.out.print("R----");
                indent += "   ";
            } else {
                System.out.print("L----");
                indent += "|  ";
            }

            String sColor = root.color == RED ? "RED" : "BLACK";
            System.out.println(root.key + "(" + sColor + ")");
            printHelper(root.left, indent, false);
            printHelper(root.right, indent, true);
        }
    }

    public static void main(String[] args) {
        RedBlackTree tree = new RedBlackTree();

        tree.insert(55);
        tree.insert(40);
        tree.insert(65);
        tree.insert(60);
        tree.insert(75);
        tree.insert(57);

        tree.printTree();
    }
}

QA:待定