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红黑树是一种自平衡二叉搜索树#xff0c;确保在插入和删除操作后#xff0c;树的高度保持平衡#xff0c;从而保证基本操作#xff08;插入、删除、查找#xff09;的时间复杂度为O(log n)。
实现原理
红黑树具有以下性质#xff1a;
每个节点要么是红色#…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
每个节点要么是红色要么是黑色。根节点是黑色的。每个叶子节点NIL节点通常是空节点是黑色的。如果一个节点是红色的则它的两个子节点都是黑色的。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
