Java实现红黑树
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红黑树（Red Black Tree） 是一种自平衡二叉查找树，红黑树和AVL树类似，都是在进行插入和删除操作时通过特定操作保持二叉查找树的平衡，从而获得较高的查找性能。
它虽然是复杂的，但它的最坏情况运行时间也是非常良好的，并且在实践中是高效的： 它可以在O(log n)时间内做查找，插入和删除。
红黑树的性质：
性质1. 节点是红色或黑色。
性质2. 根节点是黑色。
性质3 每个叶节点（NIL节点，空节点）是黑色的。
性质4 每个红色节点的两个子节点都是黑色。(从每个叶子到根的所有路径上不能有两个连续的红色节点)
性质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。
红黑树通过旋转来保持它的基本特性达到平衡，旋转的操作有左旋和右旋。
以下是用Java实现的红黑树代码：
package tree;public class RBTree { enum CORLOR{ RED,BLACK; } class RBTNode { CORLOR color; int key; RBTNode left; RBTNode right; RBTNode parent; public RBTNode(CORLOR color, int key, RBTNode left, RBTNode right, RBTNode parent) { this.color = color; this.key = key; this.left = left; this.right = right; this.parent = parent; } } private RBTNode root; public RBTNode getRoot() { return root; } public void setRoot(RBTNode root) { this.root = root; } private RBTNode parentOf(RBTNode node) { return node != null ? node.parent : null; } private boolean isRed(RBTNode node) { if(node != null && node.color == CORLOR.RED) { return true; } return false; } private boolean isBlack(RBTNode node) { if(node != null && node.color == CORLOR.BLACK) { return true; } return false; } //左旋操作 private void leftRotate(RBTNode x) { RBTNode y = x.right; //把x的右孩子赋给y x.right = y.left; //把y的左孩子即原x的右孩子的左孩子设为x的右孩子 if(y.left != null) { y.left.parent = x; //如果y的左孩子非空，把x设为y的左孩子的父结点 } y.parent = x.parent; if(x.parent == null) { this.root = y; //如果x的父结点为空，则将y设为根结点 } else { if(x.parent.left == x) { x.parent.left = y; //如果x是它父结点的左孩子，则将y设为x的父结点的左孩子 } else { x.parent.right = y; // 如果x是它父结点的右孩子，则将y设为设为x父结点的右孩子 } } y.left = x; // 将x设为y的左孩子 x.parent = y; } //右旋操作 private void rightRotate(RBTNode y) { RBTNode x = y.left; y.left = x.right; if(x.right != null) { x.right.parent = y; } x.parent = y.parent; if(y.parent == null) { this.root = x; } else { if(y == y.parent.right) { y.parent.right = x; } else { y.parent.left = x; } } x.right = y; y.parent = x; } //修正函数 private void insertFixUp(RBTNode node) { RBTNode parent, gparent; while (((parent = parentOf(node))!=null) && isRed(parent)) { gparent = parentOf(parent); if (parent == gparent.left) { RBTNode uncle = gparent.right; if ((uncle!=null) && isRed(uncle)) { uncle.color = CORLOR.BLACK; parent.color = CORLOR.BLACK; gparent.color = CORLOR.RED; node = gparent; continue; } if (parent.right == node) { RBTNode tmp; leftRotate(parent); tmp = parent; parent = node; node = tmp; } parent.color = CORLOR.BLACK; gparent.color = CORLOR.RED; rightRotate(gparent); } else { RBTNode uncle = gparent.left; if ((uncle!=null) && isRed(uncle)) { uncle.color = CORLOR.BLACK; parent.color = CORLOR.BLACK; gparent.color = CORLOR.RED; node = gparent; continue; } if (parent.left == node) { RBTNode tmp; rightRotate(parent); tmp = parent; parent = node; node = tmp; } parent.color = CORLOR.BLACK; gparent.color = CORLOR.RED; leftRotate(gparent); } } this.root.color = CORLOR.BLACK; } private void insert(RBTNode node) { RBTNode y = null; RBTNode x = this.root; while ( x != null ) { y = x; if(node.key < x.key) { x = x.left; } else { x = x.right; } } node.parent = y; if(y != null) { if(node.key < y.key) { y.left = node; } else { y.right = node; } } else { this.root = node; } node.color = CORLOR.RED; insertFixUp(node); } public void insert(int key) { RBTNode node = new RBTNode(CORLOR.BLACK, key, null, null, null); if(node != null) { insert(node); } } //删除修正函数 private void removeFixUp(RBTNode node, RBTNode parent) { RBTNode other; while( (node == null || isBlack(node)) && node != this.root) { if(parent.left == node) { other = parent.right; if( isRed(other) ) { other.color = CORLOR.BLACK; parent.color = CORLOR.RED; leftRotate(parent); other = parent.right; } if((other.left == null || isBlack(other.left)) && (other.right == null || isBlack(other.right))) { other.color = CORLOR.RED; node = parent; parent = parentOf(node); } else { if(other.right == null || isBlack(other.right)) { other.left.color = CORLOR.BLACK; other.color = CORLOR.RED; rightRotate(other); other = parent.right; } other.color = parent.color; parent.color = CORLOR.BLACK; other.right.color = CORLOR.BLACK; leftRotate(parent); node = this.root; break; } } else { other = parent.left; if(isRed(other)) { other.color = CORLOR.BLACK; parent.color = CORLOR.RED; rightRotate(parent); other = parent.left; } if( (other.left == null || isBlack(other.left)) && (other.right == null || isBlack(other.right))) { other.color = CORLOR.RED; node = parent; parent = parentOf(node); } else { if(other.left == null || isBlack(other.left) ) { other.right.color = CORLOR.BLACK; other.color = CORLOR.RED; leftRotate(other); other = parent.left; } other.color = parent.color; parent.color = CORLOR.BLACK; other.left.color = CORLOR.BLACK; rightRotate(parent); node = this.root; break; } } } if(node != null) { node.color = CORLOR.BLACK; } } //删除结点 private void remove(RBTNode node) { RBTNode child,parent; CORLOR color; if( node.left != null && node.right != null) { RBTNode replace = node; replace = replace.right; while(replace.left != null) { replace = replace.left; } if(parentOf(node) != null) { if(parentOf(node).left == node) { parentOf(node).left = replace; } else{ parentOf(node).right = replace; } } else { this.root = replace; } child = replace.right; parent = parentOf(replace); color = replace.color; if(parent == node) { parent = replace; } else { if(child != null) { child.parent = parent; } parent.left = child; replace.right = node.right; node.right.parent = replace; } replace.parent = node.parent; replace.color = node.color; replace.left = node.left; node.left.parent = replace; if(color == CORLOR.BLACK) { removeFixUp(child, parent); } node = null; return; } if(node.left != null) { child = node.left; }else { child = node.right; } parent = node.parent; color = node.color; if(child != null) { child.parent = parent; } if(parent != null) { if(parent.left == node) { parent.left = child; }else { parent.right = child; } }else { this.root = child; } if(color == CORLOR.BLACK) { removeFixUp(child, parent); } node = null; } public RBTNode search(RBTNode x,int key) { if(x == null) { return x; } if(x.key > key) { return search(x.left,key); } else if(x.key < key) { return search(x.right,key); } else return x; } public RBTNode search(int key) { return search(this.root,key); } public void remove(int key) { RBTNode node; if( (node = search(root,key) ) != null) remove(node); } //中序遍历 private void inOrder(RBTNode tree) { if(tree != null) { inOrder(tree.left); System.out.print(tree.key+" "); inOrder(tree.right); } } //先序遍历 private void preOrder(RBTNode tree) { if(tree != null) { System.out.print(tree.key+" "); preOrder(tree.left); preOrder(tree.right); } } //后序遍历 private void postOrder(RBTNode tree) { if(tree != null) { postOrder(tree.left); postOrder(tree.right); System.out.print(tree.key+" "); } } public static void main(String[] args) { RBTree tree = new RBTree(); tree.insert(10); tree.insert(40); tree.insert(30); tree.insert(60); tree.insert(90); tree.insert(70); tree.insert(20); tree.insert(50); tree.insert(80); //中序遍历 System.out.println("中序遍历："); tree.inOrder(tree.root); System.out.println("\n先序遍历："); tree.preOrder(tree.root); System.out.println("\n后序遍历："); tree.postOrder(tree.root); }}以下是测试结果：
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