紅黑樹描述

<pre name="code" class="java">/*
 * 紅黑樹
 */
public class RedBlackTree {
	public static final RbTreeNode NIL = new RbTreeNode(RbColor.BLACK);
	private RbTreeNode root = null;
	public static void main(String[] args) {
		RedBlackTree rbt = new RedBlackTree();
		//測試插入 page 179  紅黑樹不唯一
		rbt.insertRbTreeNode(new RbTreeNode(11,RbColor.BLACK));
		rbt.insertRbTreeNode(new RbTreeNode(2,RbColor.RED));
		rbt.insertRbTreeNode(new RbTreeNode(1,RbColor.BLACK));
		rbt.insertRbTreeNode(new RbTreeNode(7,RbColor.BLACK));
		rbt.insertRbTreeNode(new RbTreeNode(5,RbColor.RED));
		rbt.insertRbTreeNode(new RbTreeNode(8,RbColor.RED));
		rbt.insertRbTreeNode(new RbTreeNode(14,RbColor.BLACK));
		rbt.insertRbTreeNode(new RbTreeNode(15,RbColor.RED));
		rbt.printTree();
		rbt.deleteRbTreeNode(rbt.searchRbTreeNode(rbt.root, 7));
		rbt.printTree();
		System.out.println("最大節點的鍵爲："+rbt.searchMaximum(rbt.root).key);
	}
	
	public RedBlackTree() {
		this.root = NIL;
	}
	//中序遍歷二叉樹
	private void traverseTree(RbTreeNode x) {
		if(x != NIL) {
			traverseTree(x.left);
			System.out.print(x.key + " " + x.color + " ");
			traverseTree(x.right);
		}
	}
	private void printTree() {
		System.out.println("root:"+root.key+" "+root.color);
		traverseTree(root);
		System.out.println();
	}
	
	//查找某一子節點
	private RbTreeNode searchRbTreeNode(RbTreeNode x,int key) {
		while(x != NIL && key != x.key) {
			if(key < x.key) {
				x = x.left;
			} else {
				x = x.right;
			}
		}
		return x;
	}
	
	//插入某一子節點
	private void insertRbTreeNode(RbTreeNode z) {
		RbTreeNode y = NIL;
		RbTreeNode x = root;
		while(x != NIL) {
			y = x;
			if(z.key < x.key) {
				x = x.left;
			} else {
				x = x.right;
			}
		}
		z.parent = y;
		if(y == NIL) {
			root = z;
		} else if(z.key < y.key) {
			y.left = z;
		} else {
			y.right = z;
		}
		z.left = NIL;
		z.right = NIL;
		z.color = RbColor.RED;
		rbInsertFixUp(z);									//插入修正
	}
	
	//插入修正  
	private void rbInsertFixUp(RbTreeNode z) {
		RbTreeNode y = null;
		while(z.parent.color == RbColor.RED) {				//當z的父節點是黑色時，不需要矯正
			if(z.parent == z.parent.parent.left) {			//左分支情況
				y = z.parent.parent.right;		//根據叔節點分情況
				if(y.color == RbColor.RED) {
					z.parent.color = RbColor.BLACK;
					y.color = RbColor.BLACK;
					z.parent.parent.color = RbColor.RED;
					z = z.parent.parent;
				} else {
					if(z == z.parent.right) {
						z = z.parent;
						leftRotate(z);
					}
					z.parent.color = RbColor.BLACK;
					z.parent.parent.color = RbColor.RED;
					rightRotate(z.parent.parent);
				}
			} else {
				y = z.parent.parent.left;		//根據叔節點分情況
				if(y.color == RbColor.RED) {
					z.parent.color = RbColor.BLACK;
					y.color = RbColor.BLACK;
					z.parent.parent.color = RbColor.RED;
					z = z.parent.parent;
				} else {
					if(z == z.parent.left) { 
						z = z.parent;
						rightRotate(z);
					}
					z.parent.color = RbColor.BLACK;
					z.parent.parent.color = RbColor.RED;
					leftRotate(z.parent.parent);
				}
			}
		}
		root.color = RbColor.BLACK;
	}
	

	//刪除某一子節點
	private void deleteRbTreeNode(RbTreeNode z) {
		RbTreeNode y = z;
		RbTreeNode x = NIL;
		RbColor yOriginalColor = y.color;
		if(z.left == NIL) {
			x = z.right;
			rbTransplant(z,z.right);
		} else if(z.right == NIL) {
			x = z.left;
			rbTransplant(z,z.left);
		} else {
			y = searchMinimum(z.right);
			yOriginalColor = y.color;
			x = y.right;
			if(y.parent == z) {
				x.parent = y;
			} else {
				rbTransplant(y,y.right);
				y.right = z.right;
				z.right.parent = y;
			}
			rbTransplant(z,y);
			y.left = z.left;
			z.left.parent = y;
			y.color = z.color;
		}
		if(yOriginalColor == RbColor.BLACK) {
			rbDeleteFixUp(x);
		}
	}
	
	private void rbDeleteFixUp(RbTreeNode x) {
		//x總是指向一個具有雙重黑色的非根節點
		RbTreeNode w = NIL;
		while(x != root && x.color == RbColor.BLACK) {
			if(x == x.parent.left) {
				w = x.parent.right;		//w指向兄節點
				if(w.color == RbColor.RED) {
					w.color = RbColor.BLACK;				//case 1
					x.parent.color = RbColor.RED;			//case 1
					leftRotate(x.parent);					//case 1
					w = x.parent.right;						//case 1
				}
				if(w.left.color == RbColor.BLACK 
					&& w.right.color == RbColor.BLACK) {
					w.color = RbColor.BLACK;				//case 2
					x = x.parent;							//case 2
				}
				else {
					if(w.right.color == RbColor.BLACK) {
						w.left.color = RbColor.BLACK;		//case 3
						w.color = RbColor.RED;				//case 3
						rightRotate(w);						//case 3
						w = x.parent.right;					//case 3
					}
					w.color = x.parent.color;				//case 4
					x.parent.color = RbColor.BLACK;			//case 4
					w.right.color = RbColor.BLACK;			//case 4
					leftRotate(x.parent);					//case 4
					x = root;								//case 4
				}	
			} else {
				w = x.parent.left;		//w指向兄節點
				if(w.color == RbColor.RED) {
					w.color = RbColor.BLACK;				//case 1
					x.parent.color = RbColor.RED;			//case 1
					rightRotate(x.parent);					//case 1
					w = x.parent.left;						//case 1
				}
				if(w.right.color == RbColor.BLACK 
					&& w.left.color == RbColor.BLACK) {
					w.color = RbColor.BLACK;				//case 2
					x = x.parent;							//case 2
				}
				else {
					if(w.left.color == RbColor.BLACK) {
						w.right.color = RbColor.BLACK;		//case 3
						w.color = RbColor.RED;				//case 3
						leftRotate(w);						//case 3
						w = x.parent.left;					//case 3
					}
					w.color = x.parent.color;				
					x.parent.color = RbColor.BLACK;
					w.left.color = RbColor.BLACK;
					rightRotate(x.parent);
					x = root;
				}
			}
		}
		
	}

	private void rbTransplant(RbTreeNode u,RbTreeNode v) {
		if(u.parent == NIL) {
			root = v;
		} else if(u == u.parent.left) {
			u.parent.left = v;
		}  else {
			u.parent.right = v;
		}
		v.parent = u.parent;
	}
	
	//獲取最小鍵值節點
	private RbTreeNode searchMinimum(RbTreeNode x) {
		while(x.left != NIL) {
			x = x.left;
		}
		return x;
	}
	
	//獲取最大鍵值節點
	private RbTreeNode searchMaximum(RbTreeNode x) {
		while(x.right != NIL) {
			x = x.right;
		}
		return x;
	}
	
	//左旋
	private void leftRotate(RbTreeNode x) {
		RbTreeNode y = x.right;
		x.right = y.left;
		if(x.right != NIL) {
			y.left.parent = x;
		}
		y.parent = x.parent;
		if(x.parent == NIL) {			//如果是根節點
			root = y;
		} else if(x == x.parent.left) {
			x.parent.left = y;
		} else {
			x.parent.right = y;
		}
		y.left = x;
		x.parent = y;
	}
	
	//右旋
	private void rightRotate(RbTreeNode y) {
		RbTreeNode x = y.left;
		y.left = x.right;
		if(x.right != NIL) {
			x.right.parent = y;
		}	
		x.parent = y.parent;
		if(y.parent == NIL) {
			root = x;
		} else if(y == y.parent.left) {
			y.parent.left = x;
		} else {
			y.parent.right = x;
		}	
		x.right = y;
		y.parent = x;
	}

	//紅黑樹節點類
	private static class RbTreeNode {
		RbTreeNode left = null;
		RbTreeNode right = null;
		RbTreeNode parent = null;
		RbColor color = RbColor.RED;
		int key = 0;

		public RbTreeNode(int key,RbColor color) {
			this.key = key;
			this.color = color;
		}
		public RbTreeNode(RbColor color) {
			this.color = color;
		}
	}
	
	private enum RbColor {
		RED,BLACK
	}
}

運行結果爲：

root:7 BLACK
1 BLACK 2 RED 5 BLACK 7 BLACK 8 BLACK 11 RED 14 BLACK 15 RED 
root:7 BLACK
2 RED 5 BLACK 7 BLACK 8 BLACK 11 RED 14 BLACK 15 RED 
最大節點的鍵爲：15