二叉查找树与红黑树（2-3树）

二叉查找树是自上而下生长的，左子树比根节点小，右子树都比根节点大。

树的形状与插入顺序有关。

二叉树的查找、排序方法、最大键、最小键、选择操作、排名操作、删除最大键最小键

关键是通过size()函数，可以获取该节点的下的节点数。

package HardlyJava;import java.util.*;public class Erchashu {private class BST<Key extends Comparable<Key>,Value>{private Node root;private class Node{private Key key;private Value value;private Node left,right;private int N;public Node(Key key,Value val,int N) {this.key=key;this.value=val;this.N=N;}}public int size() {return size(root);}public int size(Node x) {if(x==null) return 0;else return x.N;}public Value get(Key key) {//查找键为key的对应的值return get(root,key);}private Value get(Node x,Key key) {//从头节点root开始，查找键为key的值if(x==null) return null;int cmp=key.compareTo(x.key);//从新定义Comparable 的compareTo函数，比较目标节点key与当前节点x.key值大小if(cmp<0) return get(x.left,key);else if(cmp>0) return get(x.right,key);else return x.value;}public void put(Key key,Value val) {//找到该键key，并更新该键的值为val，若没有改键则添加该节点root=put(root,key,val);}private Node put(Node x,Key key,Value val) {if(x==null) return new Node(key,val,1);int cmp=key.compareTo(x.key);if(cmp<0) x.left=put(x,key,val);else if(cmp>0) x.right=put(x,key,val);else x.value=val;x.N=size(x.left)+size(x.right)+1;//重新更新N值，左节点数加上右节点数加1return x;}public Key min() {return min(root).key;}private Node min(Node x) {if(x.left==null) return x;return min(x.left);}public Key max() {return max(root).key;}private Node max(Node x) {if(x.right==null) return x;return max(x.right);}public Key floor(Key key) {Node x=floor(root,key);if(x==null) return null;return x.key;}private Node floor(Node x,Key key) {if(x==null) return null;int cmp=key.compareTo(x.key);if(cmp==0) return x;if(cmp<0) return floor(x.left,key);Node t=floor(x.right,key);if(t!=null) return t;else return x;}public Key select(int k) {return select(root,k).key;}private Node select(Node x,int k) {//返回排名为k的节点if(x==null) return null;int t=size(x.left);if(t>k) return select(x.left,k);else if (t<k) return select(x.right,k-t-1);else return x;}public int rank(Key key) {return rank(key,root);}private int rank(Key key,Node x) {//返回以x为根节点的子树中小于x.key的键的数量if(x==null) return 0;int cmp=key.compareTo(x.key);if(cmp<0) return rank(key,x.left);else if(cmp>0) return 1+size(x.left)+rank(key,x.right);else return size(x.left);}public void deleteMin() {root=deleteMin(root);}private Node deleteMin(Node x) {if (x.left==null) return x.right;x.left=deleteMin(x.left);//一直递归地向左节点进行x.N=size(x.left)+size(x.right)+1;return x;}public void delete(Key key) {root=delete(root,key);}private Node delete(Node x,Key key) {if(x==null) return null;int cmp=key.compareTo(x.key);if(cmp<0) x.left=delete(x.left,key);else if(cmp>0) x.right=delete(x.right,key);else{if(x.left==null) return x.right;if(x.right==null) return x.left;Node t=x;x=min(t.right);//从右子树中找到最小节点，即当前节点的后继节点x.right=deleteMin(t.right);x.left=t.left;}x.N=size(x.left)+size(x.right)+1;return x;}public Iterable<Key> keys(){return keys(min(),max());}public Iterable<Key> keys(Key lo,Key hi){Queue<Key> queue=new Queue<Key>();keys(root,queue,lo,hi);return queue;}private void keys(Node x,Queue<Key> queue,Key lo,Key hi) {if(x==null) return ;int cmplo=lo.compareTo(x.key);int cmphi=hi.compareTo(x.key);if(cmplo<0) keys(x.left,queue,lo,hi);if(cmplo<=0&&cmphi>=0) queue.enqueue(x.key);if(cmphi>0) keys(x.right,queue,lo,hi);}}}

红黑树是自下向上生长的，关键是通过左旋，右旋操作完成的。

package HardlyJava;//import HardlyJava.Erchashu.BST.Node;public class Redblack<Key extends Comparable<Key>,Value> {private static final boolean RED=true;private static final boolean BLACK=false;private Node root;private class Node{Key key;Value value;Node left,right;int N;boolean color;Node(Key key,Value val,int N,boolean color){this.key=key;this.value=val;this.N=N;this.color=color;}}private int size() {return size(root);}private int size(Node x) {if(x==null) return 0;else return x.N;}private boolean isRed(Node x) {if(x==null) return false;return x.color=RED;}Node rotateLeft(Node h) {Node x=h.right;h.right=x.left;x.left=h;x.color=h.color;h.color=RED;x.N=h.N;h.N=1+size(h.left)+size(h.right);return x;}Node rotateRight(Node h) {Node x=h.left;h.left=x.right;x.right=h;x.color=h.color;h.color=RED;x.N=h.N;h.N=1+size(h.left)+size(h.right);return x;}void flipColors(Node h) {h.color=RED;h.left.color=BLACK;h.right.color=BLACK;}//实现红黑树的插入操作public void put(Key key,Value val) {root=put(root,key,val);root.color=BLACK;}private Node put(Node h,Key key,Value val) {if(h==null) return new Node(key,val,1,RED);int cmp=key.compareTo(h.key);if(cmp<0) h.left=put(h.left,key,val);else if(cmp>0) h.right=put(h.right,key,val);else h.value=val;//关键if(isRed(h.right)&!isRed(h.left)) h=rotateLeft(h);if(isRed(h.left)&isRed(h.left)) h=rotateRight(h);if(isRed(h.right)&isRed(h.left)) flipColors(h);h.N=size(h.left)+size(h.right)+1;return h;}}