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package Algorithms_4thEdition.b_Searching;
/**
* 二叉查找树
* <p>
* Created by nibnait on 2016/9/2.
*/
public class BST<Key extends Comparable<Key>, Value> {
private Node root;
public int size() {
return size(root);
}
private int size(Node x) {
if (x == null) {
return 0;
} else {
return x.N;
}
}
public Value get(Key key) {
//在以x为根结点的子树中查找 key对应的Value值
//如果没有，则返回null
return get(root, key);
}
private Value get(Node x, Key key) {
if (x == null) {
return null;
}
int cmp = x.key.compareTo(key);
if (cmp > 0) {
return get(x.left, key);
} else if (cmp < 0) {
return get(x.right, key);
} else {
return (Value) x.value;
}
}
public void put(Key key, Value value) {
//查找key， 存在在更新此key对应的value，否则为其创建新结点
this.root = put(root, key, value);
}
private Node put(Node x, Key key, Value value) {
if (x == null) {
return new Node(key, value, 1);
}
int cmp = x.key.compareTo(key);
if (cmp > 0) {
x.left = put(x.left, key, value);
} else if (cmp < 0) {
x.right = put(x.right, key, value);
} else {
x.value = value;
}
x.N = size(x.left) + size(x.right) + 1;
return x;
}
public Key min() {
return (Key) min(root).key;
}
private Node min(Node x) {
if (x == null) {
return x;
}
return x.left;
}
public Key max() {
return (Key) max(root).key;
}
private Node max(Node x) {
if (x == null) {
return x;
}
return x.right;
}
public Key floor(Key key) {
Node x = floor(root, key);
if (x == null) {
return null;
}
return (Key) x.key;
}
private Node floor(Node x, Key key) {
if (x == null) {
return null;
}
int cmp = x.key.compareTo(key);
//如果x的key大于 要查找的key
//则floor(x, key)一定在x的左子树中。
if (cmp == 0) {
return x;
}
if (cmp > 0) {
return floor(x.left, key);
}
//如果x的key小于 要查找的key
//那么 只有当x的右子树中存在小于等于给定key的结点时， floor(x, key)才会出现在x的右子树中
//否则x就是floor(x, key) 即小于等于key的最大键。
Node t = floor(x.right, key);
if (t != null) {
return t;
} else {
return x;
}
}
//向上取整
public Key ceiling(Key key) {
Node x = ceiling(root, key);
if (x == null) {
return null;
}
return (Key) x.key;
}
private Node ceiling(Node x, Key key) {
if (x == null) {
return null;
}
int cmp = x.key.compareTo(key);
if (cmp == 0) {
return x;
}
//向上取整：如果x的key比 要查找的key小， 则ceiling(x, key) 一定在x的右子树中
if (cmp < 0) {
return ceiling(x.right, key);
}
Node t = ceiling(x.left, key);
if (t != null) {
return t;
} else {
return x;
}
}
//查找排名为k的键
private Key select(int k) {
return (Key) select(root, k).key;
}
private Node select(Node x, int k) {
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;
}
}
//求给定key的排名
public int rank(Key key) {
return rank(root, key);
}
private int rank(Node x, Key key) {
if (x == null){
return 0;
}
int cmp = x.key.compareTo(key);
if (cmp > 0){
return rank(x.left, key);
}else if (cmp < 0){
return rank(x.right, key) + size(x.left) + 1;
}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);
x.N = size(x.left) + size(x.right) + 1;
return x;
}
public void deleteMax(){
root = deleteMax(root);
}
private Node deleteMax(Node x) {
if (x.right == null){
return x.left;
}
x.right = deleteMax(x.right);
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 = x.key.compareTo(key);
if (cmp > 0){
x.left = delete(x.left, key);
}else if (cmp < 0){
x.right = delete(x.right, key);
}else { // 找到了
if (x.right == null){
return x.left;
}
if (x.left == null){
return x.right;
}
Node t = x; // t 即为待删除的结点
x = min(t.right); //x可以说是t向上取整（第一个比t大的结点）
x.right = deleteMin(t.right);
x.left = t.left;
}
x.N = size(x.left) + size(x.right) + 1; //以x为根结点的结点总数
return x;
}
}