java——二叉查找树（BST）算法

二叉查找树（BST）定义

基本结点实现

public class BST<K extends Comparable<K>, V> {

private Node root;

private class Node {

private K key;
private V value;
private Node left;
private Node right;
private int N;

public Node(K key, V value, int N) {
this.key = key;
this.value = value;
this.N = N;
}
}

public int size() {
return size(root);
}

private int size(Node x) {
if (x == null)
return 0;
else
return x.N;
}
}

查找键获取值——get

public V get(K key) {
return get(root, key);
}

private V get(Node root, K key) {

if (root == null)
return null;

int comp = key.compareTo(root.key);

if (comp == 0)
return root.value;
else if (comp < 0)
return get(root.left, key);
else
return get(root.right, key);

}

修改值/插入新值——put

public void put(K key, V value) {
root = put(root, key, value);
}

private Node put(Node root, K key, V value) {

if (root == null)
return new Node(key, value, 1);

int comp = key.compareTo(root.key);
if (comp == 0)
root.value = value;
else if (comp < 0)
root.left = put(root.left, key, value);
else
root.right = put(root.right, key, value);

root.N = size(root.left) + size(root.right) + 1;

return root;
}

最大值/最小值——min/max

public K min() {
return min(root).key;
}

private Node min(Node root) {

if (root.left == null)
return root;

return min(root.left);

}

public K max() {
return max(root).key;
}

private Node max(Node root2) {

if (root.right == null)
return root;

return max(root.right);

}

向上/向下取整——floor/ceiling

public K floor(K key) {
Node x = floor(root, key);
if (x == null)
return null;
return x.key;
}

private Node floor(Node root, K key) {

if (root == null)
return null;

int comp = key.compareTo(root.key);

if (comp < 0)
return floor(root.left, key);
else if (comp > 0 && root.right != null
&& key.compareTo(min(root.right).key) >= 0)
return floor(root.right, key);
else
return root;

}

public K ceiling(K key) {
Node x = ceiling(root, key);
if (x == null)
return null;
return x.key;
}

private Node ceiling(Node root, K key) {

if (root == null)
return null;

int comp = key.compareTo(root.key);

if (comp > 0)
return ceiling(root.right, key);
else if (comp < 0 && root.left != null
&& key.compareTo(max(root.left).key) >= 0)
return ceiling(root.left, key);
else
return root;

}

选择——select

public K select(int k) {
//找出BST中序号为k的键
return select(root, k);
}

private K select(Node root, int k) {

if (root == null)
return null;

int comp = k - size(root.left);

if (comp < 0)
return select(root.left, k);
else if (comp > 0)
return select(root.right, k - (size(root.left) + 1));
else
return root.key;

}

排名——rank

public int rank(K key) {
//找出BST中键为key的序号是多少
return rank(root, key);
}

private int rank(Node root, K key) {

if (root == null)
return 0;

int comp = key.compareTo(root.key);

if (comp == 0)
return size(root.left);
else if (comp < 0)
return rank(root.left, key);
else
return 1 + size(root.left) + rank(root.right, key);

}

删除最小/最大键——deleteMin/deleteMax

public void deleteMin() {
root = deleteMin(root);
}

private Node deleteMin(Node root) {

if (root.left == null)
return root.right;

root.left = deleteMin(root.left);
root.N = size(root.left) + size(root.right) + 1;
return root;

}

public void deleteMax() {
root = deleteMax(root);
}

private Node deleteMax(Node root) {

if (root.right == null)
return root.left;

root.right = deleteMax(root.right);
root.N = size(root.left) + size(root.right) + 1;
return root;

}

删除任意键——delete

public void delete(K key) {
root = delete(root, key);
}

private Node delete(Node root, K key) {

if (root == null)
return null;

int comp = key.compareTo(root.key);

if (comp == 0) {

if (root.right == null)
return root = root.left;
if (root.left == null)
return root = root.right;

Node t = root;
root = min(t.right);

root.left = t.left;
root.right = deleteMin(t.right);

} else if (comp < 0)
root.left = delete(root.left, key);
else
root.right = delete(root.right, key);

root.N = size(root.left) + size(root.right) + 1;
return root;

}

中序打印树——print

public void print() {
print(root);
}

private void print(Node root) {

if (root == null)
return;
print(root.left);
System.out.println(root.key);
print(root.right);

}