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算法基础(三) 二分搜索
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文章目录
定义二分搜索树类
public class BinarySearchTree<Key extends Comparable<Key>, Value> {
private Node root;
private int count;
public BinarySearchTree() {
root = null;
count = 0;
}
public int size() {
return count;
}
public boolean isEmpty() {
return count == 0;
}
private class Node {
private Key key;
private Value value;
private Node left, right;
public Node(Key key, Value value) {
this.key = key;
this.value = value;
left = right = null;
}
public Node(Node node) {
this.key = node.key;
this.value = node.value;
this.left = node.left;
this.right = node.right;
}
}
}
1 insert 插入元素
public void insert(Key key, Value value) {
root = insert(root, key, value);
}
private Node insert(Node node, Key key, Value value) {
if (node == null) {
count++;
return new Node(key, value);
}
if (key.compareTo(node.key) == 0) {
node.value = value;
} else if (key.compareTo(node.key) < 0) {
node.left = insert(node.left, key, value);
} else {
node.right = insert(node.right, key, value);
}
return node;
}
2 search 搜索key对应的value
public Value search(Key key) {
return search(root, key);
}
private Value search(Node node, Key key) {
if (node == null) {
return null;
}
if (key.compareTo(node.key) == 0) {
return node.value;
} else if (key.compareTo(node.key) < 0) {
return search(node.left, key);
} else {
return search(node.right, key);
}
}
3 contain 判断是否包含
public boolean contain(Key key) {
return contain(root, key);
}
private boolean contain(Node node, Key key) {
if (node == null) {
return false;
}
if (key.compareTo(node.key) == 0) {
return true;
} else if (key.compareTo(node.key) < 0) {
return contain(node.left, key);
} else {
return contain(node.right, key);
}
}
4 order
4.1 preOrder 前序遍历
public void preOrder() {
System.out.println("前序遍历");
preOrder(root);
}
private void preOrder(Node node) {
if (node != null) {
System.out.print("," + node.key);
preOrder(node.left);
preOrder(node.right);
}
}
4.2 inOrder 中序遍历
public void inOrder() {
System.out.println();
System.out.println("中序遍历");
inOrder(root);
}
private void inOrder(Node node) {
if (node != null) {
inOrder(node.left);
System.out.print("," + node.key);
inOrder(node.right);
}
}
4.3 postOrder 后序遍历
public void postOrder() {
System.out.println();
System.out.println("后序遍历");
postOrder(root);
}
private void postOrder(Node node) {
if (node != null) {
postOrder(node.left);
postOrder(node.right);
System.out.print("," + node.key);
}
}
5 levelOrder 层序遍历
public void levelOrder() {
System.out.println();
System.out.println("层序遍历");
Queue<Node> queue = new LinkedList<Node>();
queue.add(root);
while (!queue.isEmpty()) {
Node node = queue.remove();
System.out.print("," + node.key);
if (node.left != null) {
queue.add(node.left);
}
if (node.right != null) {
queue.add(node.right);
}
}
}
6 max min
6.1 miniMum 最小值
public Key minimum() {
Node minNode = minimum(root);
return minNode.key;
}
private Node minimum(Node node) {
if (node.left == null) {
return node;
}
return minimum(node.left);
}
6.2 maximum 最大值
public Key maximum() {
Node maxNode = maximum(root);
return maxNode.key;
}
private Node maximum(Node node) {
if (node.right == null) {
return node;
}
return maximum(node.right);
}
7 remove
7.1 removeMin 移除最小
public void removeMin() {
if (root != null) {
root = removeMin(root);
}
}
private Node removeMin(Node node) {
if (node.left == null) {
Node rightNode = node.right;
node.right = null;
count--;
return rightNode;
}
node.left = removeMin(node.left);
return node;
}
7.2 removeMax 移除最大
public void removeMax() {
if (root != null) {
root = removeMax(root);
}
}
private Node removeMax(Node node) {
if (node.right == null) {
Node leftNode = node.left;
node.left = null;
count--;
return leftNode;
}
node.right = removeMax(node.right);
return node;
}
8 remove(Key key) 移除指定键值
public void remove(Key key) {
root = remove(root, key);
}
Node remove(Node node, Key key) {
if (node == null) {
return null;
}
if (key.compareTo(node.key) < 0) {
node.left = remove(node.left, key);
return node;
} else if (key.compareTo(node.key) > 0) {
node.right = remove(node.right, key);
return node;
} else {
//case 1: 移除最小节点
if (node.left == null) {
Node rightNode = node.right;
node.right = null;
count--;
return rightNode;
}
//case 2: 移除最大节点
if (node.right == null) {
Node leftNode = node.left;
node.left = null;
count--;
return leftNode;
}
//case 3: 移除中间节点
//创建新节点
Node successor = new Node(minimum(node.right));
count++;
//给新创建的节点左右两边赋值
successor.right = removeMin(node.right);
successor.left = node.left;
//被移除的左右两边置空
node.left = node.right = null;
count--;
return successor;
}
}
测试用例
public static void main(String[] args) {
int N = 10;
Integer[] arr = new Integer[N];
//生成有序数组
for (int i = 0; i < N; i++) {
arr[i] = new Integer(i);
}
//打乱数组
for (int i = 0; i < N; i++) {
int pos = (int) (Math.random() * (i + 1));
Integer t = arr[pos]; arr[pos] = arr[i];
arr[i] = t;
}
//将数组插入到二分搜索树中
BinarySearchTree<Integer, String> bst = new BinarySearchTree<Integer, String>();
for (int i = 0; i < N; i++) {
bst.insert(new Integer(arr[i]), Integer.toString(arr[i]));
}
String value1 = bst.search(3);
System.out.println("value1 = " + value1);
String value2 = bst.search(3000000);
System.out.println("value2 = " + value2);
//前中后序遍历
bst.preOrder();
bst.inOrder();
bst.postOrder();
//层序遍历
bst.levelOrder();
//最大
System.out.println("============= 最大值 =============");
Integer max = bst.maximum();
System.out.println("max = " + max);
//最小
System.out.println("============= 最小值 =============");
Integer min = bst.minimum();
System.out.println("max = " + min);
//移除最小
System.out.println("============= 移除最小值 =============");
bst.removeMin();
bst.inOrder();
//移除最大
System.out.println("============= 移除最大值 =============");
bst.removeMax();
bst.inOrder();
System.out.println();
System.out.println("============= 移除指定值 5 =============");
bst.remove(5);
bst.inOrder();
System.out.println();
System.out.println("============= 移除指定值 6 =============");
bst.remove(6);
bst.inOrder();
bst.preOrder();
bst.inOrder();
bst.levelOrder();
}
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