目錄
一、集合
Set 相關知識:
-
集合就是承載元素的容器,每個元素只能存在一次。這在應用時能幫助我們非常快速地進行去重工作。
-
BST、AVL 和 LinkedList 都屬於動態數據結構。因爲 BST 不能盛放重複元素,所以可用其來進行底層實現。
-
Set 可以考慮成是 Map<K, V> 中 V = null 的情況,其餘操作和 Map 相同,此時 Map 中的 get 和 set 方法沒意義。
也可以考慮成 Map 本身也是一種 Set,只是這個 Set 多了一個 value 而已。Map 中實質的邏輯其實和 Set 沒有什麼區別。 -
Set可以分爲有序集合和無需集合;
有序集合基於搜索樹實現,JDK底層是紅黑樹,即TreeSet;
無序集合基於Hash表實現,JDK底層是HashMap包裝之後,即HashSet。
接口:
public interface Set<E> {
void add(E e);
void remove(E e);
boolean contains(E e);
int getSize();
boolean isEmpty();
}
1、基於鏈表實現的集合
public class LinkedListSet<E> implements Set<E> {
private LinkedList<E> list;
//構造函數
public LinkedListSet() {
list = new LinkedList<>();
}
@Override
public int getSize() {
return list.getSize();
}
@Override
public boolean isEmpty() {
return list.isEmpty();
}
@Override
public boolean contains(E e) {
return list.contains(e);
}
@Override
public void add(E e) {
if (!list.contains(e))
list.addFirst(e);
}
@Override
public void remove(E e) {
list.removeElement(e);
}
}
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2、基於 BST 實現的集合
public class BSTSet<E extends Comparable<E>> implements Set<E> {
private BST<E> bst;
//構造函數
public BSTSet() {
bst = new BST<>();
}
@Override
public int getSize() {
return bst.size();
}
@Override
public boolean isEmpty() {
return bst.isEmpty();
}
@Override
public void add(E e) {
bst.add(e);
}
@Override
public boolean contains(E e) {
return bst.contains(e);
}
@Override
public void remove(E e) {
bst.remove(e);
}
}
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3、基於 AVL 實現的集合
public class AVLSet<E extends Comparable<E>> implements Set<E> {
private AVLTree<E, Object> avl;
public AVLSet(){
avl = new AVLTree<>();
}
@Override
public int getSize(){
return avl.size();
}
@Override
public boolean isEmpty(){
return avl.isEmpty();
}
@Override
public void add(E e){
avl.add(e, null);
}
@Override
public boolean contains(E e){
return avl.contains(e);
}
@Override
public void remove(E e){
avl.remove(e);
}
}
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二、映射
Map 圖示:
Map相關知識:
-
Map的鍵不允許重複,如果重複插入鍵相同的,則新的value覆蓋原來的value;
-
Map可以分爲有序Map和無序Map;
有序Map基於搜索樹實現,JDK底層使用紅黑樹實現,即TreeMap;
無序Map基於Hash表實現,JDK底層使用Hash表底層實現,即HashMap;
接口:
public interface Map<K, V> {
void add(K key, V value);
V remove(K key);
void set(K key, V newValue); //插入元素
boolean contains(K key);
V get(K key); //找出 key 對應的 value
int getSize(); //獲取長度
boolean isEmpty();
}
1、基於鏈表實現的映射
public class LinkedListMap<K, V> implements Map<K, V> {
//內部類
private class Node {
public K key;
public V value;
public Node next;
public Node(K key, V value, Node next) {
this.key = key;
this.value = value;
this.next = next;
}
public Node(K key) {
this(key, null, null);
}
public Node() {
this(null, null, null);
}
@Override
public String toString() {
return key.toString() + ":" + value.toString();
}
}
private Node dummyHead;
private int size;
//構造函數
public LinkedListMap() {
dummyHead = new Node();
size = 0;
}
@Override
public int getSize() {
return size;
}
@Override
public boolean isEmpty() {
return size == 0;
}
//增刪改查輔助函數
private Node getNode(K key) {
Node cur = dummyHead.next;
while (cur != null) {
if (cur.key.equals(key))
return cur;
cur = cur.next;
}
return null;
}
@Override
public boolean contains(K key) {
return getNode(key) != null;
}
@Override
public V get(K key) {
Node node = getNode(key);
return node == null ? null : node.value;
}
@Override
public void add(K key, V value) {
Node node = getNode(key);
if (node != null) {
dummyHead.next = new Node(key,value, dummyHead.next);
size++;
}
else
node.value = value;
}
@Override
public void set(K key, V newValue) {
Node node = getNode(key);
if (node == null) {
throw new IllegalArgumentException(key + "fail");
}
node.value = newValue;
}
@Override
public V remove(K key) {
Node prev = dummyHead;
while (prev.next != null) {
if (prev.next.key.equals(key))
break;
prev = prev.next;
}
if (prev.next != null) {
Node delNode = prev.next;
prev.next = delNode.next;
delNode.next = null;
size--;
return delNode.value;
}
return null;
}
}
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2、基於 BST 實現的映射
public class BSTMap<K extends Comparable<K>, V> implements Map<K, V> {
//內部類
private class Node {
public K key;
public V value;
public Node left, right;
public Node(K key, V value) {
this.key = key;
this.value = value;
left = null;
right = null;
}
}
private Node root;
private int size;
//構造函數
public BSTMap() {
root = null;
size = 0;
}
@Override
public int getSize() {
return size;
}
@Override
public boolean isEmpty() {
return size == 0;
}
@Override
public void add(K key, V value) {
root = add(root, key, value);
}
private Node add(Node node, K key, V value) {
if (node == null) {
size++;
return new Node(key, value);
}
if (key.compareTo(node.key) < 0)
node.left = add(node.left, key, value);
else if (key.compareTo(node.key) > 0)
node.right = add(node.right, key, value);
else //key.compareTo(node.key) == 0;
node.value = value;
return node;
}
//刪改查輔助函數
private Node getNode(Node node, K key) {
if (node == null)
return null;
if (key.compareTo(node.key) == 0)
return node;
else if (key.compareTo(node.key) < 0)
return getNode(node.left, key);
else
return getNode(node.right, key);
}
@Override
public boolean contains(K key) {
return getNode(root, key) != null;
}
@Override
public V get(K key) {
Node node = getNode(root, key);
return node == null ? null : node.value;
}
@Override
public void set(K key, V newValue) {
Node node = getNode(root, key);
if (node == null)
throw new IllegalArgumentException(key + "fail");
node.value = newValue;
}
@Override
public V remove(K key) {
Node node = getNode(root, key);
if(node != null) {
root = remove(root, key);
return node.value;
}
return null;
}
private Node remove(Node node, K 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 {
if (node.left == null) {
Node rightNode = node.right;
node.right = null;
size--;
return rightNode;
}
if (node.right == null) {
Node leftNode = node.left;
node.left = null;
size--;
return leftNode;
}
//左右孩子都有的情況,找到待刪除節點的後繼節點
Node successor = minimum(node.right);
successor.right = removeMin(node.right);
successor.left = node.left;
node.left = node.right = null;
return successor;
}
}
//刪除函數中需要用到的函數
private Node minimum(Node node) {
if (node.left == null) return node;
return minimum(node.left);
}
private Node removeMin(Node node) {
if (node.left == null) {
Node rightNode = node.right;
node.right = null;
size--;
return rightNode;
}
node.left = removeMin(node.left);
return node;
}
}
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3、基於 AVL 實現的映射
public class AVLMap<K extends Comparable<K>, V> implements Map<K, V> {
private AVLTree<K, V> avl;
public AVLMap(){
avl = new AVLTree<>();
}
@Override
public int getSize(){
return avl.size();
}
@Override
public boolean isEmpty(){
return avl.isEmpty();
}
@Override
public void add(K key, V value){
avl.add(key, value);
}
@Override
public boolean contains(K key){
return avl.contains(key);
}
@Override
public V get(K key){
return avl.get(key);
}
@Override
public void set(K key, V newValue){
avl.set(key, newValue);
}
@Override
public V remove(K key){
return avl.remove(key);
}
}
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