資料結構與演算法-列表

列表的linkedlist

LinkedList 是通過一個雙向連結串列來實現的，它允許插入所有元素，包括 null，同時，它是執行緒不同步的。雙向連結串列每個結點除了資料域之外，還有一個前指標和後指標，分別指向前驅結點和後繼結點（如果有前驅/後繼的話）。另外，雙向連結串列還有一個 first 指標，指向頭節點，和 last 指標，指向尾節點。

循位置訪問

列表：採用動態儲存的典型結構。

• 每個元素稱為節點（ node ）。

• 各個節點通過指標或引用彼此聯接，在邏輯上構成一個線性序列。相鄰節點彼此互稱前驅和後繼。如果存在前驅和後繼，那麼必然是唯一的。

• 沒有前驅的節點稱為首，沒有後繼的節點稱為末。此外，可以認為頭存在一個哨兵前驅稱為頭，末存在一個哨兵後繼稱為尾。

• 可以認為 頭、首、末、尾 節點的秩分別為 -1、0、n-1、n。

• 在訪問時儘量不使用循秩訪問，而使用循位置訪問。即利用節點之間的相互引用，找到特定的節點。
  

列表中元素（原始碼解析）

public class LinkedList<E>
    extends AbstractSequentialList<E>
    implements List<E>, Deque<E>, Cloneable, java.io.Serializable
{
    /**
     *連結串列的節點個數
     */
    transient int size = 0;

    /**
     * 指向頭節點的指標
     */
    transient Node<E> first;

    /**
     * 指向尾節點的指標
     */
    transient Node<E> last;
 

列表構造器

/**
     * 空構造器.
     */
    public LinkedList() {
    }

    /**
     * 包含集合中元素的構造器
     */
    public LinkedList(Collection<? extends E> c) {
        this();
        addAll(c);
    }

public boolean addAll(Collection<? extends E> c) {
        return addAll(size, c);
    }

    public boolean addAll(int index, Collection<? extends E> c) {
        checkPositionIndex(index);

        Object[] a = c.toArray();
        int numNew = a.length;
        if (numNew == 0)
            return false;

        Node<E> pred, succ;
        if (index == size) {
            succ = null;
            pred = last;
        } else {
            succ = node(index);
            pred = succ.prev;
        }

        for (Object o : a) {
            @SuppressWarnings("unchecked") E e = (E) o;
            Node<E> newNode = new Node<>(pred, e, null);
            if (pred == null)
                first = newNode;
            else
                pred.next = newNode;
            pred = newNode;
        }

        if (succ == null) {
            last = pred;
        } else {
            pred.next = succ;
            succ.prev = pred;
        }

        size += numNew;
        modCount++;//操作次數
        return true;
    }
 

元素的新增

private static class Node<E> {
        E item;
        Node<E> next;
        Node<E> prev;

        Node(Node<E> prev, E element, Node<E> next) {
            this.item = element;
            this.next = next;
            this.prev = prev;
        }
    }

/**
     * 新增為第一個元素.
     */
    private void linkFirst(E e) {
        final Node<E> f = first;
        final Node<E> newNode = new Node<>(null, e, f);
        first = newNode;
        if (f == null)//如果第一個為空，則原List為空
            last = newNode;//list的first和last都設定為加入元素
        else
            f.prev = newNode;
        size++;
        modCount++;
    }

/**
     * 新增為尾元素.
     */
    void linkLast(E e) {
        final Node<E> l = last;
        final Node<E> newNode = new Node<>(l, e, null);
        last = newNode;
        if (l == null)//同上
            first = newNode;
        else
            l.next = newNode;
        size++;
        modCount++;
    }

/**
     * 新增到指定Node之前.
     */
    void linkBefore(E e, Node<E> succ) {
        // assert succ != null;
        final Node<E> pred = succ.prev;
        final Node<E> newNode = new Node<>(pred, e, succ);
        succ.prev = newNode;
        if (pred == null)
            first = newNode;
        else
            pred.next = newNode;
        size++;
        modCount++;
    }

元素的刪除

 /**
     * 去除連結有三種
	 * 第一種：first連結
     */
    private E unlinkFirst(Node<E> f) {
        // assert f == first && f != null;
        final E element = f.item;
        final Node<E> next = f.next;
        f.item = null;
        f.next = null; // help GC
        first = next;
        if (next == null)
            last = null;
        else
            next.prev = null;
        size--;
        modCount++;
        return element;
    }

    /**
     * 第二種：last連結
     */
    private E unlinkLast(Node<E> l) {
        // assert l == last && l != null;
        final E element = l.item;
        final Node<E> prev = l.prev;
        l.item = null;
        l.prev = null; // help GC
        last = prev;
        if (prev == null)
            first = null;
        else
            prev.next = null;
        size--;
        modCount++;
        return element;
    }

    /**
     * 第三種：中間連結.
     */
    E unlink(Node<E> x) {
        // assert x != null;
        final E element = x.item;
        final Node<E> next = x.next;
        final Node<E> prev = x.prev;

        if (prev == null) {
            first = next;
        } else {
            prev.next = next;
            x.prev = null;
        }

        if (next == null) {
            last = prev;
        } else {
            next.prev = prev;
            x.next = null;
        }

        x.item = null;
        size--;
        modCount++;
        return element;
    }

常用的方法

/**一些常用的方法
     * Returns the first element in this list.
     */
    public E getFirst() {
        final Node<E> f = first;
        if (f == null)
            throw new NoSuchElementException();
        return f.item;
    }

    /**
     * Returns the last element in this list.
     */
    public E getLast() {
        final Node<E> l = last;
        if (l == null)
            throw new NoSuchElementException();
        return l.item;
    }

    /**
     * Removes and returns the first element from this list.
     */
    public E removeFirst() {
        final Node<E> f = first;
        if (f == null)
            throw new NoSuchElementException();
        return unlinkFirst(f);
    }

    /**
     * Removes and returns the last element from this list.
     */
    public E removeLast() {
        final Node<E> l = last;
        if (l == null)
            throw new NoSuchElementException();
        return unlinkLast(l);
    }

    /**
     * Inserts the specified element at the beginning of this list.
     */
    public void addFirst(E e) {
        linkFirst(e);
    }

    /**
     * Appends the specified element to the end of this list.
     */
    public void addLast(E e) {
        linkLast(e);
    }

    /**
	 * 判斷是否包含某一元素
     */
    public boolean contains(Object o) {
        return indexOf(o) != -1;
    }

    /**
     * Returns the number of elements in this list.
     */
    public int size() {
        return size;
    }

    /**
     * Appends the specified element to the end of this list.
     */
    public boolean add(E e) {
        linkLast(e);
        return true;
    }

    /**
     * Removes the first occurrence of the specified element from this list,
     * if it is present.  If this list does not contain the element, it is
     * unchanged.  More formally, removes the element with the lowest index
     * {@code i} such that
     */
    public boolean remove(Object o) {
        if (o == null) {
            for (Node<E> x = first; x != null; x = x.next) {
                if (x.item == null) {
                    unlink(x);
                    return true;
                }
            }
        } else {
            for (Node<E> x = first; x != null; x = x.next) {
                if (o.equals(x.item)) {
                    unlink(x);
                    return true;
                }
            }
        }
        return false;
    }

    /**
     * Removes all of the elements from this list.
     * The list will be empty after this call returns.
     */
    public void clear() {
        for (Node<E> x = first; x != null; ) {
            Node<E> next = x.next;
            x.item = null;
            x.next = null;
            x.prev = null;
            x = next;
        }
        first = last = null;
        size = 0;
        modCount++;
    }


    // Positional Access Operations

    /**
     * Returns the element at the specified position in this list.
     */
    public E get(int index) {
        checkElementIndex(index);
        return node(index).item;
    }

    /**
     * Replaces the element at the specified position in this list with the
     * specified element.
     */
    public E set(int index, E element) {
        checkElementIndex(index);
        Node<E> x = node(index);
        E oldVal = x.item;
        x.item = element;
        return oldVal;
    }

    /**
     * Inserts the specified element at the specified position in this list.
     * Shifts the element currently at that position (if any) and any
     * subsequent elements to the right (adds one to their indices).
     */
    public void add(int index, E element) {
        checkPositionIndex(index);

        if (index == size)
            linkLast(element);
        else
            linkBefore(element, node(index));
    }

    /**
     * Removes the element at the specified position in this list.  Shifts any
     * subsequent elements to the left (subtracts one from their indices).
     * Returns the element that was removed from the list.
     */
    public E remove(int index) {
        checkElementIndex(index);
        return unlink(node(index));
    }

    /**
     * Tells if the argument is the index of an existing element.
     */
    private boolean isElementIndex(int index) {
        return index >= 0 && index < size;
    }

    /**
     * Tells if the argument is the index of a valid position for an
     * iterator or an add operation.
     */
    private boolean isPositionIndex(int index) {
        return index >= 0 && index <= size;
    }

    /**
     * Constructs an IndexOutOfBoundsException detail message.
     * Of the many possible refactorings of the error handling code,
     * this "outlining" performs best with both server and client VMs.
     */
    private String outOfBoundsMsg(int index) {
        return "Index: "+index+", Size: "+size;
    }

    private void checkElementIndex(int index) {
        if (!isElementIndex(index))
            throw new IndexOutOfBoundsException(outOfBoundsMsg(index));
    }

    private void checkPositionIndex(int index) {
        if (!isPositionIndex(index))
            throw new IndexOutOfBoundsException(outOfBoundsMsg(index));
    }

    /**
     * Returns the (non-null) Node at the specified element index.
     */
    Node<E> node(int index) {
        // assert isElementIndex(index);

        if (index < (size >> 1)) {
            Node<E> x = first;
            for (int i = 0; i < index; i++)
                x = x.next;
            return x;
        } else {
            Node<E> x = last;
            for (int i = size - 1; i > index; i--)
                x = x.prev;
            return x;
        }
    }

    // Search Operations

    /**
     * Returns the index of the first occurrence of the specified element
     * in this list, or -1 if this list does not contain the element.
     * More formally, returns the lowest index {@code i} such that
     * <tt>(o==null&nbsp;?&nbsp;get(i)==null&nbsp;:&nbsp;o.equals(get(i)))</tt>,
     * or -1 if there is no such index.
     */
    public int indexOf(Object o) {
        int index = 0;
        if (o == null) {
            for (Node<E> x = first; x != null; x = x.next) {
                if (x.item == null)
                    return index;
                index++;
            }
        } else {
            for (Node<E> x = first; x != null; x = x.next) {
                if (o.equals(x.item))
                    return index;
                index++;
            }
        }
        return -1;
    }

    /**
     * Returns the index of the last occurrence of the specified element
     * in this list, or -1 if this list does not contain the element.
     * More formally, returns the highest index {@code i} such that
     * <tt>(o==null&nbsp;?&nbsp;get(i)==null&nbsp;:&nbsp;o.equals(get(i)))</tt>,
     * or -1 if there is no such index.
     */
    public int lastIndexOf(Object o) {
        int index = size;
        if (o == null) {
            for (Node<E> x = last; x != null; x = x.prev) {
                index--;
                if (x.item == null)
                    return index;
            }
        } else {
            for (Node<E> x = last; x != null; x = x.prev) {
                index--;
                if (o.equals(x.item))
                    return index;
            }
        }
        return -1;
    }

迭代器

/**
     * 迭代器有兩種：
	 * ListIterator
     */
    public ListIterator<E> listIterator(int index) {
        checkPositionIndex(index);
        return new ListItr(index);
    }

    private class ListItr implements ListIterator<E> {
        private Node<E> lastReturned;
        private Node<E> next;
        private int nextIndex;
        private int expectedModCount = modCount;

        ListItr(int index) {
            // assert isPositionIndex(index);
            next = (index == size) ? null : node(index);
            nextIndex = index;
        }

        public boolean hasNext() {
            return nextIndex < size;
        }

        public E next() {
            checkForComodification();
            if (!hasNext())
                throw new NoSuchElementException();

            lastReturned = next;
            next = next.next;
            nextIndex++;
            return lastReturned.item;
        }

        public boolean hasPrevious() {
            return nextIndex > 0;
        }

        public E previous() {
            checkForComodification();
            if (!hasPrevious())
                throw new NoSuchElementException();

            lastReturned = next = (next == null) ? last : next.prev;
            nextIndex--;
            return lastReturned.item;
        }

        public int nextIndex() {
            return nextIndex;
        }

        public int previousIndex() {
            return nextIndex - 1;
        }

        public void remove() {
            checkForComodification();
            if (lastReturned == null)
                throw new IllegalStateException();

            Node<E> lastNext = lastReturned.next;
            unlink(lastReturned);
            if (next == lastReturned)
                next = lastNext;
            else
                nextIndex--;
            lastReturned = null;
            expectedModCount++;
        }

        public void set(E e) {
            if (lastReturned == null)
                throw new IllegalStateException();
            checkForComodification();
            lastReturned.item = e;
        }

        public void add(E e) {
            checkForComodification();
            lastReturned = null;
            if (next == null)
                linkLast(e);
            else
                linkBefore(e, next);
            nextIndex++;
            expectedModCount++;
        }

        public void forEachRemaining(Consumer<? super E> action) {
            Objects.requireNonNull(action);
            while (modCount == expectedModCount && nextIndex < size) {
                action.accept(next.item);
                lastReturned = next;
                next = next.next;
                nextIndex++;
            }
            checkForComodification();
        }

        final void checkForComodification() {
            if (modCount != expectedModCount)
                throw new ConcurrentModificationException();
        }
    }

/**
     * 第二種：descendingIterator對ListItr的應用
     */
    public Iterator<E> descendingIterator() {
        return new DescendingIterator();
    }

    /**
     * Adapter to provide descending iterators via ListItr.previous
     */
    private class DescendingIterator implements Iterator<E> {
        private final ListItr itr = new ListItr(size());
        public boolean hasNext() {
            return itr.hasPrevious();
        }
        public E next() {
            return itr.previous();
        }
        public void remove() {
            itr.remove();
        }
    }

唯一化

無序列表

有序列表

選擇排序

原理

c++方法

效能比較

JAVA方法（不是關於LinkedList的）

public class ChooseSort {

	static int[] array = {3,2,4,1,5,0};
	
	public static void chooseSort(int[] a) 
	{
		int max = 0;
		int index = 0;
		//外層迴圈，控制選擇的次數，陣列長度為6，一共需要選擇5次
		for(int i=0;i<a.length-1;i++) 
		{
			for(int j=0;j<a.length-i;j++) 
			{
				if(max < a[j]) 
				{
					max = a[j];
					index = j;
				}
			}
			//每次選擇完成後，max中存放的是該輪選出的最大值
			//將max指向位置的元素和陣列最後一個元素位置互換
			int temp = a[a.length-i-1];
			a[a.length-i-1] = max;
			a[index] = temp;
			//清空max和index，便於下次
			max=0;
			index =0;
			System.out.println("經過第"+(i+1)+"輪選擇後，陣列為"+Arrays.toString(a));
		}
	}
	
	public static void main(String[] args) {
		chooseSort(array);
	}
}

插入排序

原理

c++方法

template <typename T> //列表的插入排序演算法：對起始於位置p的n個元素排序
void List<T>::insertionSort ( ListNodePosi(T) p, int n ) { //valid(p) && rank(p) + n <= size
	for ( int r = 0; r < n; r++ ) { //逐一為各節點
		insertA ( search ( p->data, r, p ), p->data ); //查詢適當的位置並插入
		p = p->succ; 
		remove ( p->pred ); //轉向下一節點
    }
 }

template <typename T> //在有序列表內節點p（可能是trailer）的n個（真）前驅中，找到不大於e的最後者
ListNodePosi(T) List<T>::search ( T const& e, int n, ListNodePosi(T) p ) const {
	// assert: 0 <= n <= rank(p) < _size
    do {
       p = p->pred; n--;  //從右向左
    } while ( ( -1 < n ) && ( e < p->data ) ); //逐個比較，直至命中或越界
    return p; //返回查詢終止的位置
} //失敗時，返回區間左邊界的前驅（可能是header）——呼叫者可通過valid()判斷成功與否

逆序對

JAVA方法

public  class LinkedInsertSort {
    static class ListNode {
        int val;
        ListNode next;
        ListNode(int x) {
            val = x;
            next = null;
        }
    }
 
    public static ListNode insertionSortList(ListNode head) {
        if(head==null||head.next==null)    return head;
 
        ListNode pre = head;//pre指向已經有序的節點
        ListNode cur = head.next;//cur指向待排序的節點
 
        ListNode aux = new ListNode(-1);//輔助節點
        aux.next = head;
 
        while(cur!=null){
            if(cur.val<pre.val){
              //先把cur節點從當前連結串列中刪除，然後再把cur節點插入到合適位置
                pre.next = cur.next;
 
                //從前往後找到l2.val>cur.val,然後把cur節點插入到l1和l2之間
                ListNode l1 = aux;
                ListNode l2 = aux.next;
                while(cur.val>l2.val){
                    l1 = l2;
                    l2 = l2.next;
                }
                //把cur節點插入到l1和l2之間
                l1.next = cur;
                cur.next = l2;//插入合適位置
 
                cur = pre.next;//指向下一個待處理節點
 
            }else{
                pre = cur;
                cur = cur.next;
            }
        }
        return aux.next;
    }
}

java實現

https://www.cnblogs.com/iwehdio/p/12621460.html