数据结构与算法 | 线性表 —— 链表
原文链接: https://wangwei.one/posts/jav...
链表
定义
逻辑结构上一个挨一个的数据,在实际存储时,并没有像顺序表那样也相互紧挨着。恰恰相反,数据随机分布在内存中的各个位置,这种存储结构称为线性表的链式存储。
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由于分散存储,为了能够体现出数据元素之间的逻辑关系,每个数据元素在存储的同时,要配备一个指针,用于指向它的直接后继元素,即每一个数据元素都指向下一个数据元素(最后一个指向NULL(空))。这种结构成为 "单向链表"。
在单向链表的基础上,给各个结点额外配备一个指针变量,用于指向每个结点的直接前趋元素。这样的链表被称为“双向链表”或者“双链表”。
当单向链表的尾部数据指向头部数据时,就构成了单向循环链表。
当双向链表的头部和尾部相互指向时,就构成了双向循环链表。
单向链表
单向链表在插入元素、删除元素时,需要获取前驱元素,需要从head开始遍历,时间复杂度为O(n)。
根据index查询对应元素,也需要从head开始遍历,时间复杂度为O(n)。
代码实现
package one.wangwei.algorithms.datastructures.list.impl; import one.wangwei.algorithms.datastructures.list.IList; /** * Single Linked List * * @author https://wangwei.one * @date 2018/12/25 */ public class SingleLinkedList<T> implements IList<T> { /** * size */ private int size = 0; /** * head node */ private Node<T> head; /** * tail node */ private Node<T> tail; /** * add element * * @param element * @return */ @Override public boolean add(T element) { return addLast(element); } /** * add element at index * * @param index * @param element * @return */ @Override public boolean add(int index, T element) { if (index < 0 || index > size) { throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size); } if (index == size) { return add(element); } else { return addBefore(index, element); } } /** * Add Last element * * @param element * @return */ private boolean addLast(T element) { Node<T> last = tail; Node<T> newNode = new Node<>(null, element); tail = newNode; // if linked list is empty if (last == null) { head = newNode; } else { last.next = newNode; } size++; return true; } /** * add element before certain element * * @param index * @param element * @return */ private boolean addBefore(int index, T element) { checkPositionIndex(index); // prev node Node<T> prev = null; Node<T> x = head; for (int i = 0; i < index; i++) { prev = x; x = x.next; } // current node Node<T> current = x; // new node Node<T> newNode = new Node<>(current, element); // if current node is head if (prev == null) { head = newNode; } else { prev.next = newNode; } size++; return true; } /** * remove element * * @param element * @return */ @Override public boolean remove(T element) { Node<T> prev = null; Node<T> x = head; if (element == null) { while (x != null && x.element != null) { prev = x; x = x.next; } } else { while (x != null && !x.element.equals(element)) { prev = x; x = x.next; } } // if this linked is null OR don't find element if (x == null) { return false; } Node<T> next = x.next; // if delete node is head if (prev == null) { head = next; } else { prev.next = next; } // if delete node is tail if (next == null) { tail = prev; } // for GC x.element = null; x = null; size--; return true; } /** * remove element by index * * @param index * @return */ @Override public T remove(int index) { checkPositionIndex(index); Node<T> prev = null; Node<T> x = head; for (int i = 0; i < index; i++) { prev = x; x = x.next; } // if linked is empty if (x == null) { return null; } Node<T> next = x.next; // if delete node is head if (prev == null) { head = next; } else { prev.next = next; } // if delete node is tail if (next == null) { tail = prev; } size--; return x.element; } /** * set element by index * * @param index * @param element * @return old element */ @Override public T set(int index, T element) { checkPositionIndex(index); Node<T> node = node(index); T oldElement = node.element; node.element = element; return oldElement; } /** * get element by index * * @param index * @return */ @Override public T get(int index) { Node<T> node = node(index); return node == null ? null : node.element; } /** * get element by index * * @param index * @return */ private Node<T> node(int index) { checkPositionIndex(index); Node<T> x = head; for (int i = 0; i < index; i++) { x = x.next; } return x; } /** * check index * * @param index */ private void checkPositionIndex(int index) { if (index < 0 || index >= size) { throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size); } } /** * clear list */ @Override public void clear() { for (Node<T> x = head; x != null; ) { Node<T> next = x.next; x.element = null; x.next = null; x = next; } head = tail = null; size = 0; } /** * contain certain element * * @param element */ @Override public boolean contains(T element) { if (element == null) { for (Node<T> x = head; x != null; x = x.next) { if (x.element == null) { return true; } } } else { for (Node<T> x = head; x != null; x = x.next) { if (x.element.equals(element)) { return true; } } } return false; } /** * get list size * * @return */ @Override public int size() { return size; } /** * Linked List Node * * @param <T> */ private class Node<T> { private Node<T> next; private T element; public Node(Node<T> next, T element) { this.next = next; this.element = element; } } }
源代码
双向链表
相比于单向链表,双向链表多了一个前驱指针,在查找前驱节点时,时间复杂度降低为了O(1)。
通过index查询,删除某个node节点,时间复杂度都降为了O(1)。代码如下:
代码实现
package one.wangwei.algorithms.datastructures.list.impl; import one.wangwei.algorithms.datastructures.list.IList; /** * Doubly Linked List * * @param <T> * @author https://wangwei.one * @date 2018/04/28 */ public class DoublyLinkedList<T> implements IList<T> { /** * size */ private int size = 0; /** * head element */ private Node<T> head = null; /** * tail element */ private Node<T> tail = null; /** * add element * * @param element * @return */ @Override public boolean add(T element) { return addLast(element); } /** * add element at index * * @param index * @param element * @return */ @Override public boolean add(int index, T element) { if (index < 0 || index > size) { throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size); } if (index == size) { return add(element); } else { return addBefore(element, node(index)); } } /** * Add Last element * * @param element * @return */ private boolean addLast(T element) { final Node<T> last = tail; Node<T> newNode = new Node<>(last, element, null); tail = newNode; if (last == null) { head = newNode; } else { last.next = newNode; } size++; return true; } /** * add element before certain element * * @param element * @param target * @return */ private boolean addBefore(T element, Node<T> target) { Node<T> prev = target.prev; Node<T> newNode = new Node<>(prev, element, target); target.prev = newNode; if (prev == null) { head = newNode; } else { prev.next = newNode; } size++; return true; } /** * remove node by element * * @param element * @return */ @Override public boolean remove(T element) { if (element == null) { for (Node<T> x = head; x != null; x = x.next) { if (x.element == null) { unlink(x); return true; } } } else { for (Node<T> x = head; x != null; x = x.next) { if (element.equals(x.element)) { unlink(x); return true; } } } return false; } /** * remove node by index * * @param index * @return */ @Override public T remove(int index) { return unlink(node(index)); } /** * get element by index * * @param index * @return */ private Node<T> node(int index) { checkPositionIndex(index); if (index < (size >> 1)) { Node<T> x = head; for (int i = 0; i < index; i++) { x = x.next; } return x; } else { Node<T> x = tail; for (int i = size - 1; i > index; i--) { x = x.prev; } return x; } } /** * unlink node * * @param node */ private T unlink(Node<T> node) { final T element = node.element; final Node<T> prev = node.prev; final Node<T> next = node.next; // if unlink is head if (prev == null) { head = next; } else { prev.next = next; // clear prev node.prev = null; } // if unlink is tail if (next == null) { tail = prev; } else { next.prev = prev; node.next = null; } node.element = null; size--; return element; } private void checkPositionIndex(int index) { if (index < 0 || index >= size) { throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size); } } /** * set element by index * * @param index * @param element * @return */ @Override public T set(int index, T element) { checkPositionIndex(index); Node<T> oldNode = node(index); T oldElement = oldNode.element; oldNode.element = element; return oldElement; } /** * get element by index * * @param index * @return */ @Override public T get(int index) { Node<T> node = node(index); return node == null ? null : node.element; } /** * clear list */ @Override public void clear() { for (Node<T> x = head; x != null; ) { Node<T> next = x.next; x.element = null; x.next = null; x.prev = null; x = next; } head = tail = null; size = 0; } /** * contain certain element * * @param element */ @Override public boolean contains(T element) { if (element == null) { for (Node<T> x = head; x != null; x = x.next) { if (x.element == null) { return true; } } } else { for (Node<T> x = head; x != null; x = x.next) { if (element.equals(x.element)) { return true; } } } return false; } /** * get list size * * @return */ @Override public int size() { return size; } /** * node * * @param <T> */ private class Node<T> { private T element; private Node<T> prev; private Node<T> next; public Node(Node<T> prev, T element, Node<T> next) { this.element = element; this.prev = prev; this.next = next; } } }
源代码
单向循环链表
与单向链表一样,在寻找前驱节点时,需要遍历整个链表,时间复杂度为O(n).
在第一次添加元素时,特别注意,head与tail为同一节点,并且需要自指向。
package one.wangwei.algorithms.datastructures.list.impl; import one.wangwei.algorithms.datastructures.list.IList; /** * Singly Circular Linked List * * @param <T> * @author https://wangwei.one * @date 2018/05/03 */ public class SinglyCircularLinkedList<T> implements IList<T> { /** * size */ private int size = 0; /** * head node */ private Node<T> head = null; /** * tail node */ private Node<T> tail = null; /** * add element * * @param element * @return */ @Override public boolean add(T element) { return addLast(element); } /** * add element at index * * @param index * @param element * @return */ @Override public boolean add(int index, T element) { if (index < 0 || index > size) { throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size); } if (index == size) { return add(element); } else { return addBefore(index, element); } } /** * Add Last element * * @param element * @return */ private boolean addLast(T element) { final Node<T> last = tail; Node<T> newElement = new Node<>(element, head); tail = newElement; if (last == null) { head = newElement; // we need linked itself when add an element first tail.next = head; } else { last.next = newElement; } size++; return true; } /** * add element before certain element * * @param element * @param element * @return */ private boolean addBefore(int index, T element) { checkPositionIndex(index); // prev node, start with tail Node<T> prev = tail; Node<T> x = head; for (int i = 0; i < index; i++) { prev = x; x = x.next; } // current node Node<T> current = x; // new node Node<T> newNode = new Node<>(element, current); if (index == 0) { head = newNode; } prev.next = newNode; size++; return true; } /** * remove node by element * * @param element * @return */ @Override public boolean remove(T element) { // start with tail Node<T> prev = tail; // start with head Node<T> x = head; // start with index -1 int prevIndex = -1; for (int i = 0; i < size; i++) { if (element == null && x.element == null) { break; } if (element != null && element.equals(x.element)) { break; } prev = x; x = x.next; prevIndex = i; } // if this linked list is empty if (x == null) { return false; } // if don't match element if (prevIndex == size - 1) { return false; } Node<T> next = x.next; // if delete node is head if (prevIndex == -1) { head = next; } // if delete node is tail if (prevIndex == size - 2) { tail = prev; } prev.next = next; size--; if (size == 0) { head = tail = null; } // for GC x = null; return true; } /** * remove element by index * * @param index * @return */ @Override public T remove(int index) { checkPositionIndex(index); Node<T> prev = tail; Node<T> x = head; for (int i = 0; i < index; i++) { prev = x; x = x.next; } // if linked is empty if (x == null) { return null; } Node<T> next = x.next; // if delete node is head if (index == 0) { head = next; } // if delete node is tail if (index == size - 1) { tail = prev; } prev.next = next; size--; if (size == 0) { head = tail = null; } return x.element; } /** * get element by index * * @param index * @return */ private Node<T> node(int index) { checkPositionIndex(index); Node<T> x = head; for (int i = 0; i < index; i++) { x = x.next; } return x; } private void checkPositionIndex(int index) { if (index < 0 || index >= size) { throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size); } } /** * set element by index * * @param index * @param element * @return */ @Override public T set(int index, T element) { checkPositionIndex(index); Node<T> oldNode = node(index); T oldElement = oldNode.element; oldNode.element = element; return oldElement; } /** * get element by index * * @param index * @return */ @Override public T get(int index) { return node(index).element; } /** * clear list element */ @Override public void clear() { for (Node<T> x = head; x != null; ) { Node<T> next = x.next; x.element = null; x.next = null; x = next; } head = tail = null; size = 0; } /** * contain certain element * * @param element */ @Override public boolean contains(T element) { if (head == null) { return false; } Node<T> x = head; for (int i = 0; i < size; i++) { if (element == null && x.element == null) { return true; } if (element != null && element.equals(x.element)) { return true; } x = x.next; } return false; } /** * get list size * * @return */ @Override public int size() { return size; } /** * Node * * @param <T> */ private class Node<T> { private T element; private Node<T> next; public Node(T element, Node<T> next) { this.element = element; this.next = next; } } }
源代码
双向循环链表
双向循环链表相比单向循环链表,降低了查找前驱节点的复杂度,时间复杂度为O(1).
同样第一次添加元素时,head与tail为同一元素,需要自指向。
package one.wangwei.algorithms.datastructures.list.impl; import one.wangwei.algorithms.datastructures.list.IList; /** * Doubly circular linked list * * @author https://wangwei.one * @date 2018/12/21 */ public class DoublyCircularLinkedList<T> implements IList<T> { /** * size */ private int size; /** * head node */ private Node<T> head; /** * tail node */ private Node<T> tail; /** * add element * * @param element * @return */ @Override public boolean add(T element) { return addLast(element); } /** * add element at index * * @param index * @param element * @return */ @Override public boolean add(int index, T element) { if (index < 0 || index > size) { throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size); } if (index == size) { return add(element); } else { return addBefore(index, element); } } /** * Add last element * * @param element * @return */ private boolean addLast(T element) { Node<T> last = tail; Node<T> newNode = new Node<>(element, last, head); tail = newNode; // add element at first if (last == null) { head = newNode; tail.next = head; } else { last.next = newNode; } head.prev = tail; size++; return true; } /** * add element before certain element * * @param index * @param element * @return */ private boolean addBefore(int index, T element) { Node<T> target = node(index); Node<T> prev = target.prev; Node<T> newNode = new Node<>(element, prev, target); prev.next = newNode; target.prev = newNode; if (index == 0) { head = newNode; } size++; return true; } /** * remove element * * @param element * @return */ @Override public boolean remove(T element) { // start with head Node<T> x = head; // start with index -1 int prevIndex = -1; for (int i = 0; i < size; i++) { if (element == null && x.element == null) { break; } if (element != null && element.equals(x.element)) { break; } x = x.next; prevIndex = i; } // if this linked list is empty if (x == null) { return false; } // if don't match element if (prevIndex == size - 1) { return false; } Node<T> prev = x.prev; Node<T> next = x.next; // if delete node is head if (prevIndex == -1) { head = next; } // if delete node is tail if (prevIndex == size - 2) { tail = prev; } prev.next = next; next.prev = prev; size--; if (size == 0) { head = tail = null; } // for GC x = null; return true; } /** * remove element by index * * @param index * @return */ @Override public T remove(int index) { checkPositionIndex(index); Node<T> x = head; for (int i = 0; i < index; i++) { x = x.next; } // if linked is empty if (x == null) { return null; } Node<T> prev = x.prev; Node<T> next = x.next; // if delete node is head if (index == 0) { head = next; } // if delete node is tail if (index == size - 1) { tail = prev; } prev.next = next; next.prev = prev; size--; if (size == 0) { head = tail = null; } return x.element; } private void checkPositionIndex(int index) { if (index < 0 || index >= size) { throw new IndexOutOfBoundsException("Index: " + index + ", Size: " + size); } } /** * set element by index * * @param index * @param element * @return old element */ @Override public T set(int index, T element) { Node<T> oldNode = node(index); T oldElement = oldNode.element; oldNode.element = element; return oldElement; } /** * get element by index * * @param index * @return */ @Override public T get(int index) { return node(index).element; } /** * get element by index * * @param index * @return */ private Node<T> node(int index) { checkPositionIndex(index); if (index < (size >> 1)) { Node<T> x = head; for (int i = 0; i < index; i++) { x = x.next; } return x; } else { Node<T> x = tail; for (int i = size - 1; i > index; i--) { x = x.prev; } return x; } } /** * clear list */ @Override public void clear() { for (Node<T> x = head; x != null; ) { Node<T> next = x.next; x.element = null; x.next = null; x = next; } head = tail = null; size = 0; } /** * contain certain element * * @param element * @return */ @Override public boolean contains(T element) { if (head == null) { return false; } Node<T> x = head; for (int i = 0; i < size; i++) { if (element == null && x.element == null) { return true; } if (element != null && element.equals(x.element)) { return true; } x = x.next; } return false; } /** * get list size * * @return */ @Override public int size() { return size; } /** * Node * * @param <T> */ private class Node<T> { private T element; private Node<T> prev; private Node<T> next; public Node(T element, Node<T> prev, Node<T> next) { this.element = element; this.prev = prev; this.next = next; } } }
源代码
ArrayList vs LinkedList
ArrayList | LinkedList | |
---|---|---|
插入& 删除 | O(n) | O(1) |
随机访问 | O(1) | O(n) |
优点 | 连续的内存空间,可以借助CPU的预取机制 | 内存不连续,天然支持动态扩容 |
缺点 | 无法存储大数据,数组扩容耗性能 | 频繁地插入删除操作,会导致内存碎片的增加,导致频繁的GC |
参考资料
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