数组和链表

数组

  1. 数组内存分配在连续的内存区域上。
  2. 数组需要预申请大小,可能造成内存浪费。
  3. 随机读取效率高,因为数组内存是连续的,知道每一个数据的地址,可以直接找到指定索引数据。
  4. 增删效率低,需要移动受影响的数据的位置。
  5. 由于内存区域连续,有CPU缓存命中高的优势,访问效率高。

链表

  1. 链表可分配在内存任意地方,不要求连续。
  2. 无需预指定大小,可自由调整数据量。
  3. 不支持随机读取,查询数据较慢,需要从头开始遍历查找。
  4. 增删速度快,只需要修改指针指向即可。
  5. 由于内存分散,往往前后节点数据不能同时处于缓存中,访问效率低。

时间复杂度

/ 数组 链表
读取 O(1) O(n)
插入 O(n) O(1)
删除 O(n) O(1)

动态数组

根据元素个数动态调整数组大小

实现

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public class List<T>
{
private T[] array;
private int count;

public int Count => count;

public int Capacity => array.Length;

private static T[] emptyArray = new T[0];

public List()
{
array = emptyArray;
count = 0;
}

public List(int capacity)
{
array = new T[capacity];
count = 0;
}

public void Set(int index, T value)
{
if (count == Capacity)
Resize((Capacity == 0) ? 4 : Capacity * 2);//容量从4起步,每次扩容翻倍

array[index] = value;
count++;
}

public T Get(int index)
{
if (index > count - 1)
{
throw new Exception("List out of range");
}

return array[index];
}

public void RemoveAt(int index)
{
for (int i = index; i < count ; i++)
{
array[i] = array[i + 1];
}

count--;

//若实际数据小于当前容量的1/4,容量缩小至原本的1/2
if (count > 0 && count <= Capacity / 4)
{
Resize(Capacity / 2);
}
}

//调整内部数组大小,新开辟数组,并把旧数组内容拷贝至新数组
private void Resize(int count)
{
T[] _array = new T[count];
Array.Copy(array, 0, _array, 0, this.count);
array = _array;
}
}

单链表

实现

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public class ListNode<T> where T : IComparable<T>
{
public ListNode<T> next;
public T value;

public ListNode(T value)
{
this.value = value;
}

public ListNode(ListNode<T> next, T value)
{
this.next = next;
this.value = value;
}
}

class LinkedList<T> where T : IComparable<T>
{
private ListNode<T> head;
private int count;
public int Count => count;

public ListNode<T> First => head.next;


public LinkedList()
{
head = new ListNode<T>(default(T));
}

public void AddFirst(T value)
{
AddFirst(new ListNode<T>(value));
}

public void AddFirst(ListNode<T> node)
{
if (node == null)
return;

AddNode(head, node);
}

public void AddLast(T value)
{
AddLast(new ListNode<T>(value));
}

public void AddLast(ListNode<T> node)
{
if (node == null)
return;

ListNode<T> last = head;
while (last.next != null)
{
last = last.next;
}

AddNode(last, node);
}

public void AddBefore(ListNode<T> node, T value)
{
if (node == null)
return;

AddBefore(node, new ListNode<T>(value));
}

public void AddBefore(ListNode<T> node, ListNode<T> value)
{
if (node == null || value == null)
return;

ListNode<T> pre = head;
ListNode<T> addNode = First;
while (addNode != null && addNode != node)
{
pre = pre.next;
addNode = addNode.next;
}

if (addNode == null || addNode.value.CompareTo(node.value) != 0)
return;

AddNode(pre, value);
}

public void AddAfter(ListNode<T> node, T value)
{
if (node == null)
return;

AddAfter(node, new ListNode<T>(value));
}

public void AddAfter(ListNode<T> node, ListNode<T> value)
{
if (node == null || value == null)
return;

ListNode<T> addNode = First;
while (addNode != null && addNode != node)
{
addNode = addNode.next;
}

if (addNode == null || addNode.value.CompareTo(node.value) != 0)
return;

AddNode(node, value);
}

public void DeleteNode(T value)
{
ListNode<T> pre = head;
ListNode<T> deleteNode = First;
while (deleteNode != null && deleteNode.value.CompareTo(value) != 0)
{
pre = pre.next;
deleteNode = deleteNode.next;
}

if (deleteNode == null)
return;

DeleteNode(pre, deleteNode);
}

public void DeleteNode(ListNode<T> node)
{
if (node == null)
return;

ListNode<T> pre = head;
ListNode<T> deleteNode = First;
while (deleteNode != null && deleteNode != node)
{
pre = pre.next;
deleteNode = deleteNode.next;
}

if (deleteNode == null)
return;

DeleteNode(pre, deleteNode);
}

private void DeleteNode(ListNode<T> pre, ListNode<T> deleteNode)
{
if (pre == null || deleteNode == null)
return;

ListNode<T> next = deleteNode.next;
pre.next = next;
count--;
}

public ListNode<T> Find(T value)
{
ListNode<T> node = First;
while (node != null && node.value.CompareTo(value) != 0)
{
node = node.next;
}

return node;
}

private void AddNode(ListNode<T> pre, ListNode<T> node)
{
if (pre == null || node == null)
return;

ListNode<T> next = pre.next;
pre.next = node;
node.next = next;
count++;
}

public void Clear()
{
head.next = null;
count = 0;
}
}

双链表

实现

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public class ListNode<T> where T : IComparable<T>
{
public ListNode<T> pre;
public ListNode<T> next;
public T value;

public ListNode(T value)
{
this.value = value;
}

public ListNode(ListNode<T> pre, ListNode<T> next, T value)
{
this.pre = pre;
this.next = next;
this.value = value;
}
}

class LinkedList<T> where T : IComparable<T>
{
private ListNode<T> head;
private ListNode<T> tail;
private int count;
public int Count => count;

public ListNode<T> First
{
get
{
if (count > 0)
return head.next;
else
return null;
}
}

public ListNode<T> Last
{
get
{
if (count > 0)
return tail.pre;
else
return null;
}
}


public LinkedList()
{
head = new ListNode<T>(default(T));
tail = new ListNode<T>(default(T));
head.next = tail;
tail.pre = head;
}

public void AddFirst(T value)
{
AddFirst(new ListNode<T>(value));
}

public void AddFirst(ListNode<T> node)
{
if (node == null)
return;

ListNode<T> next = First;
head.next = node;
node.next = next;
if (next != null) next.pre = node;
count++;
}

public void AddLast(T value)
{
AddLast(new ListNode<T>(value));
}

public void AddLast(ListNode<T> node)
{
if (node == null)
return;

node.pre = tail.pre;
tail.pre.next = node;
tail.pre = node;

count++;
}

public void AddBefore(ListNode<T> node, T value)
{
if (node == null)
return;

AddBefore(node, new ListNode<T>(value));
}

public void AddBefore(ListNode<T> node, ListNode<T> value)
{
if (node == null || value == null)
return;

ListNode<T> pre = head;
ListNode<T> addNode = First;
while (addNode != null && addNode != node)
{
pre = pre.next;
addNode = addNode.next;
}

if (addNode == null)
return;

pre.next = value;
if (pre != head) value.pre = pre;
value.next = node;
node.pre = value;

count++;
}

public void AddAfter(ListNode<T> node, T value)
{
if (node == null)
return;

AddAfter(node, new ListNode<T>(value));
}

public void AddAfter(ListNode<T> node, ListNode<T> value)
{
if (node == null || value == null)
return;

ListNode<T> addNode = First;
while (addNode != null && addNode != node)
{
addNode = addNode.next;
}

if (addNode == null)
return;

ListNode<T> next = node.next;
node.next = value;
value.pre = node;
value.next = next;
if (next == null) tail.pre = value;

count++;
}

public void DeleteNode(T value)
{
ListNode<T> pre = head;
ListNode<T> deleteNode = First;
while (deleteNode != null && deleteNode.value.CompareTo(value) != 0)
{
pre = pre.next;
deleteNode = deleteNode.next;
}

if (deleteNode == null)
return;

DeleteNode(pre, deleteNode);
}

public void DeleteNode(ListNode<T> node)
{
if (node == null)
return;

ListNode<T> pre = head;
ListNode<T> deleteNode = First;
while (deleteNode != null && deleteNode != node)
{
pre = pre.next;
deleteNode = deleteNode.next;
}

if (deleteNode == null)
return;

DeleteNode(pre, deleteNode);
}

private void DeleteNode(ListNode<T> pre, ListNode<T> deleteNode)
{
if (pre == null || deleteNode == null)
return;

ListNode<T> next = deleteNode.next;
pre.next = next;
if (pre != head) next.pre = pre;

count--;
}

public ListNode<T> Find(T value)
{
ListNode<T> node = First;
while (node != null && node.value.CompareTo(value) != 0)
{
node = node.next;
}

return node;
}

public void Clear()
{
head.next = tail;
tail.pre = head;
count = 0;
}
}

先进后出

应用

  1. 基于栈实现的UI框架
  2. 编辑器中撤回和重做的操作
  3. 括号合法检查
  4. 基于栈实现简单的表达式计算

数组实现

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public class Stack<T>
{
private T[] array;
private int count;

public int Count => count;

private static T[] emptyArray = new T[0];

public Stack()
{
array = emptyArray;
count = 0;
}

public Stack(int capacity)
{
array = new T[capacity];
count = 0;
}

public bool IsEmpty()
{
return count <= 0;
}

public T Peek()
{
if (count == 0)
{
throw new Exception("Stack count is 0.");
}
else
{
return array[count - 1];
}
}

public void Push(T t)
{
if (count == array.Length)
{
Resize((array.Length == 0) ? 4 : (2 * array.Length));
}

array[count++] = t;
}

public T Pop()
{
if (count == 0)
{
throw new Exception("Stack count is 0.");
}

T t = array[--count];
array[count] = default(T);

if (count > 0 && count == array.Length / 4)
{
Resize(array.Length / 2);
}

return t;
}

private void Resize(int count)
{
T[] _array = new T[count];
Array.Copy(array, 0, _array, 0, this.count);
array = _array;
}
}

链表实现

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public class Stack<T>
{
private class ListNode<Y>
{
public ListNode<Y> next;
public Y value;

public ListNode(Y value)
{
this.value = value;
}

public ListNode(ListNode<Y> node, Y value)
{
this.next = node;
this.value = value;
}
}

private ListNode<T> first;
private int count;

public int Count => count;

public bool IsEmpty()
{
return first == null;
}

public T Peek()
{
if (first == null)
{
throw new Exception("Stack count is 0.");
}
else
{
return first.value;
}
}

public void Push(T value)
{
ListNode<T> oldFirst = first;
first = new ListNode<T>(value);
first.next = oldFirst;

count++;
}

public T Pop()
{
if (count == 0)
{
throw new Exception("Stack count is 0.");
}

T value = first.value;
first = first.next;

count--;

return value;
}
}

队列

先进先出

应用

  1. 消息队列,降低峰值
  2. 动画队列,按顺序逐个播放动画
  3. BFS
  4. 排队问题等

数组实现

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public class Queue<T>
{
private int front;
private int rear;
private T[] array;

private static T[] emptyArray = new T[4];

public int Capacity => array.Length;
public int Count => (rear + Capacity - front) % Capacity;
public bool IsEmpty => front == rear;
private bool IsFull => (rear + 1) % Capacity == front;

public Queue()
{
array = emptyArray;
front = 0;
rear = 0;
}

public Queue(int capacity)
{
array = new T[capacity];
front = 0;
rear = 0;
}

public void Enqueue(T value)
{
if (IsFull)
{
Resize(Capacity * 2);
}

array[rear] = value;
rear = (rear + 1) % Capacity;
}

public T Dequeue()
{
if (IsEmpty)
{
throw new Exception(("Queue count is 0."));
}

T value = array[front];
array[front] = default(T);
front = (front + 1) % Capacity;

if (Count > 0 && Count == Capacity / 4)
{
Resize(Capacity / 2);
}

return value;
}

public T Peek()
{
if (IsEmpty)
{
throw new Exception("Queue count is 0.");
}

return array[front];
}

private void Resize(int size)
{
T[] newArray = new T[size];
Console.WriteLine(("resize:" + Capacity + " to:" + size));

int index = front;
int newIndex = 0;
while (newIndex < Count)
{
newArray[newIndex++] = array[index];
index++;
}
front = 0;
rear = newIndex;
array = newArray;
}
}

链表实现

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public class Queue<T>
{
private class Node<Y>
{
public Node<Y> next;
public Y value;

public Node(Y value)
{
this.value = value;
}

public Node(Node<Y> node, Y value)
{
this.next = node;
this.value = value;
}
}

private Node<T> first;
private Node<T> last;
private int count;

public int Count => count;
public bool IsEmpty => first == null;

public void Enqueue(T value)
{

Node<T> oldLast = last;
last = new Node<T>(value);
if (IsEmpty)
{
first = last;
}
else
{
oldLast.next = last;
}

count++;
}

public T Dequeue()
{
if (IsEmpty)
{
throw new Exception("Queue count is 0.");
}

T value = first.value;
first = first.next;

if (IsEmpty)
last = null;

count--;
return value;
}

public T Peek()
{
if (IsEmpty)
{
throw new Exception("Queue count is 0.");
}

return first.value;
}
}

双端队列

双端队列同时具有栈的先进后出特性,也具有队列的先进先出特性。

应用

  1. KTV式可插歌的点歌系统
  2. LRU