数据结构：栈(linked-stack & array-stack)

栈是一种特别的线性表。在栈中，只能在数据的一端（即栈顶）进行操作。最经典的解释这个策略的例子就是叠盘子。盘子只能一个一个不断放在之前的盘子堆上，拿盘子的时候也只能从上往下一个一个拿。这两个操作，在stack中分别对于push和pop，即压栈和出栈。这体现了栈的后进先出(LIFO)特性。

2. 栈的实现

stack的实现分为两种，一种是使用数组来模拟栈，另外一种是使用链表来模拟栈。

2 .1 数组实现（array stack）

首先，先来看使用数组的方法。

栈的结构为#define MAX_SIZE 20 //栈内最多有几个元素typedef int StackEntry;typedef struct stack {      StackEntry entry[MAX_SIZE];      int top; } Stack ;

用数组实现的栈使用连续的内存地址，为了能够知道栈顶位置，需要使用一个变量标记。

看起来，数组的实现方式十分的简单！So easy！当向栈中压入数据时，需要将top的值加1；出栈时，top的值减1。Too young，too naive！考虑两个极端的情况：在栈满时压栈，在栈空时出栈。因此在进行push和pop操作之前需要检查栈的情况，避免溢出。

 int IsFull(Stack *s) {    return (s->top >= MAX_SIZE); } int IsEmpty(Stack *s) {    return (s->top <= 0); }void Push(StackEntry item, Stack* s) {  if（IsFull(s)）    return;  else    s->entry[s->top++] = item;}void Pop(Stack* s) {   if(IsEmpty(s)）      return;   else      s->top--;}StackEntry Top(Stack* s) {   if(!IsEmpty(s)）      return s->entry[s->top-1];   else       return -1;}

2.2. 链式实现（linked stack）

链式栈使用链表的存储形式实现，其存储是不连续的。我们首先定义stack的结构如下：

typedef struct node {  StackEntry val;  struct node *next;} Node;

一般来说，很多人会自然而然的想到在stack中将心的元素加入到linked stack的末尾。但是要考虑到，对于stack，我们经常在其末尾进行操作，如果将元素插入到link的末尾，那么每次操作都要先从头到达末尾才能操作，所以我们需要换另外一种方法，采用前插的方式，将新的元素插入到列表的前面。这样每次进行push和pop操作的时候就可以直接通过top指针操作。

//push a new node onto the top of the stack (the front of the list),//and return whether successfulint Push (int val, Node* stack) {    Node* addNode = (Node*)malloc(sizeof(Node));    if (addNode == NULL) {        printf("out of memory!\n");        return 0;    }    addNode->val = val;    addNode->next = stack->next;    stack->next = addNode;    return 1;}//pop the top node from the stackint Pop (Node* stack) {    if (IsEmpty(stack)) {        printf("the stack is empty!\n");        return 0;    }    Node *tmpNode = stack->next;    stack->next = tmpNode->next;    free(tmpNode);    return 1;}//check whether the stack is emptyint IsEmpty (Node* stack) {    return (stack->next == NULL);}//get the top value of the stackint Top (Node* stack) {    if (IsEmpty(stack)) {        printf("the stack is empty!\n");        return -1;    }    return (stack->next->val);}

综合所有操作

数组实现

#include <stdio.h>#include <stdlib.h>#define MAX_SIZE 20 //栈内最多有几个元素typedef int StackEntry;typedef struct stack {      StackEntry entry[MAX_SIZE];      int top;} Stack;int IsFull(Stack *s) {    return (s->top >= MAX_SIZE); }int IsEmpty(Stack *s) {    return (s->top <= 0); }void Push(StackEntry item, Stack* s) {  if (IsFull(s))    return;  else    s->entry[s->top++] = item;}void Pop(Stack* s) {   if (IsEmpty(s))      return;   else      s->top--;}StackEntry Top(Stack* s) {   if (!IsEmpty(s))      return s->entry[s->top-1];        else            return -1;}int main () {    Stack *s = (Stack*)malloc(sizeof(Stack));    s->top = 0;    Push(1, s);    Push(2, s);    Push(3, s);    //get 3    int temp = Top(s);    printf("%d ", temp);    //pop 3    Pop(s);    temp = Top(s);    printf("%d ", temp);    Push(4, s);    temp = Top(s);    printf("%d ", temp);    //pop 4    Pop(s);    temp = Top(s); // top is 2    printf("%d ", temp);    //pop 2    Pop(s);    temp = Top(s); //top is 1    printf("%d ", temp);    //pop 1    Pop(s);    temp = Top(s); //error get top element from empty stack    printf("%d ", temp);    return 0;}

输出：3 2 4 2 1 -1

链式实现

#include <stdio.h>#include <stdlib.h>typedef struct node{    int val;    struct node *next;} Node;Node* CreateEmptyStack ();int Push (int val, Node* stack);int Pop (Node* stack);int IsEmpty (Node* stack);int Top (Node* stack);int main () {    Node *s = CreateEmptyStack();    Push(1, s);    Push(2, s);    Push(3, s);    int temp = Top(s); //top is 3    printf("%d ", temp);    Pop(s); //pop 3    temp = Top(s); //top is 2    printf("%d ", temp);    Push(4, s);    temp = Top(s); //top is 4    printf("%d ", temp);    Pop(s); //pop 4    temp = Top(s); //top is 2    printf("%d ", temp);    Pop(s); //pop 2    temp = Top(s); //top is 1    printf("%d ", temp);    Pop(s); //pop 1    temp = Top(s); //error, get top element from empty stack    printf("%d ", temp);    return 0;}//create a empty stack and return the addressNode* CreateEmptyStack () {    Node* stack = (Node*)malloc(sizeof(Node));    if (stack == NULL) {        printf("out of memory!\n");        return NULL;    }    stack->val = 0;    stack->next = NULL;    return stack;}//push a new node onto the top of the stack (the front of the list),//and return whether successfulint Push (int val, Node* stack) {    Node* addNode = (Node*)malloc(sizeof(Node));    if (addNode == NULL) {        printf("out of memory!\n");        return 0;    }    addNode->val = val;    addNode->next = stack->next;    stack->next = addNode;    return 1;}//pop the top node from the stackint Pop (Node* stack) {    if (IsEmpty(stack)) {        printf("the stack is empty!\n");        return 0;    }    Node *tmpNode = stack->next;    stack->next = tmpNode->next;    free(tmpNode);    return 1;}//check whether the stack is emptyint IsEmpty (Node* stack) {    return (stack->next == NULL);}//get the top value of the stackint Top (Node* stack) {    if (IsEmpty(stack)) {        printf("the stack is empty!\n");        return -1;    }    return (stack->next->val);}

输出：3 2 4 2 1 the stack is empty!
-1