【数据结构初阶】栈和队列

1.栈

1.1栈的概念和结构

栈：一种特殊的线性表，其只允许在固定的一端进行插入和删除元素操作。进行数据插入和删除操作的一端称为栈顶，另一端称为栈底。栈中的数据元素遵守后进先出LIFO（Last In First Out）的原则。
压栈：栈的插入操作叫做进栈/压栈/入栈，入数据在栈顶。
出栈：栈的删除操作叫做出栈。出数据也在栈顶。

1.2栈的实现

栈的实现一般可以使用数组或者链表实现，相对而言数组的结构实现更优一些。因为数组在尾上插入数据的代价比较小

Stack.h

#include<stdio.h>
#include<stdlib.h>
#include<assert.h>
#include<stdbool.h>typedef int STDateType;
typedef struct Stack
{STDateType* a;int top;int capacity;
}ST;//初始化
void STInit(ST* ps);//销毁
void STDestroy(ST* ps);//入栈
void STPush(ST* ps, STDateType x);//出栈
void STPop(ST* ps);//栈顶
STDateType SLTTop(ST* ps);//计算大小
int STSize(ST* ps);//判断是否为空
bool STEmpty(ST* ps);

Stack.c

#include"Stack.h"//初始化
void STInit(ST* ps)
{assert(ps);ps->capacity = NULL;ps->a = 0;ps->top = 0;
}//销毁
void STDestroy(ST* ps)
{assert(ps);free(ps->a);ps->a = NULL;ps->capacity = ps->top = 0;
}//入栈
void STPush(ST* ps, STDateType x)
{assert(ps);if (ps->top == ps->capacity){int NewCapacity = ps->capacity == 0 ? 4 : ps->capacity * 2;STDateType* tmp = (STDateType*)realloc(ps->a, sizeof(STDateType) * NewCapacity);if (tmp == NULL){perror("realloc fail");exit(-1);}ps->a = tmp;ps->capacity = NewCapacity;}ps->a[ps->top] = x;ps->top++;
}//出栈
void STPop(ST* ps)
{assert(ps);assert(ps->a > 0);--ps->top;
}//栈顶
STDateType STTop(ST* ps)
{assert(ps);assert(ps->a > 0);return ps->a[ps->top - 1];
}//计算
int STSize(ST* ps)
{assert(ps);return ps->top;
}//判断是否为空
bool STEmpty(ST* ps)
{assert(ps);return ps->top == NULL;
}

test.c

#include"Stack.h"void TestStack()
{ST st;STInit(&st);STPush(&st, 1);STPush(&st, 2);STPush(&st, 3);STPush(&st, 4);STPush(&st, 5);while (!STEmpty(&st)){printf("%d ", STTop(&st));STPop(&st);}printf("\n");STDestroy(&st);
}int main()
{TestStack();return 0;
}

2.队列

2.1队列的概念和结构

队列：只允许在一端进行插入数据操作，在另一端进行删除数据操作的特殊线性表，队列具有先进先出FIFO(First In First Out) 入队列：进行插入操作的一端称为队尾出队列：进行删除操作的一端称为队头

2.2队列的实现

队列也可以数组和链表的结构实现，使用链表的结构实现更优一些，因为如果使用数组的结构，出队列在数组头上出数据，效率会比较低。

Queue.h

#include<stdio.h>
#include<stdlib.h>
#include<assert.h>
#include<stdbool.h>
typedef int QDataType;
typedef struct QueueNode
{struct QueueNode* next;QDataType data;
}QNode;
typedef struct Queue
{QNode* head;QNode* tail;int size;
}Que;
void QueueInit(Que* pq);
void QueueDestroy(Que* pq);
void QueuePush(Que* pq, QDataType x);
void QueuePop(Que* pq);
QDataType QueueFront(Que* pq);
QDataType QueueBack(Que* pq);
bool QueueEmpty(Que* pq);
int QueueSize(Que* pq);

Queue.c

#include"Queue.h"//初始化
void QueueInit(Que* pq)
{assert(pq);pq->head = pq->tail = NULL;pq->size = 0;
}//销毁
void QueueDestroy(Que* pq)
{assert(pq);QNode* cur = pq->head;while (cur){QNode* next = cur->next;free(cur);cur = cur->next;}pq->head = pq->tail = NULL;pq->size = 0;
}//入队
void QueuePush(Que* pq, QDateType x)
{assert(pq);QNode* newnode = (QNode*)malloc(sizeof(QNode));if (newnode == NULL){perror("malloc fail");exit(-1);}newnode->date = x;newnode->next = NULL;if (pq->tail == NULL){pq->head = pq->tail = newnode;}else{pq->tail->next = newnode;pq->tail = newnode;}pq->size++;
}//出队
void QueuePop(Que* pq)
{assert(pq);assert(!QueueEmpty(pq));if (pq->head->next == NULL){pq->head = pq->tail = NULL;}else{QNode* next = pq->head->next;free(pq->head);pq->head = next;}pq->size--;
}//队头
QDateType QueueFront(Que* pq)
{assert(pq);assert(!QueueEmpty(pq));return pq->head->date;
}//队尾
QDateType QueueBack(Que* pq)
{assert(pq);assert(!QueueEmpty);return pq->tail->date;
}//判断是否为空
bool QueueEmpty(Que* pq)
{assert(pq);return pq->head == NULL;
}//计算
int QueueSize(Que* pq)
{assert(pq);return pq->size;
}

test.c

#include"Queue.h"void QueueTest()
{Que pq;QueueInit(&pq);QueuePush(&pq, 1);QueuePush(&pq, 2);QueuePush(&pq, 3);QueuePush(&pq, 4);while (!QueueEmpty(&pq)){printf("%d ", QueueFront(&pq));QueuePop(&pq);}printf("\n");QueueDestroy(&pq);
}int main()
{QueueTest();return 0;
}

3.栈和队列面试题

3.1括号匹配问题
OJ

#include<stdio.h>
#include<stdlib.h>
#include<assert.h>
#include<stdbool.h>
//有效括号
typedef char STDateType;
typedef struct Stack
{STDateType* a;int top;int capacity;
}ST;
//初始化
void STInit(ST* ps);
//销毁
void STDestroy(ST* ps);
//入栈
void STPush(ST* ps, STDateType x);
//出栈
void STPop(ST* ps);
//栈顶
STDateType SLTTop(ST* ps);
//计算大小
int STSize(ST* ps);
//判断是否为空
bool STEmpty(ST* ps);//初始化
void STInit(ST* ps)
{assert(ps);ps->capacity = NULL;ps->a = 0;ps->top = 0;
}
//销毁
void STDestroy(ST* ps)
{assert(ps);free(ps->a);ps->a = NULL;ps->capacity = ps->top = 0;
}
//入栈
void STPush(ST* ps, STDateType x)
{assert(ps);if (ps->top == ps->capacity){int NewCapacity = ps->capacity == 0 ? 4 : ps->capacity * 2;STDateType* tmp = (STDateType*)realloc(ps->a, sizeof(STDateType) * NewCapacity);if (tmp == NULL){perror("realloc fail");exit(-1);}ps->a = tmp;ps->capacity = NewCapacity;}ps->a[ps->top] = x;ps->top++;
}
//出栈
void STPop(ST* ps)
{assert(ps);assert(ps->a > 0);--ps->top;
}
//栈顶
STDateType STTop(ST* ps)
{assert(ps);assert(ps->a > 0);return ps->a[ps->top - 1];
}
//计算
int STSize(ST* ps)
{assert(ps);return ps->top;
}
//判断是否为空
bool STEmpty(ST* ps)
{assert(ps);return ps->top == NULL;
}bool isValid(char* s) 
{ST st;STInit(&st);char topVal;while (*s){//数量不匹配if (*s == '(' || *s == '[' || *s == '{'){STPush(&st, *s);}else{if (STEmpty(&st)){STDestroy(&st);return false;}topVal = STTop(&st);STPop(&st);if ((*s == ')' && topVal != '(') || (*s == ']' && topVal != '[') || (*s == ' }' && topVal != '{')){STDestroy(&st);return false;}}s++;}//栈不为空，false,说明数量不匹配bool ret = STEmpty(&st);STDestroy(&st);return ret;
}int main()
{isValid("[(({})}]");#include<stdio.h>
#include<stdlib.h>
#include<assert.h>
#include<stdbool.h>
typedef int STDateType;
typedef struct Stack
{STDateType* a;int top;int capacity;
}ST;
//初始化
void STInit(ST* ps);
//销毁
void STDestroy(ST* ps);
//入栈
void STPush(ST* ps, STDateType x);
//出栈
void STPop(ST* ps);
//栈顶
STDateType SLTTop(ST* ps);
//计算大小
int STSize(ST* ps);
//判断是否为空
bool STEmpty(ST* ps);
//初始化
void STInit(ST* ps)
{assert(ps);ps->capacity = NULL;ps->a = 0;ps->top = 0;
}
//销毁
void STDestroy(ST* ps)
{assert(ps);free(ps->a);ps->a = NULL;ps->capacity = ps->top = 0;
}
//入栈
void STPush(ST* ps, STDateType x)
{assert(ps);if (ps->top == ps->capacity){int NewCapacity = ps->capacity == 0 ? 4 : ps->capacity * 2;STDateType* tmp = (STDateType*)realloc(ps->a, sizeof(STDateType) * NewCapacity);if (tmp == NULL){perror("realloc fail");exit(-1);}ps->a = tmp;ps->capacity = NewCapacity;}ps->a[ps->top] = x;ps->top++;
}
//出栈
void STPop(ST* ps)
{assert(ps);assert(ps->a > 0);--ps->top;
}
//栈顶
STDateType STTop(ST* ps)
{assert(ps);assert(ps->a > 0);return ps->a[ps->top - 1];
}
//计算
int STSize(ST* ps)
{assert(ps);return ps->top;
}
//判断是否为空
bool STEmpty(ST* ps)
{assert(ps);return ps->top == NULL;
}
typedef struct 
{ST pushst;ST popst;
} MyQueue;
MyQueue* myQueueCreate() 
{MyQueue* obj = (MyQueue*)malloc(sizeof(MyQueue));STInit(&obj->popst);STInit(&obj->pushst);return obj;
}void myQueuePush(MyQueue* obj, int x)
{STPush(&obj->pushst, x);
}int myQueuePeek(MyQueue* obj)
{if (STEmpty(&obj->popst)){while (!STEmpty(&obj->pushst)){STPush(&obj->popst, STTop(&obj->pushst));STPop(&obj->pushst);}}return STTop(&obj->popst);
}int myQueuePop(MyQueue* obj) 
{int front = myQueuePeek(obj);STPop(&obj->popst);return front;
}bool myQueueEmpty(MyQueue* obj) 
{return STEmpty(&obj->popst) && STEmpty(&obj->pushst);
}void myQueueFree(MyQueue* obj) 
{STDestroy(&obj->popst);STDestroy(&obj->pushst);free(obj);
}}

3.2用队列实现栈
OJ

3.3用栈实现队列
OJ

#include<stdio.h>
#include<stdlib.h>
#include<assert.h>
#include<stdbool.h>
typedef int STDateType;
typedef struct Stack
{STDateType* a;int top;int capacity;
}ST;
//初始化
void STInit(ST* ps);
//销毁
void STDestroy(ST* ps);
//入栈
void STPush(ST* ps, STDateType x);
//出栈
void STPop(ST* ps);
//栈顶
STDateType SLTTop(ST* ps);
//计算大小
int STSize(ST* ps);
//判断是否为空
bool STEmpty(ST* ps);
//初始化
void STInit(ST* ps)
{assert(ps);ps->capacity = NULL;ps->a = 0;ps->top = 0;
}
//销毁
void STDestroy(ST* ps)
{assert(ps);free(ps->a);ps->a = NULL;ps->capacity = ps->top = 0;
}
//入栈
void STPush(ST* ps, STDateType x)
{assert(ps);if (ps->top == ps->capacity){int NewCapacity = ps->capacity == 0 ? 4 : ps->capacity * 2;STDateType* tmp = (STDateType*)realloc(ps->a, sizeof(STDateType) * NewCapacity);if (tmp == NULL){perror("realloc fail");exit(-1);}ps->a = tmp;ps->capacity = NewCapacity;}ps->a[ps->top] = x;ps->top++;
}
//出栈
void STPop(ST* ps)
{assert(ps);assert(ps->a > 0);--ps->top;
}
//栈顶
STDateType STTop(ST* ps)
{assert(ps);assert(ps->a > 0);return ps->a[ps->top - 1];
}
//计算
int STSize(ST* ps)
{assert(ps);return ps->top;
}
//判断是否为空
bool STEmpty(ST* ps)
{assert(ps);return ps->top == NULL;
}
typedef struct 
{ST pushst;ST popst;
} MyQueue;
MyQueue* myQueueCreate() 
{MyQueue* obj = (MyQueue*)malloc(sizeof(MyQueue));STInit(&obj->popst);STInit(&obj->pushst);return obj;
}void myQueuePush(MyQueue* obj, int x)
{STPush(&obj->pushst, x);
}int myQueuePeek(MyQueue* obj)
{if (STEmpty(&obj->popst)){while (!STEmpty(&obj->pushst)){STPush(&obj->popst, STTop(&obj->pushst));STPop(&obj->pushst);}}return STTop(&obj->popst);
}int myQueuePop(MyQueue* obj) 
{int front = myQueuePeek(obj);STPop(&obj->popst);return front;
}bool myQueueEmpty(MyQueue* obj) 
{return STEmpty(&obj->popst) && STEmpty(&obj->pushst);
}void myQueueFree(MyQueue* obj) 
{STDestroy(&obj->popst);STDestroy(&obj->pushst);free(obj);
}

3.4设计循环队列
OJ

#include<stdio.h>
#include<stdlib.h>
#include<assert.h>
#include<stdbool.h>
//计循环队列
typedef struct 
{int* a;int front;int rear;int k;
} MyCircularQueue;MyCircularQueue* myCircularQueueCreate(int k) 
{MyCircularQueue* obj = (MyCircularQueue*)malloc(sizeof(MyCircularQueue));obj->a = (int*)malloc(sizeof(int) * (k + 1));obj->front = obj->rear = 0;obj->k = k;return obj;
}bool myCircularQueueIsEmpty(MyCircularQueue* obj)
{return obj->front == obj->rear;
}bool myCircularQueueIsFull(MyCircularQueue* obj)
{return (obj->rear + 1) % (obj->k + 1) == obj->front;
}bool myCircularQueueEnQueue(MyCircularQueue* obj, int value)
{if (myCircularQueueIsFull(obj))return false;obj->a[obj->rear] = value;obj->rear++;obj->rear %= (obj->k + 1);return true;
}bool myCircularQueueDeQueue(MyCircularQueue* obj) 
{if (myCircularQueueIsEmpty(obj))return false;obj->front++;obj->front %= (obj->k + 1);return true;
}int myCircularQueueFront(MyCircularQueue* obj) 
{if (myCircularQueueIsEmpty(obj))return -1;return obj->a[obj->front];
}int myCircularQueueRear(MyCircularQueue* obj)
{if (myCircularQueueIsEmpty(obj))return -1;return obj->a[(obj->rear + obj->k) % (obj->k + 1)];
}void myCircularQueueFree(MyCircularQueue* obj)
{free(obj->a);free(obj);
}

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