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【数据结构初阶】栈和队列

乘风 • • IT • 阅读 34

栈和队列

    • 1.栈
      • 1.1栈的概念和结构
      • 1.2栈的实现
    • 2.队列
      • 2.1队列的概念和结构
      • 2.2队列的实现

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);
}

💘不知不觉，【数据结构初阶】栈和队列以告一段落。通读全文的你肯定收获满满，让我们继续为数据结构学习共同奋进!!!

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