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【数据结构初阶】栈和队列
作者：我家自动化 | 2024-03-04 06:43:19
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【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);
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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; }
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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; }
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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);
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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; }
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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; }
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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); } }
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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); }
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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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