栈与队列

本文总阅读量次

10.6栈与队列

栈

栈不存在的条件：base == NULL;
栈为空的条件： base == top;
栈满的条件：top-base == stacksize;

  1. 初始化栈

  2. 获取栈顶元素 top()

  3. 入栈 push()

  4. 出栈 pop()

练习一：十进制n转为r进制数

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int n,d,r;
std::stack<int>(s);
std::cin>>n>>r;
while (n!=0){
    d = n%r;
    n = n/r;
    s.push(d);
}
while (!s.empty()){
    std::cout<<s.top();
    s.pop();
}

练习二：括号匹配

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char a[20];
std::stack<char>(s);
cin>>a;
for (int i = 0; a[i] != '\0'; ++i) {
    if (s.empty()){
        s.push(a[i]);
    } else if (((s.top() == '(')&&(a[i] == ')'))||((s.top() == '[')&&(a[i] == ']'))||((s.top() == '{')&&(a[i] == '}'))){
        s.pop();
    } else if (a[i] == '('||a[i] == '['||a[i] == '{'){
        s.push(a[i]);
    }
}
if (s.empty()){
    cout<<"YES";
} else{
    cout<<"NO";
}

10.9 队列

队列

空队列：front == rear
满队列：(rear + 1) % max == front

  1. 循环队列的初始化

  2. 入队

  3. 出队

10.9 上机

栈与队列的基本操作（内含进制转换与括号匹配[STL模版]）

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#include <iostream>
#include <stack>
//#include <queue>
#include <iomanip>

#pragma GCC optimize(2)

using namespace std;

typedef struct node {
    int data;
    node *next;
}Qnode,Snode;

typedef struct{
    Qnode *rear,*front;
}Qlink;

typedef struct{
    Snode *base,*top;
}Slink;

void InitStack(Slink &s){
    s.top = s.base = NULL;
}

void push(Slink &s,int n){
    Snode *p;
    p = new (Snode);
    p->data = n;
    p->next = NULL;
    if (s.base == NULL){
        s.top = s.base = p;
    } else{
        s.top->next = p;
        s.top = p;
    }
}

void pop(Slink &s){
    Snode *p;
    p = s.base;
    if ((s.base == s.top)&&(s.base != NULL)){
        free(s.base);
        s.base = s.top = NULL;
        return;
    }
    while (p->next != s.top) p = p->next;
    s.top = p;
    free(p->next);
    p->next =NULL;
}

int top(Slink s){
    return s.top->data;
}

int empty(Slink s){
    if (s.base == NULL)
        return 1;
    else
        return 0;
}

void InitQue(Qlink &q){
    Qnode *p = new (node);
    p->next = NULL;
    q.rear = q.front = p;
}

void InsertQue(Qlink &q,int n){
    Qnode *p = new (node);
    p->data = n;
    p->next = NULL;
    q.rear->next = p;
    q.rear = p;
}

void DelQue(Qlink &q,int &e){
    if (q.front == q.rear){
        return;
    }
    Qnode *p;
    p = q.front;
    e = q.front->next->data;
    q.front = q.front->next;
    free(p);
}

void PrintQue(Qlink q){
    Qnode *p;
    p = q.front->next;
    while (p != NULL){
        cout<<p->data<<" ";
        p = p->next;
    }
}

int main() {
    int temp;
    Qlink q;
    InitQue(q);
    cin>>temp;
    for (int i = 0; i < temp; ++i) {
        InsertQue(q,rand()%100);
    }
    cout<<"输出队列："<<endl;
    PrintQue(q);
    DelQue(q,temp);
    cout<<endl;
    cout<<"出队元素：";
    cout<<temp<<endl;
    cout<<"出队后队列："<<endl;
    PrintQue(q);
    cout<<endl;
    //TODO:
    Slink s;
    InitStack(s);
    cin>>temp;
    for (int i = 0; i < temp; ++i) {
        push(s,rand()%100);
    }
    cout<<"压栈完成："<<endl;
    for (int i = 0; i < temp; ++i) {
        int t = top(s);
        cout<<t<<" ";
        pop(s);
    }
    cout<<endl;
    int n,r,d;
    cout<<"进制转换,输入十进制数n与目标进制r:"<<endl;
    InitStack(s);
    cin>>n>>r;
    while (n!=0){
        d = n%r;
        n = n/r;
        push(s,d);
    }
    cout<<"转换完成：";
    while (!empty(s)){
        std::cout<<top(s);
        pop(s);
    }
    cout<<"("<<r<<")"<<endl;
    cout<<"括号匹配，输入一行括号："<<endl;
    char a[100];
    stack<char>(S);
    cin>>a;
    for (int i = 0; a[i] != '\0'; ++i) {
        if (S.empty()){
            S.push(a[i]);
        } else if (((S.top() == '(')&&(a[i] == ')'))||((S.top() == '[')&&(a[i] == ']'))||((S.top() == '{')&&(a[i] == '}'))){
            S.pop();
        } else if (a[i] == '('||a[i] == '['||a[i] == '{'){
            S.push(a[i]);
        }
    }
    if (S.empty()){
        cout<<"YES";
    } else{
        cout<<"NO";
    }
}


/*
 * //TODO:进制转换
 *     int n,d,r;
    stack<int>(s);
    cin>>n>>r;
    while (n!=0){
        d = n%r;
        n = n/r;
        s.push(d);
    }
    while (!s.empty()){
        std::cout<<s.top();
        s.pop();
    }
*/

/*
 * //TODO:括号匹配
 * char a[20];
    stack<char>(s);
    cin>>a;
    for (int i = 0; a[i] != '\0'; ++i) {
        if (s.empty()){
            s.push(a[i]);
        } else if (((s.top() == '(')&&(a[i] == ')'))||((s.top() == '[')&&(a[i] == ']'))||((s.top() == '{')&&(a[i] == '}'))){
            s.pop();
        } else if (a[i] == '('||a[i] == '['||a[i] == '{'){
            s.push(a[i]);
        }
    }
    if (s.empty()){
        cout<<"YES";
    } else{
        cout<<"NO";
    }
*/

栈实现计算表达式的值

``使用STL模版```

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#include<iostream>
#include<cstdio>
#include<cctype>
#include<stack>

#pragma GCC optimize(2)

using namespace std;

//stack<char> OPTR;
//stack<double> OPND;

typedef struct node {
    char data;
    node *next;
}Qnode,Snode;

typedef struct Cnode {
    int data;
    Cnode *next;
}SnodeC;

typedef struct{
    Qnode *rear,*front;
}Qlink;

typedef struct{
    SnodeC *base,*top;
}SlinkC;

typedef struct {
    Snode *base, *top;
}Slink;

template<class T>
void InitStack(T &s){
    s.top = s.base = NULL;
}

//void InitStack(Slink &s){
//    s.top = s.base = NULL;
//}
//
//void InitStack(SlinkC &s){
//    s.top = s.base = NULL;
//}

void push(Slink &s,int n){
    Snode *p;
    p = new (Snode);
    p->data = n;
    p->next = NULL;
    if (s.base == NULL){
        s.top = s.base = p;
    } else{
        s.top->next = p;
        s.top = p;
    }
}

void push(SlinkC &s,char n){
    SnodeC *p;
    p = new (SnodeC);
    p->data = n;
    p->next = NULL;
    if (s.base == NULL){
        s.top = s.base = p;
    } else{
        s.top->next = p;
        s.top = p;
    }
}

void pop(Slink &s){
    Snode *p;
    p = s.base;
    if ((s.base == s.top)&&(s.base != NULL)){
        free(s.base);
        s.base = s.top = NULL;
        return;
    }
    while (p->next != s.top) p = p->next;
    s.top = p;
    free(p->next);
    p->next =NULL;
}

void pop(SlinkC &s){
    SnodeC *p;
    p = s.base;
    if ((s.base == s.top)&&(s.base != NULL)){
        free(s.base);
        s.base = s.top = NULL;
        return;
    }
    while (p->next != s.top) p = p->next;
    s.top = p;
    free(p->next);
    p->next =NULL;
}

int top(Slink s){
    return s.top->data;
}

char top(SlinkC s){
    return s.top->data;
}

template<class T>
int empty(T s){
    if (s.base == NULL)
        return 1;
    else
        return 0;
}

int getIndex(char theta)        //中文"（"与"）"不可用
{
    int index = 0;
    switch (theta)
    {
        case '+':
            index = 0;
            break;
        case '-':
            index = 1;
            break;
        case '*':
            index = 2;
            break;
        case '/':
            index = 3;
            break;
        case '(':
            index = 4;
            break;
        case ')':
            index = 5;
            break;
        case '#':
            index = 6;
        default:break;
    }
    return index;
}

char Precede(char theta1, char theta2)
{
    const char priority[][7] =          //优先度
            {
                    { '>','>','<','<','<','>','>' },
                    { '>','>','<','<','<','>','>' },
                    { '>','>','>','>','<','>','>' },
                    { '>','>','>','>','<','>','>' },
                    { '<','<','<','<','<','=','0' },
                    { '>','>','>','>','0','>','>' },
                    { '<','<','<','<','<','0','=' },
            };

    int index1 = getIndex(theta1);
    int index2 = getIndex(theta2);
    return priority[index1][index2];
}

double calculate(double b, char theta, double a)
{
    switch (theta)
    {
        case '+':
            return b + a;
        case '-':
            return b - a;
        case '*':
            return b * a;
        case '/':
            return b / a;
        default:
            break;
    }
}

double getAnswer(SlinkC &OPTR,Slink &OPND)
{
    push(OPTR,'#');
    int counter = 0;            //用来记录数字的位数
    char c = getchar();
    while (c != '#' || top(OPTR) != '#')
    {
        if (isdigit(c))     //判断是否是数字
        {
            if (counter == 1)
            {
                double t = top(OPND);      //保留栈顶
                pop(OPND);
                push(OPND,t * 10 + (c - '0'));
                counter = 1;
            }
            else
            {
                push(OPND,c - '0');
                counter++;          //第二位也是数字，则counter变为1，弹出原有数字并压入新的数字
            }
            c = getchar();
        }
        else
        {
            counter = 0;        //数字结束
            switch (Precede(top(OPTR), c))
            {
                case '<':
                    push(OPTR,c);
                    c = getchar();
                    break;
                case '=':
                    pop(OPTR);
                    c = getchar();
                    break;
                case '>':
                    char theta = top(OPTR);
                    pop(OPTR);
                    double a = top(OPND);
                    pop(OPND);
                    double b = top(OPND);
                    pop(OPND);
                    push(OPND,calculate(b, theta, a));
            }
        }
    }
    return top(OPND);
}

template<class T>
void clearstack(T s)      //清空栈
{
    while (!empty(s))
        pop(s);
}


int main()
{
    Slink OPND;
    SlinkC OPTR;
    InitStack(OPND);
    InitStack(OPTR);
    int t;
    cin >> t;
    getchar();
    while (t--)
    {
        clearstack(OPND);
        clearstack(OPTR);
        double ans = getAnswer(OPTR,OPND);
        cout << ans << endl<< endl;
        getchar();
    }
    return 0;
}

未使用STL，正常做法

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#include<iostream>
#include<cstdio>
#include<cctype>
#include<stack>

#pragma GCC optimize(2)

using namespace std;

stack<char> OPTR;
stack<double> OPND;

int getIndex(char theta)        //将运算符转为下标
{
    int index = 0;
    switch (theta)
    {
        case '+':
            index = 0;
            break;
        case '-':
            index = 1;
            break;
        case '*':
            index = 2;
            break;
        case '/':
            index = 3;
            break;
        case '(':
            index = 4;
            break;
        case ')':
            index = 5;
            break;
        case '#':
            index = 6;
        default:break;
    }
    return index;
}

char Precede(char theta1, char theta2)          //计算优先度
{
    const char priority[][7] =
            {
                    { '>','>','<','<','<','>','>' },
                    { '>','>','<','<','<','>','>' },
                    { '>','>','>','>','<','>','>' },
                    { '>','>','>','>','<','>','>' },
                    { '<','<','<','<','<','=','0' },
                    { '>','>','>','>','0','>','>' },
                    { '<','<','<','<','<','0','=' },
            };

    int index1 = getIndex(theta1);
    int index2 = getIndex(theta2);
    return priority[index1][index2];
}

double calculate(double b, char theta, double a)        //根据theta计算结果
{
    switch (theta)
    {
        case '+':
            return b + a;
        case '-':
            return b - a;
        case '*':
            return b * a;
        case '/':
            return b / a;
        default:
            break;
    }
}

double getAnswer()
{
    OPTR.push('#');
    int counter = 0;
    char c = getchar();
    while (c != '#' || OPTR.top() != '#')
    {
        if (isdigit(c))         //如果是数字则进入OPND栈中
        {
            if (counter == 1)       //可能为两位数或者是更多位数，所以要先判断前一个数是否为数字
            {
                double t = OPND.top();
                OPND.pop();
                OPND.push(t * 10 + (c - '0'));
                counter = 1;
            }
            else
            {
                OPND.push(c - '0');
                counter++;
            }
            c = getchar();
        }
        else        //如果是运算符，则判断
        {
            counter = 0;
            switch (Precede(OPTR.top(), c))
            {
                case '<':
                    OPTR.push(c);
                    c = getchar();
                    break;
                case '=':
                    OPTR.pop();
                    c = getchar();
                    break;
                case '>':
                    char theta = OPTR.top();
                    OPTR.pop();
                    double a = OPND.top();          //计算a与b运算的值，并将运算得到的结果压入栈中
                    OPND.pop();
                    double b = OPND.top();
                    OPND.pop();                     //弹出a，b，并将运算结果存入
                    OPND.push(calculate(b,theta,a));
            }
        }
    }
    return OPND.top();
}

void clearstack()       //清空栈
{
    while (!OPTR.empty())
        OPTR.pop();
    while (!OPND.empty())
        OPND.pop();
}

int main()
{
    int t;
    cin >> t;
    getchar();
    while (t--)
    {
        clearstack();
        double ans = getAnswer();
        cout << ans << endl<< endl;
        getchar();
    }
    return 0;
}
逆波兰表达式、波兰表达式