目录
参考资料
迷宫探路
顺序栈头文件SqStack.h
顺序栈函数实现SqStack.cpp
迷宫探路主函数
表达式求值
链式顺序栈头文件LinkStack.h
链式顺序栈函数实现LinkStack.cpp
表达式求值主函数
测试结果
参考资料
数据结构严蔚敏版
2021-9-22【数据结构/严蔚敏】【顺序栈&链式栈&迷宫求解&表达式求值】【代码实现算法3.1-3.5】_数据结构表达式求值代码严老师-CSDN博客
栈和队列-数据结构与算法(C语言版)_调用pop(&s,&e)函数,让队头数据出队,赋值给参数e,printf输出e-CSDN博客
迷宫探路
顺序栈头文件SqStack.h
#pragma once
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>#define TRUE 1
#define FALSE 0
#define OK 1
#define ERROR 0
#define INFEASIBLE -1
#define OVERFLOW -2
typedef int Status;//Status是函数的类型，其值是函数结果状态代码/*宏函数*/
//函数暂停一段时间
#define Wait(x)\{\double _Loop_Num_;\for(_Loop_Num_=0.01; _Loop_Num_<=100000.0*x; _Loop_Num_+=0.01)\;\}//设立一个空循环 typedef struct {int x;int y;
}PosType;//坐标位置
typedef struct {int ord; //通道块在路径上的“序号”PosType seat; //通道块在迷宫中的“坐标位置”int di; //从此通道块走向下一通道块的“方向”
}SElemType;//-----栈的顺序存储表示-----
#define STACK_INIT_SIZE 100 //存储空间初始分配量
#define STACKINCREMENT 10 //存储空间分配增量
typedef struct SqStack {SElemType* base;//在栈构造之前和销毁之后，base的值为NULLSElemType* top; //栈顶指针int stacksize; //当前已分配的存储空间，以元素为单位
}SqStack;
//-----基本操作的函数原型说明-----
Status InitStack(SqStack& S);
//构造一个空栈S
Status DestroyStack(SqStack& S);
//销毁栈S，S不再存在
Status ClearStack(SqStack& S);
//把S置为空栈
Status StackEmpty(SqStack S);
//若栈S为空栈，则返回TRUE,否则返回FALSE
int StackLength(SqStack S);
//返回S的元素个数，即栈的长度
Status GetTop(SqStack S, SElemType& e);
//若栈不空，则用e返回S的栈顶元素，并返回OK；否则返回ERROR
Status Push(SqStack& S, SElemType e);
//插入元素e为新的栈顶元素
Status Pop(SqStack& S, SElemType& e);
//若栈不空，则删除S的栈顶元素，用e返回其值，并返回OK；否则返回ERROR
Status StackTraverse(SqStack S, void(*visit)(SElemType));
//从栈顶到栈底依次对栈中每个元素调用函数visit()。一旦visit()失败，则操作失败顺序栈函数实现SqStack.cpp
#include "SqStack.h"//-----基本操作的函数算法描述（部分）-----
Status InitStack(SqStack& S) {//构造一个空栈SS.base = (SElemType*)malloc(STACK_INIT_SIZE * sizeof(SElemType));if (!S.base)exit(OVERFLOW);//存储分配失败，警告C6011S.top = S.base;S.stacksize = STACK_INIT_SIZE;return OK;
}Status DestroyStack(SqStack& S) {free(S.base);S.top = S.base = NULL;S.stacksize = 0;return OK;
}Status ClearStack(SqStack& S) {if (!S.base)return ERROR;S.top = S.base;return OK;
}Status StackEmpty(SqStack S) {if (S.base == S.top)return OK;return ERROR;
}int StackLength(SqStack s) {if (!s.base)return ERROR;return (int)(s.top - s.base);
}Status GetTop(SqStack s, SElemType& e) {//若栈不空，则用e返回S的栈顶元素，并返回OK；否则返回ERRORif (s.base == s.top)return ERROR;e = *(s.top - 1);return OK;
}Status Push(SqStack& s, SElemType e) {//插入元素e为新的栈顶元素if (!s.base)return ERROR;if (s.top - s.base >= s.stacksize) {//栈满，追加存储空间s.base = (SElemType*)realloc(s.base, (s.stacksize + STACKINCREMENT) * sizeof(SElemType));if (!s.base)exit(_OVERFLOW);//存储分配失败s.top = s.base + s.stacksize;s.stacksize += STACKINCREMENT;}*s.top++ = e;//*s.top=e; s.top++;return OK;
}Status Pop(SqStack& s, SElemType& e) {//若栈不空，则删除S的栈顶元素，用e返回其值，并返回OK；否则返回ERRORif (!s.base || s.top == s.base) return ERROR;e = *--s.top;//--s.top; e=*s.top;return OK;
}Status StackTraverse(SqStack s, void (*visit)(SElemType)) {SElemType* p = s.base;if (!s.base)return ERROR;while (p < s.top)visit(*p++);printf("\n");return OK;
}迷宫探路主函数
#include "SqStack.h"#define MAXSIZE 15
#define X 4
#define SleepTime 3
/* 迷宫类型定义 */
typedef enum {Wall, // 外墙Obstacle, // 迷宫内部障碍Way, // 通路Impasse, // 死胡同East, South, West, North //当前探索方向：东南西北
} CellType;typedef int MazeType[MAXSIZE][MAXSIZE];//用到的函数
SElemType Construct(int ord, PosType seat, int di);
//创建通道块信息并返回，序号、坐标位置和下一个访问方向
PosType NextPos(PosType seat, int di);
//获得下一个应当探索的位置
Status MazePath(MazeType maze, PosType start, PosType end);
//迷宫寻路主函数，第一个变量类型为int*，是地图的首地址。
void InitMaze(MazeType maze, PosType& start, PosType& end);
//初始化迷宫，start和end分别为迷宫的入口坐标和出口坐标
Status Pass(MazeType maze, PosType seat);
//判断当前位置是否为首次探索
void FootPrint(MazeType maze, PosType seat);
//留下初始访问足迹，初始访问足迹即向东访问
void MarkPrint(MazeType maze, PosType seat, int mark);
//留下标记+绘制迷宫
Status Equals(PosType a, PosType b);
//比较两个结构体
void PaintMaze(MazeType maze);
//绘制迷宫，以图形的方式呈现迷宫当前的状态Status MazePath(MazeType maze, PosType start, PosType end) {//若迷宫maze中存在从入口start到出口end的通道，则求得一条存放在栈中//（从栈底到栈顶），并返回TRUE；否则返回FALSESqStack S; //存储探索过的通道块PosType curpos; //当前位置SElemType e; //当前通道块信息int curstep; //当前通道块序号InitStack(S);curpos = start;//设定“当前位置”为“入口位置”curstep = 1; //探索第一步do {if (Pass(maze, curpos)) {//当前位置可以通过，即是未曾走到过的通道块FootPrint(maze, curpos);//留下足迹e = Construct(curstep, curpos, East);Push(S, e); //加入路径if (Equals(curpos, end) == TRUE) {printf("\n寻路成功\n\n");return TRUE; //到达终点(出口)}curpos = NextPos(curpos, East);//下一位置是当前位置的东邻curstep++; //探索下一步}else {//当前位置不能通过if (!StackEmpty(S)) {Pop(S, e);while (e.di == North && !StackEmpty(S)) {MarkPrint(maze, e.seat, Impasse);Pop(S, e);}if (e.di < North) {e.di++;MarkPrint(maze, e.seat, e.di);Push(S, e);curpos = NextPos(e.seat, e.di);//不需要curstep++，因为还是上次入栈的位置块}}}} while (!StackEmpty(S));printf("\n寻路失败！！\n\n");return FALSE;
}//初始化一个规模为N*N迷宫
//start和end分别为迷宫的入口坐标和出口坐标
//注：教材中无此操作，但该操作是必须存在的
void InitMaze(MazeType maze, PosType& start, PosType& end) {int i, j, tmp;srand((unsigned)time(NULL));//用系统时间做随机数种子for (i = 0;i < MAXSIZE;i++) {for (j = 0;j < MAXSIZE;j++) {//边缘部分设置围墙if (i == 0 || j == 0 || i == MAXSIZE - 1 || j == MAXSIZE - 1) {maze[i][j] = Wall;}else {//生成随机数[0,X-1]填充迷宫tmp = rand() % X;//1/X之一的概率生成障碍，否则生成通路块if (tmp == 0)maze[i][j] = Obstacle;elsemaze[i][j] = Way;}}}//迷宫内部设障完毕start.x = 1;start.y = 0;end.x = MAXSIZE - 2;end.y = MAXSIZE - 1;maze[1][0] = maze[MAXSIZE - 2][MAXSIZE - 1] = Way;//显示迷宫的初始状态PaintMaze(maze);
}Status Pass(MazeType maze, PosType seat) {int x = seat.x;int y = seat.y;if (x<0 || y<0 || x>MAXSIZE - 1 || y>MAXSIZE - 1)return FALSE;if (maze[x][y] != Way)return FALSE;return TRUE;
}PosType NextPos(PosType seat, int di) {PosType tmp = seat;switch (di) {case East:tmp.y++;//向东break;case South:tmp.x++;//向东break;case West:tmp.y--;//向东break;case North:tmp.x--;//向东break;}return tmp;
}void FootPrint(MazeType maze, PosType seat) {MarkPrint(maze, seat, East);
}void MarkPrint(MazeType maze, PosType seat, int mark) {maze[seat.x][seat.y] = mark;PaintMaze(maze);
}SElemType Construct(int ord, PosType seat, int di) {SElemType e;e.di = di;e.seat = seat;e.ord = ord;return e;
}Status Equals(PosType a, PosType b) {if (a.x == b.x && a.y == b.y)return TRUE;elsereturn FALSE;
}
/** 绘制迷宫* 以图形的方式呈现迷宫当前的状态**【注】* 教材中无此操作* 此处增加该操作的目的是观察寻路过程的每一步*/
void PaintMaze(MazeType maze) {int i, j;Wait(SleepTime);system("cls"); //清空，下面是重新打印for (i = 0; i < MAXSIZE; i++) {for (j = 0; j < MAXSIZE; j++) {if (maze[i][j] == Wall) { // 外墙printf("▇");}else if (maze[i][j] == Obstacle) { // 迷宫内部的障碍printf("X");}else if (maze[i][j] == East) { // 正在朝东探索printf("→");}else if (maze[i][j] == South) { // 正在朝南探索printf("↓");}else if (maze[i][j] == West) { // 正在朝西探索printf("←");}else if (maze[i][j] == North) { // 正在朝北探索printf("↑");}else if (maze[i][j] == Impasse) { // 死胡同，即四个方向都探索过，但无法通过的位置printf("★");}else { // 还未探索过的路径结点printf(" ");}if (j != 0 && j % (MAXSIZE - 1) == 0) { // 每隔N个结点换行printf("\n");}}}printf("\n");
}int main(int argc, char* argv[]){MazeType maze;PosType start, end;char ch,Re = 'Y';while (Re == 'Y' || Re == 'y') {InitMaze(maze, start, end); // 初始化迷宫，包括出入口MazePath(maze, start, end); // 迷宫寻路printf("重置？（Y/N）：");scanf_s("%c", &Re, 1);ch = getchar();printf("\n");}return 0;
}表达式求值
链式顺序栈头文件LinkStack.h
#pragma once
#pragma once
#include <cstdio>
#include <cstdlib>
#include <cstring>#define TRUE 1
#define FALSE 0
#define OK 1
#define ERROR 0
#define INFEASIBLE -1
#define OVERFLOW -2
typedef int Status;//Status是函数的类型，其值是函数结果状态代码
typedef char SElemType;//-----栈的顺序存储表示-----
#define STACK_INIT_SIZE 100 //存储空间初始分配量
#define STACKINCREMENT 10 //存储空间分配增量
typedef struct SNode {SElemType data;//数据域struct SNode* next;//
}SNode,*LinkStack;
//-----基本操作的函数原型说明-----
Status InitStack(LinkStack& S);
//构造一个空栈S
Status DestroyStack(LinkStack& S);
//销毁栈S，S不再存在
Status ClearStack(LinkStack& S);
//把S置为空栈
Status StackEmpty(LinkStack S);
//若栈S为空栈，则返回TRUE,否则返回FALSE
int StackLength(LinkStack S);
//返回S的元素个数，即栈的长度
Status GetTop(LinkStack S, SElemType& e);
//若栈不空，则用e返回S的栈顶元素，并返回OK；否则返回ERROR
Status Push(LinkStack& S, SElemType e);
//插入元素e为新的栈顶元素
Status Pop(LinkStack& S, SElemType& e);
//若栈不空，则删除S的栈顶元素，用e返回其值，并返回OK；否则返回ERROR
Status StackTraverse(LinkStack S, void(*visit)(SElemType));
//从栈底到栈顶依次对栈中每个元素调用函数visit()。一旦visit()失败，则操作失败
Status StackTraverse_Top(LinkStack S, Status(*pfn_visit)(SElemType));
//从栈顶到栈底依次对栈中每个元素调用函数visit()。一旦visit()失败，则操作失败
链式顺序栈函数实现LinkStack.cpp
#include "LinkStack.h"Status InitStack(LinkStack& S) {S = (LinkStack)malloc(sizeof(SNode));if (!S)exit(OVERFLOW);S->next = NULL;return OK;
}Status DestroyStack(LinkStack& S) {LinkStack p = S->next, pp;while (p) {pp = p->next;free(p);p = pp;}free(S);return OK;
}Status ClearStack(LinkStack& S) {LinkStack p = S->next, pp;while (p) {pp = p->next;free(p);p = pp;}S->next = NULL;return OK;
}Status StackEmpty(LinkStack S) {if (S->next == NULL)return OK;elsereturn FALSE;
}int StackLength(LinkStack S) {int n = 0;LinkStack p = S->next;while (p) {n++;p = p->next;}return n;
}Status GetTop(LinkStack S, SElemType& e) {if (S->next == NULL)return ERROR;e = S->next->data;return OK;
}Status Push(LinkStack& S, SElemType e) {LinkStack p = (LinkStack)malloc(sizeof(SNode));p->data = e;p->next = S->next;S->next = p;return OK;
}Status Pop(LinkStack& S, SElemType& e) {if (S->next == NULL)return ERROR;e = S->next->data;LinkStack pp = S->next->next;free(S->next);S->next = pp;return OK;
}Status StackTraverse(LinkStack S, void(*visit)(SElemType)) {if (S->next == NULL) {printf("栈为空！\n");return ERROR;}for (int i = StackLength(S);i > 0;i--) {LinkStack p = S->next;int j = 1;while (p && j < i) {p = p->next;++j;}visit(p->data);}printf("\n");return OK;
}Status StackTraverse_Top(LinkStack S, Status(*pfn_visit)(SElemType)) {if (S->next == NULL) {printf("栈为空！\n");return ERROR;}LinkStack p = S->next;while (p) {pfn_visit(p->data);p = p->next;}printf("\n");return OK;
}表达式求值主函数
#include "LinkStack.h"
#define OperandType charStatus visit(SElemType e) {printf(" %c", e);return OK;
}//-----算法部分-----
//判定运算符栈的（栈顶运算符Θ1）与（读入的运算符Θ2）之间的优先关系SElemType Precede(SElemType t1, SElemType t2) {SElemType t;switch (t1) {case '+':case '-':if (t2 == '*' || t2 == '/' || t2 == '(')t = '<';else t = '>';break;case '*':case '/':if (t2 == '(')t = '<';else t = '>';break;case '(':if (t2 == ')')t = '=';else if (t2 == '#')return ERROR;else t = '<';break;case ')':if (t2 == '(')return ERROR;else t = '>';break;case '#':if (t2 == ')')return ERROR;else if (t2 == '#')t = '=';else t = '<';break;}return t;
}//进行二元运算aΘb
SElemType Operator(SElemType a, SElemType theta, SElemType b) {SElemType ret;switch (theta){case '+':ret = (a - 48) + (b - 48) + 48;break;case '-':ret = (a - 48) - (b - 48) + 48;break;case '*':ret = (a - 48) * (b - 48) + 48;break;case '/':ret = (a - 48) / (b - 48) + 48;break;default:return NULL;}return ret;
}Status In(SElemType c) {switch (c) {case'+':case'-':case'*':case'/':case'(':case')':case'#':case'=':return OK;break;default:return ERROR;}
}//算法3.4
OperandType EvaluateExpression() {//算术表达式求值的算符优先算法。//设OPTR和OPND分别为运算符栈和运算数栈，OP为运算符集合。LinkStack OPTR;//运算符栈：寄存运算符LinkStack OPND;//运算数栈：寄存操作数或运算结果//VS中变量上加注释，当鼠标移到下一次同变量的地方会显示注释char c, x, theta, a, b, e;InitStack(OPTR);InitStack(OPND);Push(OPTR, '#');c = getchar();GetTop(OPTR, e);while (c != '#' || e != '#') {if (!In(c)) {//运算数Push(OPND, c);c = getchar();}else {//运算符GetTop(OPTR, e);switch (Precede(e, c)) {case '<'://栈顶元素优先权低Push(OPTR, c);c = getchar();break;case '='://脱括号并接受下一个字符Pop(OPTR, x);c = getchar();break;case '>'://退栈并将运算结果入栈Pop(OPTR, theta);Pop(OPND, b);Pop(OPND, a);Push(OPND, Operator(a, theta, b));break;}}GetTop(OPTR, e);}GetTop(OPND, e);return e;
}//运算数只能是一位自然数
int main(int argc, char** argv) {char c;c = EvaluateExpression();//3*5#=15printf("%d", c - 48);return 0;
}
