堆栈之表达式求值

堆栈之表达式求值

@[.DataStructure]

文章目录

• 堆栈之表达式求值
• 1. 后缀表达式求值
• 2. 中缀表达式求值
• 数据结构动图资源

1. 后缀表达式求值

#include<iostream>
#include<cstdio>
#include<string.h>
#include<math.h>

using namespace std;

#define ElementType double
#define MAXSIZE 100
#define MAXOP 100
#define INFINITY 1e9 //表明正无穷
typedef enum {num, opr, end1} Type;

typedef struct SNode * PtrtoSNode;
struct SNode
{
	ElementType Data;
	PtrtoSNode Next;
};

typedef PtrtoSNode Stack;


bool IsEmpty(Stack S)
{
	return(S->Next == NULL);
}






Stack CreatStack()
{
	Stack S = (Stack)malloc(sizeof(struct SNode));
	S->Next = NULL;

	return S;
}




bool Push(Stack S, ElementType X)
{

	PtrtoSNode TmpCell;
	TmpCell = (PtrtoSNode)malloc(sizeof(struct SNode));
	TmpCell->Data = X;
	TmpCell->Next = S->Next;
	S->Next = TmpCell;
	return true;

}



#define Error -100

ElementType Pop(Stack S)
{
	//删除并返回栈顶元素
	PtrtoSNode FirstCell;
	ElementType TopElem;

	if (IsEmpty(S))
	{
		cout << "the stack is empty" << endl;
		return Error;
	}
	else
	{
		FirstCell = S->Next;
		TopElem = FirstCell->Data;
		S->Next = FirstCell->Next;
		free(FirstCell);
		return TopElem;

	}

}

Type GetOp(char * Expr, int * start,char * str)
{
	//从*start开始读入下一个 对象（操做数或运算符），并保存在字符串str中
	int i = 0;

	//跳过表达式前的空格
	while ((str[0] = Expr[(*start)++]) == ' ');

	while (str[i] != ' '&& str[i] != '\0')
		str[++i] = Expr[(*start)++];

	if (str[i]=='\0')
	{
		(*start)--;
	}
	str[i] = '\0';

	if (i == 0)
	{
		return end1;
	}
	else if (isdigit(str[0]) || isdigit(str[1]))
		return  num;
	else
		return opr;

}

ElementType PostfixExp(char * Expr)
{
	Stack S;
	Type T;
	ElementType Op1, Op2;
	char str[MAXOP];
	int start = 0;
	// 申请一个新堆栈
	S = CreatStack();
	Op1 = Op2 = 0;
	while ((T=GetOp(Expr, &start, str))!= end1)
	{
		if (T == num)
			Push(S, atof(str));
		else
		{
			if (!IsEmpty(S)) Op2 = Pop(S);
			else
			{
				Op2 = INFINITY;
			}

			if (!IsEmpty(S)) Op1 = Pop(S);
			else
			{
				Op2 = INFINITY;
			}

			switch (str[0])
			{
				case '+': Push(S, Op1 + Op2); break;
				case '-': Push(S, Op1 - Op2); break;
				case '*': Push(S, Op1 * Op2); break;
				case '/':
				{
					if (Op2 != 0.0)
					{
						Push(S, Op1 / Op2);
					}
					else
					{
						cout << "Error have a non-zero term in the denominator" << endl;
						Op2 = INFINITY;
					}

				}
				break;



				default:
					cout << "Unknown operator" << endl;
					Op2 = INFINITY;
					break;
			}
		
			if (Op2 >= INFINITY) break;
		}
	}

	if (Op2 < INFINITY)
	{
		if (!IsEmpty(S))
			Op2 = Pop(S);
		else
			Op2 = INFINITY;

	}

	free(S);
	return Op2;

}


int main()
{
	char Expr[MAXOP];
	ElementType f;
	gets_s(Expr);
	f = PostfixExp(Expr);
	if (f < INFINITY)
	{
		cout << f << endl;
	}
	else
	{
		cout << "the exression is illegal" << endl;
	}

	return 0;
}

2. 中缀表达式求值

数据结构动图资源

https://www.cs.usfca.edu/~galles/visualization/Algorithms.html