中缀表达式转后缀表达式c语言实现

Posted 2020-07-05

1.运行环境：VS2015/Win7

2.头文件：

stack.h

 1 typedef char ElementType;
 2 /* START:  */
 3 #ifndef _Stack_h
 4 #define _Stack_h
 5 
 6 struct StkNode;
 7 typedef struct StkNode *PtrStk;
 8 typedef PtrStk Stack;
 9 
10 int IsEmpty(Stack S);
11 Stack CreateStack(void);
12 void DisposeStack(Stack S);
13 void MakeEmpty(Stack S);
14 void Push(ElementType X, Stack S);
15 ElementType Top(Stack S);
16 void Pop(Stack S);
17 ElementType GetTopAndPop(Stack S);
18 #endif  /* _Stack_h */
19 
20 /* END */

postfix.h

 1 #include<stdio.h>
 2 #include"stack.h"
 3 #define IS_OPERATOR 1
 4 #define IS_OPEN_PARENTHESIS 2
 5 #define IS_CLOSE_PARENTHESIS 3
 6 
 7 int IsOperator(ElementType Elem);
 8 void OutPut(ElementType Elem);
 9 int IsLowerOrEqual(ElementType TopElem, ElementType Elem);
10 int Judge(ElementType Elem);
11 void OutPutPostfix(ElementType X,Stack S);

 

3.实现文件：

stack.c

 1 #include "stack.h"
 2 #include<stdio.h>
 3 #include<stdlib.h>
 4 
 5 struct StkNode
 6 {
 7     ElementType Element;
 8     PtrStk Next;
 9 };
10 
11 int IsEmpty(Stack S)
12 {
13     return S->Next == NULL;
14 }
15 
16 Stack CreateStack(void)
17 {
18     Stack S;
19 
20     S = malloc(sizeof(struct StkNode));
21     if (S == NULL)
22         printf("Out of Memory");
23 
24     S->Next = NULL;
25     MakeEmpty(S);
26     return S;
27 }
28 void DisposeStack(Stack S)
29 {
30     MakeEmpty(S);
31     free(S);
32 }
33 void MakeEmpty(Stack S)
34 {
35     while (S->Next != NULL)
36     {
37         Pop(S);
38     }
39     S->Element = 0;
40 }
41 void Push(ElementType X, Stack S)
42 {
43     PtrStk tmpCell;
44     tmpCell = malloc(sizeof(struct StkNode));
45     tmpCell->Element = X;
46 
47     //表顶端插入实现Push;
48     tmpCell->Next = S->Next;
49     S->Next = tmpCell;
50 
51 }
52 ElementType Top(Stack S)
53 {
54     if (!IsEmpty(S))
55     {
56      return S->Next->Element;
57     }
58     else
59     {
60         return NULL;
61     }
62     
63 
64 }
65 void Pop(Stack S)
66 {
67     if (IsEmpty(S))
68     {
69         printf("Empty Stack !");
70     }
71     else
72     {
73         PtrStk tmpCell = S->Next;//标记栈顶结点
74         S->Next = tmpCell->Next;//指向新栈顶结点
75         free(tmpCell);//释放标记结点
76     }
77 }

postfix.c

  1 #include<stdio.h>
  2 #include"postfix.h"
  3 
  4 
  5 int IsOperator(ElementType Elem)
  6 {
  7     return Elem == ‘+‘ || Elem == ‘-‘ || Elem == ‘*‘ || Elem == ‘/‘;
  8 }
  9 
 10 void OutPut(ElementType Elem)
 11 {
 12     printf("%c", Elem);
 13 }
 14 
 15 //设置运算符优先级
 16 int IsLowerOrEqual(ElementType TopElem, ElementType Elem)
 17 {
 18     if (TopElem == ‘(‘) return 0;
 19     if (TopElem == ‘+‘&& Elem == ‘-‘) return 1;
 20     if (TopElem == ‘+‘&& Elem == ‘+‘) return 1;
 21     if (TopElem == ‘-‘&& Elem == ‘+‘) return 1;
 22     if (TopElem == ‘-‘&& Elem == ‘-‘) return 1;
 23     if (TopElem == ‘*‘&& Elem == ‘*‘) return 1;
 24     if (TopElem == ‘*‘&& Elem == ‘/‘) return 1;
 25     if (TopElem == ‘*‘&& Elem == ‘+‘) return 1;
 26     if (TopElem == ‘*‘&& Elem == ‘-‘) return 1;
 27     if (TopElem == ‘/‘&& Elem == ‘*‘) return 1;
 28     if (TopElem == ‘/‘&& Elem == ‘/‘) return 1;
 29     if (TopElem == ‘/‘&& Elem == ‘+‘) return 1; 
 30     if (TopElem == ‘/‘&& Elem == ‘-‘) return 1;
 31     return 0;
 32 
 33 }
 34 
 35 //返回元素类型
 36 int Judge(ElementType Elem)
 37 {
 38     if (IsOperator(Elem)) return IS_OPERATOR;//运算符
 39     else if (Elem == ‘(‘) return IS_OPEN_PARENTHESIS;//左圆括号
 40     else if (Elem == ‘)‘) return IS_CLOSE_PARENTHESIS;//右圆括号
 41 
 42 }
 43 
 44 //输入：中缀表达式的字符串；栈
 45 //输出：打印后缀表达式
 46 void OutPutPostfix(ElementType *Str, Stack S)
 47 {
 48     for (int i = 0; Str[i] != ‘\\0‘; i++)
 49     {
 50         switch (Judge(Str[i]))
 51         {
 52             //检测到左括号则入栈
 53         case IS_OPEN_PARENTHESIS:
 54             Push(Str[i], S); break;
 55 
 56             //检测到为右括号，则打印栈内运算符并出栈，直至栈顶元素匹配到左括号
 57         case IS_CLOSE_PARENTHESIS:
 58             do
 59             {
 60                 OutPut(Top(S));
 61                 Pop(S);
 62             } while (Judge(Top(S)) != IS_OPEN_PARENTHESIS);
 63             Pop(S);//弹出左圆括号；
 64             break;
 65 
 66             //检测到为运算符，若优先级比栈内运算符小则将栈内运算符打印并出栈，直至栈空或栈顶元素为左括号；
 67         case IS_OPERATOR:
 68             if (IsLowerOrEqual(Top(S), Str[i]) && !IsEmpty(S))
 69             {
 70                 do {
 71                     OutPut(Top(S));
 72                     Pop(S);
 73                 } while (Judge(Top(S)) != IS_OPEN_PARENTHESIS && !IsEmpty(S));
 74             }
 75             Push(Str[i], S);//将运算符压栈
 76             break;
 77 
 78             //检测到为操作数，则直接打印
 79         default: OutPut(Str[i]); break;
 80         }
 81 
 82     }
 83     
 84     //打印栈内剩下的运算符
 85     while (!IsEmpty(S))
 86     {
 87         OutPut(Top(S));
 88         Pop(S);
 89     }
 90 
 91 }

 

4.测试demo：

 1 #include<stdio.h>
 2 #include"stack.h"
 3 #include "postfix.h"
 4 
 5 int main()
 6 {
 7 
 8 printf("*****************************************************\\n");
 9 printf("此demo实现功能：中缀表达式转换为后缀表达式\\n");
10 printf("注意：输入的表达式必须为合法的；\\n");
11 printf("示例：\\n");
12 printf("input:  a+b*c+(d*e+f)*g\\n");
13 printf("output: abc*+de*f+g*+\\n");
14 printf("*****************************************************\\n");
15 printf("请输入中缀表达式：");
16 
17 ElementType str[100];
18 scanf_s("%s", str,100);
19 Stack S = CreateStack();
20 OutPutPostfix(str, S);
21 DisposeStack(S);
22 getchar();
23 
24 return 0;

5.输出结果：