其实这个东西早在7月开始的时候我就写好了，本来想等小师妹写好了她的版本再放到网上的。。。无奈她写的实在是太慢了。这个东西还是有改进的空间的，比如升级成浮点模型啥的。
逆波兰表达式的可以以O（N）时间复杂度处理任意表达式，其实也叫后缀表达式，中缀表达式（就是我们一般看到的表达式（1+1=2）），处理的时候分两个栈，一个符号栈，一个表达式栈：
（注意我只选二元运算符为例，只处理+-*/和括号）
1. 如果遇到数字，压入表达式栈
2. 如果遇到符号
a. 如果符号是左括号，则直接压入符号栈
b. 如果是*/符号，且符号栈顶符号为+-或者( ，那么直接压入当前符号即可；如果符号栈顶为*/，弹出符号栈顶符号到表达式栈，压入当前符号。
c. 如果是+-号，如果符号栈栈顶是*/，则pop符号栈顶到最近的+-号或者（；如果是+-或者（，那就直接弹出上一个+/-号然后压入当前+/-号。
d. 遇到）就pop符号栈到（
e. 如果把中缀表达式扫完了符号栈还有东西，那么将符号栈的东西全部pop到表达式栈。
后缀转中缀是上面的逆过程，看代码就知道了。
之前有想过改成C++的，但是那段时间忙着出Qt，就没写了，这以后可能每三天就写个算法或者复习下以前的数据结构，备战下下一年的面试，就酱~
以后博客的名字就不分类型拉~感觉直接分类更快。
1 //main.c
2
3 #include <stdio.h>
4 #include "plug.h"
5 #include "stack.h"
6 #include <stdlib.h>
7 #include <string.h>
8 #include <math.h>
9 #include <assert.h>
10
11 int main(int argc, char *argv[])
12 {
13 int error_exp = 0;
14 char symnum[81] = { ‘\0‘ };
15 FILE *fp_in = fopen("D:\\input.txt", "r");
16 FILE *fp_out = fopen("D:\\output.txt", "w");
17 if (fp_in == NULL)
18 exit(1);
19
20 while (!feof(fp_in))
21 {
22 fscanf(fp_in, "%s", symnum);
23 fprintf(fp_out, " Infix expression: %s\n", symnum);
24 error_exp += scan_Infix_to_Suffix(symnum, fp_out);
25 fprintf(fp_out, "\n");
26 }
27 fprintf(fp_out, "\nSum of error expression: %d\n", error_exp);
28
29 return EXIT_SUCCESS;
30 }
31
32 int scan_Infix_to_Suffix(char *input, FILE *fp)
33 {
34 int i = 0;
35 Stack_manager *num_stack = allcoate_stack_man(),
36 *stack_man = allcoate_stack_man(),
37 *sym_man = allcoate_stack_man();
38 Stack **list = (Stack **)malloc(sizeof(Stack)*MAX);//存指向栈的指针的表
39
40 for (;input[i]!=‘\0‘;i++)
41 {
42 if (input[i] >= ‘0‘ && input[i] <= ‘9‘)
43 //把所有连续的数字先结合起来形成一个数，如果遇到符号，则把num栈转化为数字存入主栈中
44 push_in_int(num_stack, input[i] - ‘0‘);
45 //遇到‘(‘，优先级最高，直接压栈
46 else if (input[i] == ‘(‘)
47 push_in_char(sym_man, input[i]);
48 else if (input[i] == ‘*‘ || input[i] == ‘/‘)
49 {
50 //遇到乘除号，如果栈中含有（‘+‘或者‘-‘），压入符号栈
51 if (input[i - 1] != ‘)‘)
52 push_in_int(stack_man, combine_Stack_to_Num(num_stack));
53
54 //错误处理
55 if ((stack_man->top->type == is_int && input[i] == ‘/‘)//除数不能为0
56 || i == 0 //开头出现单独乘除号
57 || input[i - 1] == ‘+‘ || input[i - 1] == ‘-‘ //两个符号连续
58 || input[i - 1] == ‘*‘ || input[i - 1] == ‘/‘
59 )
60 {
61 error(sym_man, stack_man, num_stack, list, fp);
62 return 1;
63 }
64
65 if (sym_man->top == NULL
66 || (sym_man->top->sym == ‘+‘ || sym_man->top->sym == ‘-‘)
67 && sym_man->top->sym == ‘(‘)
68 //除非处理闭括号，否则看到‘(‘什么符号都压栈
69 push_in_char(sym_man, input[i]);
70
71 //否则弹出上一个乘除号
72 else if (sym_man->top->sym == ‘*‘ || sym_man->top->sym == ‘/‘)
73 {
74 push_in_char(stack_man, sym_man->top->sym);
75 pop_out(sym_man);
76 push_in_char(sym_man, input[i]);
77 }
78 }
79 else if (input[i] == ‘+‘ || input[i] == ‘-‘)
80 {
81 if (input[i - 1] != ‘(‘ && input[i - 1] != ‘)‘ && i != 0)
82 push_in_int(stack_man, combine_Stack_to_Num(num_stack));
83
84 //错误处理（开头连续两个加减号或者连续三个符号）
85 if (i == 1 && (input[i - 1] == ‘+‘ || input[i - 1] == ‘-‘))
86 {
87 error(sym_man, stack_man, num_stack, list, fp);
88 return 1;
89 }
90 if (i >= 2 && (input[i - 1] == ‘+‘ || input[i - 1] == ‘-‘)
91 && (input[i - 2] == ‘+‘ || input[i - 1] == ‘-‘ || input[i - 1] == ‘*‘ || input[i - 1] == ‘/‘
92 || input[i - 1] == ‘(‘ || input[i - 1] == ‘)‘))
93 {
94 error(sym_man, stack_man, num_stack, list, fp);
95 return 1;
96 }
97
98 //如果前一个为符号或者左括号或者没有符号，则为数的正负，压入数栈
99 if (i == 0
100 || input[i - 1] == ‘+‘ || input[i - 1] == ‘-‘
101 || input[i - 1] == ‘*‘ || input[i - 1] == ‘/‘
102 || input[i - 1] == ‘(‘)
103 push_in_char(num_stack, input[i]);
104
105 //如果有比+-优先级更高的运算符（‘*‘,‘/‘），则把符号弹出直到上一次的加减号或者‘(‘为止
106 else if (!sym_man->top
107 || sym_man->top->sym == ‘*‘ || sym_man->top->sym == ‘/‘
108 || sym_man->top->sym == ‘(‘)//符号为‘(‘的情况合并到这里了
109 {
110 for (;sym_man->top != NULL
111 && sym_man->top->sym != ‘(‘;)
112 {
113 push_in_char(stack_man, sym_man->top->sym);
114 pop_out(sym_man);
115 }
116 push_in_char(sym_man, input[i]);
117 }
118 //如果上一个符号是+-号，那么直接弹出上一个加减号到主栈，并且把当前符号压入符号栈
119 else if (sym_man->top->sym == ‘+‘ || sym_man->top->sym == ‘-‘)
120 {
121 push_in_char(stack_man, sym_man->top->sym);
122 pop_out(sym_man);
123 push_in_char(sym_man, input[i]);
124 }
125 }
126 else if (input[i] == ‘)‘)
127 {
128 push_in_int(stack_man, combine_Stack_to_Num(num_stack));
129
130 for (;sym_man->top != NULL && sym_man->top->sym != ‘(‘;)
131 {
132 push_in_char(stack_man, sym_man->top->sym);
133 pop_out(sym_man);
134 }
135 if (sym_man->top->sym != ‘(‘)//只有右括号括号，出错
136 {
137 error(sym_man, stack_man, num_stack, list, fp);
138 return 1;
139 }
140 pop_out(sym_man);//弹掉‘(‘
141 }
142 else//其他情况均为不合法的情况，out
143 {
144 error(sym_man, stack_man, num_stack, list, fp);
145 return 1;
146 }
147 }
148 //最后应该还有一个数字的
149 if (input[i - 1] != ‘)‘)
150 push_in_int(stack_man, combine_Stack_to_Num(num_stack));
151
152 //把剩下的符号弹入栈中
153 for (;sym_man->top!=NULL;)
154 {
155 if (sym_man->top->sym == ‘(‘)//只有左括号，出错
156 {
157 error(sym_man, stack_man, num_stack, list, fp);
158 return 1;
159 }
160 push_in_char(stack_man, sym_man->top->sym);
161 pop_out(sym_man);
162 }
163 copy_Stack_to_List(list, stack_man);
164 print_list(list, stack_man->node_sum, fp);
165 caculate_Infix(list, stack_man->node_sum,fp);
166
167 //正常退出
168 delete_stack(&sym_man);
169 delete_stack(&stack_man);
170 delete_stack(&num_stack);
171 free(list);
172 return 0;
173 }
174
175 int combine_Stack_to_Num(Stack_manager *const num_stack)
176 {
177 int sum = 0, num_pow = 0;
178 for (;num_stack->top != NULL;)
179 {
180 if (num_stack->top->type == is_int)
181 sum += (int)(num_stack->top->num*pow(10.0, (double)num_pow++));
182 else
183 sum = num_stack->top->sym == ‘+‘ ? sum : -sum;
184 pop_out(num_stack);
185 }
186 return sum;
187 }
188
189 void copy_Stack_to_List(Stack **const list, Stack_manager *const stack_man)
190 {
191 int j = stack_man->node_sum - 1;
192 Stack *tmp = stack_man->top;
193 for (;j != -1;j--, tmp = tmp->prev)
194 list[j] = tmp;
195 }
196
197 void get_Ans(Stack_manager *const s, char operation)
198 {
199 assert(s->top != NULL || s->top->prev != NULL);
200 int tmp1 = s->top->num, tmp2 = s->top->prev->num, ans;
201 if (operation == ‘+‘)
202 ans = tmp1 + tmp2;
203 else if (operation == ‘-‘)
204 ans = tmp2 - tmp1;
205 else if (operation == ‘*‘)
206 ans = tmp1*tmp2;
207 else if (operation == ‘/‘)
208 ans = tmp2 / tmp1;
209 //连续pop两次，把tmp1和tmp2弹出去
210 pop_out(s); pop_out(s);
211 //把答案压栈
212 push_in_int(s, ans);
213 }
214
215 void print_list(Stack **const list, int const node_sum, FILE *fp)
216 {
217 int i;
218 fprintf(fp,"Suffix expression: ");
219 for (i = 0;i < node_sum;i++)
220 {
221 if (list[i]->type == is_sym)
222 fprintf(fp, "%c ", list[i]->sym);
223 else
224 fprintf(fp, "%d ", list[i]->num);
225 }
226 fprintf(fp,"\n");
227 }
228
229 void caculate_Infix(Stack **const suffix_list, int const node_sum, FILE *fp)
230 {
231 int i;
232 Stack_manager *stack_man = allcoate_stack_man();
233 for (i = 0;i < node_sum;i++)
234 {
235 if (suffix_list[i]->type == is_int)
236 push_in_int(stack_man, suffix_list[i]->num);
237 else if (suffix_list[i]->type == is_sym)
238 get_Ans(stack_man, suffix_list[i]->sym);
239 }
240 fprintf(fp, " Answer: %d\n", stack_man->top->num);
241
242 delete_stack(&stack_man);
243 }
244
245 void error(Stack_manager *s1, Stack_manager *s2, Stack_manager *s3, Stack**L,FILE *fp)
246 {
247 fprintf(fp, "< illegal expression! >\n");
248 delete_stack(&s1);
249 delete_stack(&s2);
250 delete_stack(&s3);
251 free(L);
252 }
1 //plug.h
2
3 #ifndef Suffix_to_Infix
4 #define Suffix_to_Infix
5 #define MAX 256
6 #include <stdio.h>
7
8 enum symbol_or_interget { is_sym, is_int };
9
10 typedef struct _stack
11 {
12 char sym;
13 int num, type;
14 struct _stack *prev;
15 }Stack;
16
17 typedef struct _stack_manager
18 {
19 int node_sum;
20 struct _stack *top;
21 }Stack_manager;
22
23 void push_in_int(Stack_manager *const, const int);
24 void push_in_char(Stack_manager *const, const char);
25 void pop_out(Stack_manager *const);
26 int scan_Infix_to_Suffix(char *,FILE *);
27 int combine_Stack_to_Num(Stack_manager *const);
28 void copy_Stack_to_List(Stack **const, Stack_manager *const);
29 void caculate_Infix(Stack **const, int const, FILE *);
30 void get_Ans(Stack_manager *const, char);
31 void print_list(Stack **const,int const, FILE *);
32 void error(Stack_manager *, Stack_manager *, Stack_manager *, Stack**, FILE *fp);
33
34 #endif // !Suffix_to_Infix
1 //stack.cpp
2
3 #include "plug.h"
4 #include "stack.h"
5 #include <stdio.h>
6 #include <stdlib.h>
7
8 Stack_manager *allcoate_stack_man(void)
9 {
10 Stack_manager *stack_man = (Stack_manager *)malloc(sizeof(Stack_manager));
11 stack_man->top = NULL, stack_man->node_sum = 0;
12 return stack_man;
13 }
14
15 void push_in_int(Stack_manager *const s_head, const int item)
16 {
17 Stack *tmp = NULL;
18
19 tmp = (Stack *)malloc(sizeof(Stack));
20
21 tmp->prev = s_head->top;
22 tmp->num = item, tmp->sym = ‘\0‘;
23 tmp->type = is_int;
24
25 s_head->node_sum++;
26 s_head->top = tmp;
27 }
28
29 void push_in_char(Stack_manager *const s_head, const char item)
30 {
31 Stack *tmp = NULL;
32
33 tmp = (Stack *)malloc(sizeof(Stack));
34
35 tmp->prev = s_head->top;
36 tmp->sym = item, tmp->num = 0;
37 tmp->type = is_sym;
38
39 s_head->node_sum++;
40 s_head->top = tmp;
41 }
42
43 void pop_out(Stack_manager *const s)
44 {
45 Stack *tmp = s->top->prev;
46 s->node_sum--;
47 free(s->top);
48 s->top = tmp;
49 }
50
51 void delete_stack(Stack_manager **stack_man)
52 {
53 for (;(*stack_man)->top != NULL;)
54 pop_out(*stack_man);
55 free(*stack_man);
56 *stack_man = NULL;
57 }
58
59 void print_stack(Stack_manager *const s)
60 {
61 Stack *tmp = s->top;
62 for (;tmp != NULL;tmp = tmp->prev)
63 {
64 if (tmp->type == is_sym)
65 printf("%c ", tmp->sym);
66 else
67 printf("%d ", tmp->num);
68 }
69 printf("\n");
70 }
1 //stack.h 2 3 #ifndef STACK 4 #define STACK 5 6 void push_in_int(Stack_manager *const, const int); 7 void push_in_char(Stack_manager *const, const char); 8 void pop_out(Stack_manager *const); 9 Stack_manager *allcoate_stack_man(void); 10 void delete_stack(Stack_manager **); 11 void print_stack(Stack_manager *const); 12 13 #endif // !STACK
时间： 2024-08-15 10:44:39