中缀表达式转换为后缀表达式

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问题：给出一个表达式，含有括号，将其转化成后缀表达式输出

算法：用栈维护将要输出的运算符(operator)

读入一个token

1）如果是数，直接输出

2）如果是运算符（不含括号），比较其与栈顶元素优先级

若栈顶元素同级或更高级，则将其出栈并输出，直到栈为空或者栈顶运算符级别更低

3）如果是左括号'('，则将其入栈

4）如果是右括号')'，则将栈顶元素依次出栈并输出，直到有匹配的‘('

最后遇到的’('出栈不输出

当所有读入完成，将栈顶元素依次出栈输出

这里有几个例子。

例题：UVa 727 Equation

Write a program that changes an infix expression to a postfix expression according to the followingspecifications.

Input

The infix expression to be converted is in the input file in the format of one character per line,with a maximum of 50 lines in the file. For example, (3+2)*5 would be in the form:
(3+2)*5
The input starts with an integer on a line by itself indicating the number of test cases. Severalinfix expressions follows, preceded by a blank line.
The program will only be designed to handle the binary operators+,-,*,/.
The operands will be one digit numerals.
The operators *and /have the highest priority. The operators + and -have the lowest priority.Operators at the same precedence level associate from left to right. Parentheses act as groupingsymbols that over-ride the operator priorities.
Each testcase will be an expression with valid syntax.

Output

The output file will have each postfix expression all on one line. Print a blank line between differentexpressions.

Sample Input

(

)

Sample Output

32+5*

/*PROG: UVa727*/#include <cstdio>#include <cstring>#include <cctype>#include <vector>using namespace std;#define MAXN 100char s[MAXN], sp;#define DEBUG 1#define LOG(...) do { if (DEBUG) fprintf(stderr, __VA_ARGS__); } while(0)int main(void) {int Z; scanf("%d", &Z);getchar(); getchar();for (int z = 0; z < Z; ++z) {if (z) printf("\n");sp = 0;int cnt = 0;while (1) {++cnt;if (cnt > 100) break;int ch = getchar();// LOG("%c ", ch);if (ch != '\n' && ch != EOF) {getchar();if (isdigit(ch)) putchar(ch);else switch (ch) {case '(': s[sp++] = ch; break;case '+': case '-':while (sp && s[sp-1]!='(') putchar(s[--sp]);s[sp++] = ch;break;case '*': case '/':while (sp && (s[sp-1]=='*'||s[sp-1]=='/')) putchar(s[--sp]);s[sp++] = ch;break;case ')':while (sp && s[sp-1]!='(') putchar(s[--sp]);--sp;break;}}else {while (sp) putchar(s[--sp]);putchar('\n');break;}}}return 0;}

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