波兰表达式是一种把运算符前置的算术表达式, 例如普通的表达式2+3的波兰表示法为+ 2 3. 波兰表达式的优点是运算符之间不必有优先级关系, 也不必用括号改变运算次序, 例如(2+3)*4的波兰表达法为* + 2 3 4.

Description

题目要求求解波兰表达式的值, 其中运算符包括+-*/四个.

分析

这种表达式本身就是为了方便计算机分析而构造的，因此编程求值较为容易。只需利用一个操作数栈s，从表达式末尾遍历，遇到数字则push入栈，遇到运算符则依次pop出栈两个数进行运算，然后将结果push入栈。这样扫描完整个表达式之后，栈中剩下的即为表达式的值。

代码如下

//poland.c
#include <stdio.h>
#include <string.h>
#define INPUT argv[1]
struct STACK{
    float s[BUFSIZ];
    int sp;
};
typedef struct STACK STACK;
STACK s;
#define push(x) (s.s[s.sp++] = x)
#define pop() (s.s[--s.sp])
float calc(char op){
    float p1 = pop();
    float p2 = pop();
    printf("pop: %f\npop: %f\ncase: %c\n", p1, p2, op);
    switch(op){
        case '+': return p1 + p2; break;
        case '-': return p1 - p2; break;
        case '*': return p1 * p2; break;
        case '/': return p1 / p2; break;
        default: return 0; break;
    }
}
#define isop(x) (x == '+' || x == '-' || x == '*' || x == '/')
int main(int argc, char **argv){
    float num = 0.;
    for(int i = strlen(INPUT) - 1; i >= 0; i--){
        if(INPUT[i] == ' ' || !i){
            if(isop(INPUT[i?i + 1:0])) push(calc(INPUT[i?i + 1:0]));
            else{
                sscanf(INPUT + (i?i + 1:0), "%f", &num);
                printf("push: %f\n", num);
                push(num);
            }
        }
    }
    printf("%f\n", pop());
    return 0;
}

测试如下

$ ./poland "* + 11.0 12.0 + 24.0 35.0"
push: 35.000000
push: 24.000000
pop: 35.000000
case: +
push: 12.000000
push: 11.000000
pop: 11.000000
pop: 12.000000
case: +
pop: 23.000000
pop: 59.000000
case: *
1357.000000
$ ./poland "+ 1 + 2 + 3 + 4 5"        
push: 5.000000
push: 4.000000
pop: 4.000000
pop: 5.000000
case: +
push: 3.000000
pop: 9.000000
case: +
push: 2.000000
pop: 2.000000
pop: 12.000000
case: +
push: 1.000000
pop: 1.000000
pop: 14.000000
case: +
15.000000
$ ./poland "+ + + 1 2 + 3 4 + 5 6"    
push: 6.000000
push: 5.000000
pop: 5.000000
pop: 6.000000
case: +
push: 4.000000
push: 3.000000
pop: 3.000000
pop: 4.000000
case: +
push: 2.000000
push: 1.000000
pop: 1.000000
pop: 2.000000
case: +
pop: 3.000000
pop: 7.000000
case: +
pop: 10.000000
pop: 11.000000
case: +
21.000000