如何将 RPN 算法的值相加

Question

I'm writing calculator that calculates values from expressions:

3+(23/24)*34/24

I used RPN algorithm: https://en.wikipedia.org/wiki/Reverse_Polish_notation

I have now sorted expression in String:

3 23 24 / 34 * 24 / +

I don't have any idea how can I get value from this expression.

Thx

Answer 1

The basic idea behind RPN is that there is a stack that all the arguments get put on, then taken off for an operation.

For this set, the basic flow will be:

Element	Stack	a	b
push 3	3
push 23	3,23
push 24	3,23,24
-divide
pop b	3,23		24
pop a	3	23	24
push a/b	3, 0.9583
end-divide
push 34	3, 0.9583, 34
-multiply
pop b	3, 0.9583		34
pop a	3	0.9583	34
push a*b	3, 32.5833
end-multiply
push 24	3, 32.5833, 24
-divide
pop b	3, 32.5833		24
pop a	3	32.5833	24
push a/b	3, 1.3576
end-divide
add
pop b	3		1.3576
pop a		3	1.3576
push a+b	4.3576
end-add

pop solution!

Answer 2

The basic algorithm is based on a stack-like structure

For each token in the expression:

• if it is a number: push it
• if it is a symbol: pop 2 values; do the matched operation; push the result

Eg:

"3 23 24 / 34 * 24 / +"
                                             Stack
3:  push 3                                   |   3
23: push 23                                  |   3    23
24: push 24                                  |   3    23     24
/:  pop (24),   pop (23),    push 23/24      |   3     0.95
34: push 34                                  |   3     0.95  34
*:  pop (34),   pop (0.95),  push 0.95*34    |   3    32.58
24: push 24                                  |   3    32.58  24
/:  pop (24),   pop (32.58), push 32.58/24   |   3     1.35
+:  pop (1.35), pop (3),     push 3+1.35     |   4.35

The last value that remains in the stack is the result