Two-Stack arithmetic expression

1. Introduction

The calculation of arithmetic expressions is a more common problem, but the idea behind this problem is hidden in the stack.

Here's how to use two stacks to evaluate an expression.

2. Algorithm 2.1 defines:

A) build two stacks:

One is the data stack Datastak, for storing data;

One is the symbol stack operatorstack, which is used for storing operators;

b) Establish a priority table between the operational symbols to compare the priority between the two symbols;

The priority is defined as the result of three operations:> (denoted above),< (denoted below), = (denotes equality);

And for "(" and ")", think that the two are the same priority, do not do any operations;

2.2 Calculation conditions:

A) when (b) c) d) is met, calculations can be made;

b) The current token is an operator (that is, it cannot be a string terminator or an operand);

c) The symbol stack is non-empty (because it needs to be compared with the top element of the stack);

d) Priority of stack top element of symbol stack < current token;

The remaining operand of the last operand stack is the final result of the calculation;

2.3 Priority Symbol Table

Char[,] priority =New Char[6,6] {            //+   -    *   /  (   ){'>','>','<','<','<','>'},//+{'>','>','<','<','<','>'},//-{'>','>','>','>','<','>'},//*{'>','>','>','>','<','>'},///{'<','<','<','<','<','='},//({'<','<','<','<','<','>'}//)};

2.4 Pseudo-code

for each tokenif(token is a number) {Datastack.push (token);}Else{    Switch(token versus operatorstack stack top element for precedence comparison) { Casegreater than: Datastack.push (token);  Break;  Caseless than: operator=Operatorstack.pop (); A=Datastack.pop (); b=Datastack.pop (); C=a operator B;                Datastack.push (c);  Break;  Caseequals: Datastack.pop ();  Break; }}

Two-Stack arithmetic expression