利用栈结构求取后缀表达式的值

后缀表达式的求值准则：

从左到右依次读取表达式，每遇到一个操作符，就读取该操作符之前的最后两个操作数，计算其值并把计算结果作为一个新的操作数，然后继续向后读取直到结束。从过程上可以看出，优先计算的是后出现的操作数，符合栈结构的特点，所以可以用栈结构来实现。

具体来说，用一个栈来存储操作数，每遇到一个操作符，就执行两次出栈操作。然后把计算的结果在推入栈中。当扫描完整个后缀表达式后，栈中就只剩一个数值，也就是最后的计算结果。

// postfix.java
// parses postfix arithmetic expressions
// to run this program: C>java PostfixApp
import java.io.*;              // for I/O
////////////////////////////////////////////////////////////////
class StackX//定义栈结构
{
private int maxSize;
private int[] stackArray;
private int top;
//--------------------------------------------------------------
public StackX(int size)      // constructor
{
maxSize = size;
stackArray = new int[maxSize];
top = -1;
}
//--------------------------------------------------------------
public void push(int j)     // put item on top of stack
{ stackArray[++top] = j; }
//--------------------------------------------------------------
public int pop()            // take item from top of stack
{ return stackArray[top--]; }
//--------------------------------------------------------------
public int peek()           // peek at top of stack
{ return stackArray[top]; }
//--------------------------------------------------------------
public boolean isEmpty()    // true if stack is empty
{ return (top == -1); }
//--------------------------------------------------------------
public boolean isFull()     // true if stack is full
{ return (top == maxSize-1); }
//--------------------------------------------------------------
public int size()           // return size
{ return top+1; }
//--------------------------------------------------------------
public int peekN(int n)     // peek at index n
{ return stackArray
; }
//--------------------------------------------------------------
public void displayStack(String s)
{
System.out.print(s);
System.out.print("Stack (bottom-->top): ");
for(int j=0; j<size(); j++)
{
System.out.print( peekN(j) );
System.out.print(' ');
}
System.out.println("");
}
//--------------------------------------------------------------
}  // end class StackX
////////////////////////////////////////////////////////////////
class ParsePost//计算后缀表达式
{
private StackX theStack;
private String input;
//--------------------------------------------------------------
public ParsePost(String s)
{ input = s; }
//--------------------------------------------------------------
public int doParse()
{
theStack = new StackX(20);             // make new stack
char ch;
int j;
int num1, num2, interAns;//定义两个操作数和计算结果

for(j=0; j<input.length(); j++)       // for each char,
{
ch = input.charAt(j);              // read from input
theStack.displayStack(""+ch+" ");  // *diagnostic*
if(ch >= '0' && ch <= '9')         // if it's a number
theStack.push( (int)(ch-'0') ); //(int)(ch-'0')是ch的数值，不加int是AScii
else                               // it's an operator
{
num2 = theStack.pop();          // pop operands
num1 = theStack.pop();
switch(ch)                      // do arithmetic
{
case '+':
interAns = num1 + num2;
break;
case '-':
interAns = num1 - num2;
break;
case '*':
interAns = num1 * num2;
break;
case '/':
interAns = num1 / num2;
break;
default:
interAns = 0;
}  // end switch
theStack.push(interAns);        // push result
}  // end else
}  // end for
interAns = theStack.pop();            // get answer
return interAns;
}  // end doParse()
}  // end class ParsePost
////////////////////////////////////////////////////////////////
class PostfixApp
{
public static void main(String[] args) throws IOException
{
String input;
int output;

while(true)
{
System.out.print("Enter postfix: ");
System.out.flush();
input = getString();         // read a string from kbd
if( input.equals("") )       // quit if [Enter]
break;
// make a parser
ParsePost aParser = new ParsePost(input);
output = aParser.doParse();  // do the evaluation
System.out.println("Evaluates to " + output);
}  // end while
}  // end main()
//--------------------------------------------------------------
public static String getString() throws IOException
{
InputStreamReader isr = new InputStreamReader(System.in);
BufferedReader br = new BufferedReader(isr);
String s = br.readLine();
return s;
}
//--------------------------------------------------------------
}  // end class PostfixApp
////////////////////////////////////////////////////////////////