技術標籤：C語言

  之前一個好兄弟問我表示式計算的一個程式，這個主要鍛鍊棧的使用。但是他向我提出了一個問題，如果多位數計算，好像常規的表示式轉化就不靈了。即常規的程式只能計算10以下的數字，對於這個問題進行下探索。
  舉個例子，常規的方法，生成的字尾表示式會是這樣的：123-*，這樣無法判斷是1還是12。也就是對多位數失效。最終確定的思路是在中綴轉字尾的過程中，對數字進行判斷：如果是多位數，則通過空格隔開。同時在後綴計算中，時刻檢查空格的存在，最後完成計算。原始碼如下：

#include<stdio.h>
#include<stdlib.h>
#include<
 
ctype.h>
#include<string.h>

#define SIZE 100

//字元棧目的是進行中綴轉字尾
char stack[SIZE];
int top = -1;

//整數棧目的是進行字尾表示式的計算
int stack_int[SIZE];
int top_int = -1;

//字元棧操作
void push(char item)
{
	if(top >= SIZE-1)
	{
		printf("\nStack Overflow.");
	}
	else
	{
		top = top+1;
		stack[top] = item;
 

	}
}

//字元棧操作
char pop()
{
	char item ;

	if(top <0)
	{
		printf("stack under flow: invalid infix expression");
		getchar();
		exit(1);
	}
	else
	{
		item = stack[top];
		top = top-1;
		return(item);
	}
}

//整數棧操作
void push_int(int num)
{
	if(top_int >= SIZE-1)
	{
		printf("\nStack Overflow."
 
);
	}
	else
	{
		top_int = top_int+1;
		stack_int[top_int] = num;
	}
}

//整數棧操作
int pop_int()
{
	int num ;

	if(top_int <0)
	{
		printf("stack under flow: invalid infix expression");
		getchar();
		exit(1);
	}
	else
	{
		num = stack_int[top_int];
		top_int = top_int-1;
		return(num);
	}
}

//funciton:判斷是否為操作符
int is_operator(char symbol)
{
	if(symbol == '*' || symbol == '/' || symbol == '+' || symbol == '-')
	{
		return 1;
	}
	else
	{
	return 0;
	}
}

//function:確定優先順序
int precedence(char symbol)
{
	if(symbol == '*' || symbol == '/')
	{
		return(2);
	}
	else if(symbol == '+' || symbol == '-')
	{
		return(1);
	}
	else
	{
		return(0);
	}
}

//function:中綴表示式轉字尾表示式，結果存於postfix_exp形參中
void InfixToPostfix(char infix_exp[], char postfix_exp[])
{
	int i, j;
	char item;
	char x;

	push('(');
	strcat(infix_exp,")");

	i=0;
	j=0;
	int tag = 0;
	item=infix_exp[i];

	while(item != '\0')
	{
		if(item == '(')
		{
			push(item);
		}
		else if( isdigit(item) || isalpha(item))
		{
			//when meet a digit, judge if the number is bigger than 10
			//if so, add ' ' before it  and ' ' after it
			//use tag as a symbol to add the first ' '
			char next = infix_exp[i+1];
			while (isdigit(next))
			{
				if (tag == 0)
				{
					postfix_exp[j++] = ' '; 
					tag = 1;
					postfix_exp[j++] = item;
					i++;
					item = next;
					next = infix_exp[i+1];
				}
				else
				{
					postfix_exp[j++] = item;
					i++;
					item = next;
					next = infix_exp[i+1];
				}
			}
			//when tag equals to 1, it means a number bigger than 10 appears
			if (tag == 1)
			{
				tag = 0;
				postfix_exp[j++] = item;
				postfix_exp[j++] = ' ';
				item = next;
				i++;
				continue;
			}
			postfix_exp[j] = item;
			j++;
		}
		else if(is_operator(item) == 1)
		{
			x=pop();
			while(is_operator(x) == 1 && precedence(x)>= precedence(item))
			{
				postfix_exp[j] = x;
				j++;
				x = pop();
			}
			push(x);
			push(item);
		}
		else if(item == ')')
		{
			x = pop();
			while(x != '(')
			{
				postfix_exp[j] = x;
				j++;
				x = pop();
			}
		}
		else
		{
			printf("\nInvalid infix Expression.\n");
			getchar();
			exit(1);
		}
		i++;


		item = infix_exp[i];
	}
	if(top>0)
	{
		printf("\nInvalid infix Expression.\n");
		getchar();
		exit(1);
	}
	if(top>0)
	{
		printf("\nInvalid infix Expression.\n");
		getchar();
		exit(1);
	}


	postfix_exp[j] = '\0';
}

//function:字尾表示式計算
long int EvalPostfix(char postfix[])
{
	int i;
	char ch;
	int val; 
	int A, B;
	for ( i = 0; postfix[i] != '\0'; i++)
	{
		ch = postfix[i];
		if(isdigit(ch))
		{
			val = ch-'0';
			push_int(val);
		}
		else if (ch == ' ')
		{
			i++;
			val = 0;
			ch = postfix[i];
			while (ch != ' ')
			{
				val = val*10 + (postfix[i]-'0');
				i++;
				ch = postfix[i];
			}
			push_int(val);
		}
		else if(ch == '+' || ch == '-' || ch == '*' || ch == '/')
		{
			A = pop_int();
			B = pop_int();
		switch(ch)
		{
			case '/':
			val = B / A;
			break;
			
			case '*':
			val = B * A;
			break;
			
			case '+':
			val = B + A;
			break;
			
			case '-':
			val = B - A; 
			break; 
		}
    	push_int(val);
		}
	}

	return pop_int();
}

int main()
{
	char infix[SIZE], postfix[SIZE];
    int value;
	printf("ASSUMPTION: The infix expression contains single letter variables and single digit constants only.\n");
	printf("\nEnter Infix expression : ");
	gets(infix);
	
	InfixToPostfix(infix,postfix);
	printf("Postfix Expression: ");
	puts(postfix);
	
	value = EvalPostfix(postfix);
    printf("Result of expression evaluation : %d", value);
    system("pause");

	return 0;
}

  計算結果如下：
  輸入中綴表示式為：10-6*(12-8/4)+3