表達式求值及轉換算法

後綴表達式求值算法

stack operands;  //運算數棧
while(沒到表達式尾)
{
    scanf("一個運算對象op");
    if(op is 運算數)
        operands.push(op);
    else if(op is 運算符)
    {
        operand_right = operands.pop();
        operand_left = operands.pop();
        result = operand_left op operand_right;
        operands.push(result);
    }
    else
    {
        printf("Suffix expression is invalid !");
    }
}
if(operands.size() == 1)
    return operands.top();
else
    printf("Suffix expression is invalid!");

前綴表達式求值算法

算法一：從表達式尾部開始處理(從右至左)

僞代碼描述：

stack operands;   //運算數棧
while(沒到達表達式首)
{
    scanf("一個運算對象op");
    if(op is Operand)
        operands.push(op);
    else if(op is Operator)
    {
        operand_left = operands.pop();
        operand_right = operands.pop();
        result = operand_left op operand_right;
        operands.push(result);
    }
    else
    {
        printf("Prefix expression is invalid!");
    }
}
if(operands.size() == 1)
{
    return operands.top();
}
else
    printf("Prefix expression is invalid!");

算法二：從表達式首部開始處理(從左至右)

stack operations;  //運算對象棧，元素既能夠是雲算法，也能夠是運算數
while(沒到表達式尾)
{
    scanf("一個運算對象op");
    if(op is Operator)
    {
        operations.push(op);
    }
    else if(op is Operand)
    {
        if(operations.top() is Operator)
        {
            operations.push(op);
        }
        else
        {
            while(operations.top() is Operand)
            {
                operand_right = op;
                operand_left = operations.pop();
                operator = operations.pop();
                op = operand_left operator operand_right;
            }
            operations.push(op);
        }
    }
    else
    {
        printf("Prefix expression is invalid!");
    }
}
if(operations.size() == 1)
    return operations.top();
else
    printf("Prefix expression is invalid!");

中綴表達式轉換爲後綴表達式算法

stack operators;   //運算符棧
while(沒到表達式尾)
{
    scanf("一個運算對象op");
    if(op is Operand)
    {
        printf(op);
    }
    else if(op is Operator)
    {
        if(op 優先級大於 operator.top() && op is not 右括號)
            operator.push(op);
        else if(op is 右括號)
        {
            do
            {
                tmp = operators.pop();
                if(tmp is not 對應左括號)
                {
                    printf(tmp);
                }
                else
                {
                    break;
                }
                if(operators.empty())
                {
                    printf("Infix expression is invalid!");
                }
            }while(1);
        }
        else
        {
            do
            {
                tmp = operators.pop();
                printf(tmp);
            }while(op 優先級小於 operators.top());
            operators.push(op);
        }
    }
    else
    {
        printf("Infix expression is invalid!");
    }
}
while(!operators.empty())
{
    tmp = operators.pop();
    printf(tmp);
}

中綴表達式轉換爲前綴表達式算法

從表達式尾部開始處理

stack operators;  //運算符棧stack operations;  //運算對象棧，元素既能夠是運算符，也能夠是運算數while (沒到表達式首){
    scanf("一個運算對象op");
    if (op is Operand)
    {
        operations.push(op);
    }
    else if (op is Operator)
    {
        if (op 優先級大於 operators.top() && op is not 左括號)
            operators.push(op);
        else if (op is 左括號)
        {
            do
            {
                tmp = operators.pop();
                if (tmp is not 對應右括號)
                {
                    operations.push(tmp);
                }
                else
                {
                    break;
                }
                if (operators.empty())
                {
                    printf("Infix expression is invalid!");
                }
            }while(1);
        }
        else
        {
            do
            {
                tmp = operators.pop();
                operations.push(tmp);
            }while(op 優先級小於 operators.top());
            operators.push(op);
        }
    }
    else
    {
        printf("Infix expression is invalid!");
    }}while(!operators.empty()){
    tmp = operators.pop();
    operations.push(tmp);}while(!operations.empty()){
    tmp = operations.pop();
    printf(tmp);}