表达式求值及转换算法

后缀表达式求值算法

stack operands;  //运算数栈
while(没到表达式尾)
{
    scanf("一个运算对象op");
    if(op is 运算数)
        operands.push(op);
    else if(op is 运算符)
    {
        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!");

前缀表达式求值算法

算法一：从表达式尾部开始处理(从右至左)

伪代码描述：

stack operands;   //运算数栈
while(没到达表达式首)
{
    scanf("一个运算对象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：从表达式首部开始处理(从左至右)

stack operations;  //运算对象栈，元素既可以是云算法，也可以是运算数
while(没到表达式尾)
{
    scanf("一个运算对象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!");

中缀表达式转换为后缀表达式算法

stack operators;   //运算符栈
while(没到表达式尾)
{
    scanf("一个运算对象op");
    if(op is Operand)
    {
        printf(op);
    }
    else if(op is Operator)
    {
        if(op 优先级大于 operator.top() && op is not 右括号)
            operator.push(op);
        else if(op is 右括号)
        {
            do
            {
                tmp = operators.pop();
                if(tmp is not 对应左括号)
                {
                    printf(tmp);
                }
                else
                {
                    break;
                }
                if(operators.empty())
                {
                    printf("Infix expression is invalid!");
                }
            }while(1);
        }
        else
        {
            do
            {
                tmp = operators.pop();
                printf(tmp);
            }while(op 优先级小于 operators.top());
            operators.push(op);
        }
    }
    else
    {
        printf("Infix expression is invalid!");
    }
}
while(!operators.empty())
{
    tmp = operators.pop();
    printf(tmp);
}

中缀表达式转换为前缀表达式算法

从表达式尾部开始处理

stack operators;  //运算符栈stack operations;  //运算对象栈，元素既可以是运算符，也可以是运算数while (没到表达式首){
    scanf("一个运算对象op");
    if (op is Operand)
    {
        operations.push(op);
    }
    else if (op is Operator)
    {
        if (op 优先级大于 operators.top() && op is not 左括号)
            operators.push(op);
        else if (op is 左括号)
        {
            do
            {
                tmp = operators.pop();
                if (tmp is not 对应右括号)
                {
                    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 优先级小于 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);}