用python实现如下内容。设计算法,将一个表达式转换为后缀表达式,并按照后缀表达式进行计算,得出表达式得结果。给出完整代码
时间: 2024-04-29 15:25:44 浏览: 51
本题需要用到栈来实现,具体思路如下:
1. 遍历表达式的每一个字符,如果是数字则直接添加到后缀表达式中;
2. 如果是运算符,则判断栈顶元素的优先级是否大于等于当前运算符,如果是则将栈顶元素弹出并加入到后缀表达式中,直到栈顶元素优先级小于当前运算符或栈为空,然后将当前运算符入栈;
3. 如果是左括号,则直接入栈;
4. 如果是右括号,则将栈顶元素依次弹出并加入到后缀表达式中,直到遇到左括号,将左括号弹出并丢弃;
5. 遍历完成后,如果栈中还有元素,则依次弹出并加入到后缀表达式中;
6. 最后计算后缀表达式的值,遇到数字直接入栈,遇到运算符则弹出栈顶两个元素进行运算,并将结果入栈,最终栈中只剩一个元素,即为最终结果。
以下是完整代码:
```python
class Stack:
def __init__(self):
self.items = []
def isEmpty(self):
return len(self.items) == 0
def push(self, item):
self.items.append(item)
def pop(self):
return self.items.pop()
def top(self):
return self.items[-1]
def infixToPostfix(expression):
precedence = {'+':1,'-':1,'*':2,'/':2,'^':3}
stack = Stack()
postfix = ''
for char in expression:
if char.isdigit():
postfix += char
elif char in precedence:
while not stack.isEmpty() and stack.top() in precedence and precedence[stack.top()] >= precedence[char]:
postfix += stack.pop()
stack.push(char)
elif char == '(':
stack.push(char)
elif char == ')':
while not stack.isEmpty() and stack.top() != '(':
postfix += stack.pop()
stack.pop()
while not stack.isEmpty():
postfix += stack.pop()
return postfix
def evaluatePostfix(postfix):
stack = Stack()
for char in postfix:
if char.isdigit():
stack.push(int(char))
else:
num2 = stack.pop()
num1 = stack.pop()
if char == '+':
stack.push(num1+num2)
elif char == '-':
stack.push(num1-num2)
elif char == '*':
stack.push(num1*num2)
elif char == '/':
stack.push(num1/num2)
elif char == '^':
stack.push(num1**num2)
return stack.pop()
expression = input('请输入表达式:')
postfix = infixToPostfix(expression)
print('后缀表达式为:', postfix)
result = evaluatePostfix(postfix)
print('计算结果为:', result)
```
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