编写程序实现一元多项式的创建以及两个一元多项式相加和相乘的操作。 2.编写程序实现将输入的单链表排序成为有序单链表的操作。 3.编写程序实现算术表达式求值。

1. 实现一元多项式的创建和基本操作： ```python class Polynomial: def __init__(self): self.coefficients = [] def add_term(self, coefficient, exponent): self.coefficients.append((coefficient, exponent)) def __add__(self, other): result = Polynomial() for c1, e1 in self.coefficients: for c2, e2 in other.coefficients: if e1 == e2: result.add_term(c1 + c2, e1) elif e1 > e2: result.add_term(c1, e1) else: # e2 > e1 result.add_term(c2, e2) return result def multiply(self, other): result = Polynomial() for c1, e1 in self.coefficients: for c2, e2 in other.coefficients: result.add_term(c1 * c2, e1 + e2) return result # 示例 poly1 = Polynomial() poly1.add_term(3, 0) # 3x^0 poly1.add_term(2, 1) # 2x^1 poly2 = Polynomial() poly2.add_term(4, 0) # 4x^0 poly2.add_term(-1, 2) # -1x^2 sum_poly = poly1 + poly2 product_poly = poly1.multiply(poly2) ``` 2. 排序单链表： ```python class ListNode: def __init__(self, val=0, next=None): self.val = val self.next = next def sort_list(head): if not head or not head.next: return head dummy = ListNode(0) dummy.next = head slow, fast = dummy, head.next while fast and fast.next: fast = fast.next.next slow = slow.next if slow.val < fast.val: temp = slow.next slow.next = fast fast.prev = slow slow = temp return dummy.next # 示例 head = ListNode(5, ListNode(3, ListNode(8, ListNode(6)))) sorted_head = sort_list(head) ``` 3. 算术表达式求值： ```python import operator as op from collections import deque def evaluate(expression: str): tokens = deque(expression.split()) operators = {'+': op.add, '-': op.sub, '*': op.mul, '/': op.truediv} num_stack, op_stack = [], [] while tokens: token = tokens.popleft() if token.isdigit(): num_stack.append(int(token)) elif token in operators: right = num_stack.pop() left = num_stack.pop() op_stack.append((operators[token], (left, right))) elif token == '(': op_stack.append(token) elif token == ')': while op_stack[-1] != '(': operator, args = op_stack.pop() num_stack.append(operator(*args)) op_stack.pop() # remove the '(' while op_stack: operator, args = op_stack.pop() num_stack.append(operator(*args)) return num_stack[0] # 示例 expression = "2 * 3 + 4 / 2" result = evaluate(expression) ```