用简单的示例通俗易懂地解析两数相加算法

2023-12-19 13:51:01

两数相加算法的解析

两数相加算法是一种用于计算两个非负整数和的算法。该算法以链表的形式存储这两个整数，链表中的每个节点存储一个数字，节点的顺序与整数的数字顺序相反。例如，数字123将被存储为一个链表，其中第一个节点存储数字3，第二个节点存储数字2，第三个节点存储数字1。

两数相加算法采用递归的方法，从链表的尾部开始逐位相加。当两个链表的长度不同时，较短链表的末尾节点将被视为存储数字0的节点。在相加过程中，如果两个数字的和大于或等于10，则将进位1到下一位。例如，如果两个数字是5和7，那么它们的和是12，我们将把2存储在当前节点，并将1进位到下一位。

两数相加算法的伪代码如下：

def add_two_numbers(l1, l2):
  """
  Calculates the sum of two non-negative integers represented as linked lists.

  Args:
    l1: The first linked list.
    l2: The second linked list.

  Returns:
    The sum of the two integers represented by the linked lists.
  """

  # Initialize the sum linked list.
  sum_list = ListNode(0)

  # Initialize the current node of the sum linked list.
  current_node = sum_list

  # Initialize the carryover.
  carryover = 0

  # While both linked lists are not empty, add the digits and update the carryover.
  while l1 or l2 or carryover:
    # Get the digits from the current nodes of the two linked lists.
    digit1 = l1.val if l1 else 0
    digit2 = l2.val if l2 else 0

    # Add the digits and the carryover.
    sum = digit1 + digit2 + carryover

    # Update the carryover.
    carryover = sum // 10

    # Create a new node with the digit and add it to the sum linked list.
    current_node.next = ListNode(sum % 10)

    # Update the current node of the sum linked list.
    current_node = current_node.next

    # Advance the current nodes of the two linked lists.
    l1 = l1.next if l1 else None
    l2 = l2.next if l2 else None

  # Return the sum linked list.
  return sum_list.next