Add Two Numbers Ii

To solve this coding challenge, you need to add two numbers represented by two linked lists where each node contains a single digit, and the most significant digit comes first. The output should also be in the form of a linked list where each node contains a single digit. Here’s an in-depth explanation followed by pseudocode with detailed comments:

Explanation

The key idea here is to add the two numbers digit by digit, considering the most significant digit first. Because you cannot easily add from the most significant to the least significant without knowing the complete structure of the numbers, one effective way is to use stacks to store the digits temporarily. Here’s the step-by-step process:
  1. Use two stacks to hold the digits of the two input numbers (linked lists). Traverse each linked list and push its values to its respective stack. This way, the most significant digit is at the bottom of the stack, and the least significant is at the top.
  2. Initialize a variable
    sum
    to zero and create a dummy node for the result linked list.
  3. Use a loop to pop elements from both stacks (if available), add them along with any carry from the previous addition, and then handle the carry for the next significant digit.
  4. Create nodes for the resulting linked list and insert them at the required positions.
  5. Return the resultant linked list after handling any remaining carry.
  6. Pseudocode

    Initial pseudo-code can look like this in steps:
                                                
    # Define a function to add two numbers represented by linked lists
    Function addTwoNumbers(l1, l2):
    
    # Initialize two empty stacks to hold the digits of the two linked lists
    Initialize stack1 as an empty list
    Initialize stack2 as an empty list
    
    # Traverse the first linked list and push all the values onto stack1
    While l1 is not None:
    Push l1.val to stack1
    Move to the next node in l1
    
    # Traverse the second linked list and push all the values onto stack2
    While l2 is not None:
    Push l2.val to stack2
    Move to the next node in l2
    
    # Initialize the sum as 0
    Initialize sum as 0
    
    # Dummy node to start the result linked list
    Initialize result as a new ListNode with value 0
    
    # Loop until both stacks are empty
    While stack1 is not empty or stack2 is not empty:
    
    # If stack1 is not empty, pop the top element and add it to sum
    If stack1 is not empty:
    sum = sum + Pop(stack1)
    
    # If stack2 is not empty, pop the top element and add it to sum
    If stack2 is not empty:
    sum = sum + Pop(stack2)
    
    # Update the value of the current node in the result list
    result.val = sum % 10
    
    # Calculate the carry for the next iteration
    Initialize head as a new ListNode with value as sum // 10
    
    # Set the next of new head node to current result list
    head.next = result
    
    # Move result to the new head node
    result = head
    
    # Update sum for the next iteration
    sum = sum // 10
    
    # If the dummy node's value is 0, return the next node
    If result.val == 0:
    Return result.next
    
    # Else, return the result node
    Return result
    
    # Function call example
    # addTwoNumbers(l1, l2)
    
                                            

    Detailed Steps in Pseudocode

  7. Initialize two empty stacks called
    stack1
    and
    stack2
    .
    • Iterate through the first linked list (
      l1
      ), pushing each node’s value onto
      stack1
      .
    • Iterate through the second linked list (
      l2
      ), pushing each node’s value onto
      stack2
      .
  8. Initialize a variable
    sum
    to zero. This will be used to hold the sum of the current digits plus any carryover.
  9. Create a dummy node called
    result
    that will serve as the starting point of the resultant linked list.
  10. Enter a loop that continues while either
    stack1
    or
    stack2
    contains elements.
    • Pop the top element from
      stack1
      (if it exists) and add it to
      sum
      .
    • Pop the top element from
      stack2
      (if it exists) and add it to
      sum
      .
    • Update the value of the current result node to be
      sum % 10
      – this represents the current digit of the resultant linked list.
    • Calculate the carry for the next digit addition using
      sum // 10
      .
    • Create a new node called
      head
      with the value of
      sum // 10
      .
    • Set
      head.next
      to the current result node.
    • Move
      result
      to the new head node.
    • Update
      sum
      to be
      sum // 10
      for the next iteration (carryover).
  11. After the loop, check if the dummy node’s value is zero. If it is, return
    result.next
    (to skip the leading zero); otherwise, return
    result
    .
By following this structured approach and detailed pseudocode, you can implement a solution that adds two numbers represented by linked lists without reversing the input lists.