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. Hereβs 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. Hereβs the step-by-step process:- 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.
-
Initialize a variable
sum
- 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.
- Create nodes for the resulting linked list and insert them at the required positions.
- Return the resultant linked list after handling any remaining carry.
-
Initialize two empty stacks called
stack1
stack2
-
Iterate through the first linked list (
l1
stack1
-
Iterate through the second linked list (
l2
stack2
-
Initialize a variable
sum
-
Create a dummy node called
result
-
Enter a loop that continues while either
stack1
stack2
-
Pop the top element from
stack1
sum
-
Pop the top element from
stack2
sum
-
Update the value of the current result node to be
sum % 10
-
Calculate the carry for the next digit addition using
sum // 10
-
Create a new node called
head
sum // 10
-
Set
head.next
-
Move
result
-
Update
sum
sum // 10
-
After the loop, check if the dummy nodeβs value is zero. If it is, return
result.next
result
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)