Plus One

To solve this coding challenge, you'll need to address the problem of incrementing a large number, which is represented using an array of its digits. The number is given in a left-to-right order, starting with the most significant digit. The key point is to handle cases where carrying over is necessary, especially when the digits are all 9's, converting to a higher significant place during the addition.

Explanation

Given an array where each element is a digit of a large integer in order, the challenge requires adding 1 to the number and returning the resulting array. It involves iterating over the array from the end (least significant digit) and handling carrying over effectively. For example:

1. For
   [1, 2, 3]
   , adding 1 directly to the least significant digit results in
   [1, 2, 4]
   .
2. For
   [4, 3, 2, 1]
   , adding 1 results in
   [4, 3, 2, 2]
   .
3. For
   [9]
   , since 9 + 1 results in 10, a carry is involved, resulting in
   [1, 0]
   .
To implement this solution, consider each element starting from the end, and if a value becomes 10, set it to 0 and move the carry to the next significant digit to the left.

Detailed Steps in Pseudocode

4. Initialization : Start from the last element of the list (the least significant digit).
5. Iteration :
• Traverse the list from the end to the start.
• For each digit, check if it is less than 9:
• If it is, add 1 to it and return the list immediately as there's no carry-over needed.
• If the digit is 9, set it to 0 (as adding 1 would result in 10, causing a carry).
6. Edge Case :
• If after the entire loop you still have carrying forward (i.e., you have handled the digit 9s in all positions), then you need to add a new most significant digit which is 1 at the beginning of the list.
Here's the pseudocode for the solution:

                                            
# Function to increment a large integer represented as an array of digits
function plusOne(digits):
# length of the digits array
length = len(digits)

# Traverse the digits array from the last element to the first
for index from length-1 to 0 (decreasing):
# Check if the current digit is less than 9
if digits[index] < 9:
# Increment the digit by 1
digits[index] += 1
# Return the updated digits array as no further handling is required
return digits
else:
# Set the current digit to 0 as it was 9, and we have carry over
digits[index] = 0

# If loop completes without returning, all digits were 9
# Hence, insert 1 at the beginning of the array to handle overflow
return [1] + digits

# Example usage
example1 = [1, 2, 3]
result1 = plusOne(example1)  # Output should be [1, 2, 4]

example2 = [4, 3, 2, 1]
result2 = plusOne(example2)  # Output should be [4, 3, 2, 2]

example3 = [9]
result3 = plusOne(example3)  # Output should be [1, 0]

                                        

Step-by-Step Explanation of Pseudocode

7. Initialization and Setup :
• Define a function
  plusOne
  that takes
  digits
  as an input.
• Calculate the length of the input array.
8. Iteration Logic :
• A loop runs from the last index (
  length-1
  ) to the first index (
  0
  ).
• For each digit, check if it is less than 9. If so, increment the digit and return the modified array immediately.
• If the digit is 9, set it to 0 since adding 1 to it will cause a carry, and continue to the next left digit.
9. Carry Handling :
• If after looping through all digits, all were 9's, there will be no returned value inside the loop.
• In such a case, we need to handle the carry by adding a new digit
  1
  to the start of the array, followed by the rest of the digits which are now all zeros.

By following these steps closely, your solution will correctly handle the transformation of the digit array according to the problem's requirements.