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Add to Array-Form of Integer

Difficulty: Easy

Problem Description

Given the array-form of an integer num and an integer k, return the array-form of the integer num + k.

Key Insights

  • The array-form represents the digits of an integer in left-to-right order.
  • We need to handle the addition digit by digit, similar to how it is done on paper, keeping track of carry.
  • The length of num may not be enough to accommodate the sum, so we need to consider additional digits from k.

Space and Time Complexity

Time Complexity: O(max(n, m)), where n is the length of num and m is the number of digits in k.
Space Complexity: O(max(n, m)), for the result array storage.

Solution

To solve the problem, we will use a two-pointer approach with a carry variable. We will iterate through the digits of the array-form of the number and the digits of k, adding them together while managing any carry that results from the sum. We will build the result array from the least significant digit to the most significant one.

Code Solutions

def addToArrayForm(num, k):
    result = []
    carry = 0
    n = len(num)
    
    # Start from the end of the array 'num'
    for i in range(n - 1, -1, -1):
        digit_sum = num[i] + (k % 10) + carry
        result.append(digit_sum % 10)
        carry = digit_sum // 10
        k //= 10
    
    # If there are remaining digits in k
    while k > 0:
        digit_sum = (k % 10) + carry
        result.append(digit_sum % 10)
        carry = digit_sum // 10
        k //= 10

    # If there's a carry left
    if carry > 0:
        result.append(carry)
    
    # Reverse the result to get the correct order
    return result[::-1]
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