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The problem is to find the difference between the sum of the elements of an array and the sum of the digits of the elements in the array.

Specifically:

• Given an integer array nums, find the difference between the sum of the elements in nums and the sum of the digits of the elements in nums.
• The sum of the digits of a number is defined as the sum of its individual digits. For example, the sum of the digits of 123 is 1 + 2 + 3 = 6.
• Return the absolute difference between the sum of the elements and the sum of the digits of the elements.

Clarifying Questions

1. Does the array contain only positive integers?
   • Assume yes, as there is no mention of negative numbers or zero in the problem.
2. Can the array be empty?
   • Typically, edge cases like an empty array should be considered. If the array is empty, both sums will be zero and hence the difference will also be zero.
3. What is the range of the numbers in the array?
   • Assuming the numbers will fit within typical integer ranges as used in most programming contests.

Strategy

To solve this problem, we need to perform the following steps:

1. Calculate the sum of the elements in the array.
2. Calculate the sum of the digits for each number in the array and accumulate these sums.
3. Compute the absolute difference between the sum of the elements and the sum of the digits.

Let’s break this down:

1. Iterate through the array and sum the elements.
2. For each element, convert it to a string to iterate through its digits easily or use arithmetic operations to sum the digits.
3. Sum the digits of each element.
4. Compute and return the absolute difference between the sum of the elements and the sum of the digits.

Code Implementation

def differenceOfSum(nums):
    element_sum = sum(nums)
    digit_sum = 0
    
    for num in nums:
        while num > 0:
            digit_sum += num % 10
            num = num // 10
    
    return abs(element_sum - digit_sum)

# Example usage:
nums = [12, 34, 56]
print(differenceOfSum(nums))  # should output the difference between the sum of elements and sum of digits

Time Complexity

• Sum of elements (element_sum): This is (O(n)) where (n) is the number of elements.
• Sum of digits: Each number is processed digit by digit. If the maximum number has d digits, the overall complexity can be seen as (O(n \cdot d)). However, since d is a small constant (about 10 for numbers up to billions), the complexity approximates to (O(n)).

Thus, the overall time complexity is (O(n)), making the approach efficient for large arrays.

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