Sum of Digits in the Minimum Number - Solution & Explanation

Problem Overview: You are given an integer array. Find the smallest element, compute the sum of its digits, and return 1 if the digit sum is even, otherwise return 0. The challenge is straightforward: identify the minimum efficiently and apply simple digit math.

Approach 1: Sort Then Process (O(n log n) time, O(1) extra space)

Sort the array so the smallest element appears at the first index. After sorting, take nums[0], repeatedly extract digits using % 10 and divide by 10 to compute the digit sum. Finally, check if the sum is even using sum % 2. This approach is easy to reason about but sorting performs unnecessary work since the full ordering of the array is not required.

Approach 2: Single Pass Minimum Scan (O(n) time, O(1) space)

Iterate through the array once and track the minimum value using a variable like minVal. This avoids sorting and directly solves the first part of the problem in linear time. After finding the minimum, compute the digit sum using repeated modulus and division operations. The final step checks parity: if the sum is even return 1, otherwise return 0. The logic relies only on basic iteration and arithmetic from Array traversal and Math digit manipulation.

The key insight is that only the minimum value matters. Any algorithm that processes the entire ordering of the array is doing extra work. A simple linear scan gives the optimal result while keeping memory usage constant.

Recommended for interviews: The single-pass scan is the expected solution. Interviewers want to see that you avoid sorting when only the minimum is required. Mentioning the sort-based idea first shows baseline reasoning, but implementing the O(n) scan demonstrates stronger algorithmic judgment and familiarity with array traversal and basic math operations.