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Minimum Element After Replacement With Digit Sum

Difficulty: Easy

Problem Description

You are given an integer array nums. You replace each element in nums with the sum of its digits. Return the minimum element in nums after all replacements.

Key Insights

  • Each number can be transformed to the sum of its digits, which reduces it to a potentially smaller number.
  • The minimum element after replacements can be found by applying the digit sum function to each element and then determining the minimum value.
  • The digit sum function can be implemented efficiently and is straightforward given the constraints.

Space and Time Complexity

Time Complexity: O(n * d), where n is the number of elements in nums and d is the maximum number of digits in the elements (at most 5 for the upper limit of 10,000).

Space Complexity: O(1), as we are using a constant amount of space for the calculations (excluding the input space).

Solution

To solve the problem, we will iterate through each element in the nums array and compute the sum of its digits. We will maintain a variable to keep track of the minimum value found after all replacements.

  1. For each number in the array, calculate the sum of its digits.
  2. Update the minimum value based on the calculated digit sums.
  3. Return the minimum value after processing all elements.

Code Solutions

def digit_sum(n):
    return sum(int(digit) for digit in str(n))

def minimum_element_after_replacement(nums):
    min_value = float('inf')
    for num in nums:
        min_value = min(min_value, digit_sum(num))
    return min_value

# Example usage
print(minimum_element_after_replacement([10, 12, 13, 14]))  # Output: 1
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