How do you solve Minimum Addition to Make Integer Beautiful on LeetCode?

Minimum Addition to Make Integer Beautiful (LeetCode #2457) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(log n) time complexity and O(1) space complexity. Key insight: Understanding digit sums is crucial for this problem.

What is the time complexity of Minimum Addition to Make Integer Beautiful?

The optimal solution for Minimum Addition to Make Integer Beautiful runs in O(log n) time and uses O(1) space. The time complexity is O(log n) because we are processing each digit of n, which has at most log n digits.

What is the brute force solution for Minimum Addition to Make Integer Beautiful?

The brute force approach for Minimum Addition to Make Integer Beautiful is Brute Force, with O(n²) time complexity and O(1) space complexity. We can check every possible value of x starting from 0 and see if n + x has a digit sum less than or equal to the target. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(log n).

What algorithm or data structure is used to solve Minimum Addition to Make Integer Beautiful?

Minimum Addition to Make Integer Beautiful uses the following concepts: Math, Greedy. The recommended patterns to study are: Greedy, Mathematical Manipulation.

What are the interview tips for Minimum Addition to Make Integer Beautiful?

Always consider edge cases, such as when n is already beautiful. Think about how to manipulate digits directly rather than brute-forcing through additions. Practice breaking down the problem into smaller parts to simplify your approach.

What are common mistakes when solving Minimum Addition to Make Integer Beautiful?

Not checking if the digit sum is already within the target before starting the loop. Overcomplicating the addition logic instead of focusing on the last digit.

#2457

Minimum Addition to Make Integer Beautiful

Medium

MathGreedyGreedyMathematical Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(log n)
Space	O(1)	O(1)

💡

Intuition

Time O(log n)Space O(1)

Instead of checking each x, we can directly calculate how much we need to add to make the digit sum beautiful by rounding up the digits of n to the next multiple of 10.

⚙️

Algorithm

5 steps

1Step 1: Calculate the digit sum of n.
2Step 2: If the digit sum is already less than or equal to target, return 0.
3Step 3: Starting from the least significant digit, find the first digit that causes the digit sum to exceed target.
4Step 4: Calculate how much to add to turn this digit into zero and carry over to the next digit.
5Step 5: Return the calculated addition.

solution.py18 lines

1# Full working Python code
2
3def min_addition(n, target):
4    def digit_sum(num):
5        return sum(int(d) for d in str(num))
6    if digit_sum(n) <= target:
7        return 0
8    x = 0
9    multiplier = 1
10    while digit_sum(n) > target:
11        last_digit = n % 10
12        if last_digit != 0:
13            x += (10 - last_digit) * multiplier
14            n += (10 - last_digit) * multiplier
15        n //= 10
16        multiplier *= 10
17    return x
18

ℹ

Complexity note: The time complexity is O(log n) because we are processing each digit of n, which has at most log n digits.

1Understanding digit sums is crucial for this problem.
2Rounding up digits can help quickly achieve the target.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.