Is Largest Multiple of Three easy or hard?

Largest Multiple of Three is classified as a Hard problem on LeetCode because it requires combining number theory (divisibility by 3) with greedy selection and careful edge-case handling. The key challenge is maximizing the resulting number while maintaining the divisibility constraint.

Largest Multiple of Three Python/Java solution

Python solutions often sort the digits and remove the smallest remainder digits or use collections.Counter for digit counts. Java implementations typically use an int[10] frequency array and reconstruct the final number from 9 to 0. Both implementations follow the same greedy modulo adjustment strategy.

How to solve Largest Multiple of Three in O(n)?

Count how many times each digit (0–9) appears and compute the total digit sum. If sum % 3 is 1 or 2, remove the smallest digit(s) whose modulo fixes the remainder. Finally rebuild the number from digit 9 down to 0 using the remaining counts. Because digit range is fixed, the entire process runs in linear O(n) time.

What is the best approach for Largest Multiple of Three?

The most efficient approach uses digit counting with modulo manipulation. Compute the sum of digits, adjust by removing the smallest digits that fix the remainder modulo 3, then rebuild the number in descending order. This runs in O(n) time and O(1) space because digit values are limited to 0–9.

Is Largest Multiple of Three asked at Google/Amazon/Meta?

Largest Multiple of Three is a common greedy and modulo arithmetic interview problem and has appeared in coding interviews at companies that emphasize algorithmic reasoning, including large tech firms. It tests understanding of divisibility rules, greedy removal strategies, and efficient digit handling.

What data structure is used in Largest Multiple of Three?

Typical solutions use arrays or frequency counters to track digit occurrences. The optimized solution uses a fixed-size array of length 10 to count digits and manipulate them based on modulo conditions. Sorting-based approaches also rely on arrays to reorder digits.

What is the time complexity of Largest Multiple of Three?

The optimal solution runs in O(n) time using digit frequency counting and modulo adjustments. A simpler greedy solution that sorts digits takes O(n log n) time due to sorting. Both approaches use O(n) or O(1) extra space depending on whether sorting or fixed-size counting is used.

1363. Largest Multiple of Three - Practice Online

Given an array of digits digits, return the largest multiple of three that can be formed by concatenating some of the given digits in any order. If there is no answer return an empty string.

Since the answer may not fit in an integer data type, return the answer as a string. Note that the returning answer must not contain unnecessary leading zeros.

Example 1:

Input: digits = [8,1,9]
Output: "981"

Example 2:

Input: digits = [8,6,7,1,0]
Output: "8760"

Example 3:

Input: digits = [1]
Output: ""

Constraints:

1 <= digits.length <= 10⁴
0 <= digits[i] <= 9