How do you solve Find the Divisibility Array of a String on LeetCode?

Find the Divisibility Array of a String (LeetCode #2575) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Using a running total for the remainder avoids recalculating the entire prefix value each time.

What is the time complexity of Find the Divisibility Array of a String?

The optimal solution for Find the Divisibility Array of a String runs in O(n) time and uses O(n) space. This complexity is O(n) because we only make a single pass through the string, updating the remainder in constant time for each character.

What is the brute force solution for Find the Divisibility Array of a String?

The brute force approach for Find the Divisibility Array of a String is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks each prefix of the string one by one and determines if it's divisible by m. This is straightforward but inefficient, as it recalculates the numeric value for each prefix from scratch. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Divisibility Array of a String?

Find the Divisibility Array of a String uses the following concepts: Array, Math, String. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Find the Divisibility Array of a String?

Always consider the efficiency of your approach; aim for O(n) solutions when possible. Practice breaking down the problem into smaller parts and solving them step by step. Be prepared to explain your thought process clearly; interviewers value understanding over just getting the right answer.

What are common mistakes when solving Find the Divisibility Array of a String?

Failing to update the remainder correctly, leading to incorrect results. Not considering the constraints of large numbers when converting substrings to integers.

#2575

Find the Divisibility Array of a String

Medium

ArrayMathStringHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

Instead of recalculating the numeric value for each prefix, we can maintain a running total that updates as we add each digit. This allows us to compute the divisibility in constant time for each new character.

⚙️

Algorithm

3 steps

1Step 1: Initialize an empty array div of length n and a variable remainder set to 0.
2Step 2: For each index i from 0 to n-1, update the remainder using the formula: remainder = (remainder * 10 + int(word[i])) % m.
3Step 3: If remainder is 0, set div[i] to 1, otherwise set it to 0.

solution.py9 lines

1# Full working Python code
2word = '998244353'
3m = 3
4div = []
5remainder = 0
6for i in range(len(word)):
7    remainder = (remainder * 10 + int(word[i])) % m
8    div.append(1 if remainder == 0 else 0)
9print(div)

ℹ

Complexity note: This complexity is O(n) because we only make a single pass through the string, updating the remainder in constant time for each character.

1Using a running total for the remainder avoids recalculating the entire prefix value each time.
2Understanding how to manipulate remainders can simplify many problems involving divisibility.

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