How do you solve Check If Array Pairs Are Divisible by k on LeetCode?

Check If Array Pairs Are Divisible by k (LeetCode #1497) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(k) space complexity. Key insight: Understanding modular arithmetic is crucial for solving problems involving divisibility.

What is the brute force solution for Check If Array Pairs Are Divisible by k?

The brute force approach for Check If Array Pairs Are Divisible by k is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves generating all possible pairs of elements in the array and checking if their sums are divisible by k. This is straightforward but inefficient, especially for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Check If Array Pairs Are Divisible by k?

Check If Array Pairs Are Divisible by k uses the following concepts: Array, Hash Table, Counting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Check If Array Pairs Are Divisible by k?

Always consider edge cases and how they might affect your solution. Explain your thought process clearly while coding; it helps interviewers understand your approach. Practice problems that involve modular arithmetic to become more comfortable with the concepts.

What are common mistakes when solving Check If Array Pairs Are Divisible by k?

Failing to account for special cases like remainders of 0 or k/2. Not using a frequency array to simplify the pairing logic.

#1497

Check If Array Pairs Are Divisible by k

Medium

ArrayHash TableCountingHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n)Space O(k)

The optimal solution leverages the properties of modular arithmetic. By counting the frequencies of remainders when elements are divided by k, we can efficiently check if pairs can be formed that satisfy the divisibility condition.

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Algorithm

5 steps

1Step 1: Create a frequency array to count occurrences of each remainder when elements are divided by k.
2Step 2: For each remainder, check if it can be paired with its complement (k - remainder).
3Step 3: Special case for remainder 0: must have an even count.
4Step 4: Special case for k/2 if k is even: must also have an even count.
5Step 5: If all conditions are satisfied, return true; otherwise, return false.

solution.py11 lines

1# Full working Python code
2from collections import Counter
3
4def canArrange(arr, k):
5    remainder_count = Counter((num % k + k) % k for num in arr)
6    if remainder_count[0] % 2 != 0:
7        return False
8    for i in range(1, (k // 2) + 1):
9        if remainder_count[i] != remainder_count[k - i]:
10            return False
11    return True

ℹ

Complexity note: The time complexity is linear because we traverse the array once to count remainders, and the space complexity is linear with respect to k for the frequency array.

1Understanding modular arithmetic is crucial for solving problems involving divisibility.
2Using frequency counts can significantly reduce the complexity of pairing problems.

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