Leetcode 1497. Check If Array Pairs Are Divisible by k

TL;DR

We analyze how to determine if pairs in an array are divisible by a given integer K.

Transcript

hello everyone welcome back to decoding today we are going to solve the problem check if arepas are divisible by key in this problem we are given an array of integers of size N and another integer K we want to divide the array into exactly n by 2 pills such that the summation of each element in the pair is divisible by K we have to return true in c... Read More

Key Insights

• 💁 The essential requirement is to form pairs from the given integers so their sums are multiples of K.
• 📁 Using a modulus approach helps analyze the relationship between numbers without direct summation, optimizing computation.
• 🥺 The pairing rules are strict; mismatched counts regarding opposite moduli lead to an immediate conclusion that pairing isn't feasible.
• 🍵 Handling negative numbers requires transformation to maintain proper moduli for valid pairing.
• 👻 An unordered map facilitates storing moduli counts efficiently, allowing linear time complexity for operations.
• 💨 The solution should be structured in such a way to handle both positive and negative integers uniformly.
• ❓ Pairing elements together into correct configurations is critical for satisfying the problem condition of divisibility.

Questions & Answers

Q: What is the main objective of the problem regarding pairs of integers?

The primary objective is to determine if the integers in the provided array can be paired such that the sum of each pair is divisible by a given integer K. It's crucial to find a specific pairing strategy that satisfies this divisibility requirement.

Q: Why must elements with a modulus of 0 appear in even counts?

Elements that yield a modulus of 0 when divided by K must be in even numbers to form pairs, as each pair must consist of two elements. An odd count would leave one element without a partner, thus making it impossible to ensure all sums are divisible by K.

Q: How can negative integers affect the solution, and what adjustments are necessary?

Negative integers can yield negative moduli during computations. To address this, we must adjust the negative values to their positive equivalents using the formula: modulo = (value + K) % K, ensuring consistent pairing possibilities with positive integers.

Q: How do we check if specific moduli can form valid pairs?

We check the counts of numbers having specific moduli. For instance, the count of elements with modulus 1 must equal those with modulus K-1, and counts of elements with modulus 2 should equal those with modulus K-2. If counts do not match, pairing is impossible.

Summary & Key Takeaways

• The problem involves pairing elements of an integer array so their sums are divisible by a specified integer K. The goal is to find efficient ways to create these pairs based on their modulus with K.

• Pairs can only be formed if the counts of specific moduli match; for example, moduli that sum to K or are both 0 must be even in count. This ensures equal opportunity to create valid pairs.

• The solution uses a map to count occurrences of each modulus and checks combinations for these moduli to create valid pairs. The approach also accounts for negative integers by adjusting their modulus values.