How do you solve X of a Kind in a Deck of Cards on LeetCode?

X of a Kind in a Deck of Cards (LeetCode #914) 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: The problem can be reduced to finding the GCD of card frequencies.

What is the brute force solution for X of a Kind in a Deck of Cards?

The brute force approach for X of a Kind in a Deck of Cards is Brute Force, with O(n²) time complexity and O(1) space complexity. We can check every possible group size starting from 2 up to the maximum frequency of any card. For each group size, we verify if we can partition the deck into groups of that size with the same card values. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve X of a Kind in a Deck of Cards?

X of a Kind in a Deck of Cards uses the following concepts: Array, Hash Table, Math, Counting, Number Theory. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for X of a Kind in a Deck of Cards?

Always think about the mathematical properties of the problem, like GCD. Discuss your thought process clearly; explain why you choose a particular approach. Check for edge cases and constraints before finalizing your solution.

What are common mistakes when solving X of a Kind in a Deck of Cards?

Not considering the GCD approach and sticking to brute force. Overlooking edge cases where all cards are the same.

#914

X of a Kind in a Deck of Cards

Easy

ArrayHash TableMathCountingNumber TheoryHash 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 checking each possible group size, we can use the greatest common divisor (GCD) of the frequencies of the cards. If the GCD is greater than 1, we can partition the deck into valid groups.

⚙️

Algorithm

3 steps

1Step 1: Count the frequency of each card in the deck.
2Step 2: Compute the GCD of all frequencies.
3Step 3: If the GCD is greater than 1, return true; otherwise, return false.

solution.py10 lines

1# Full working Python code
2from collections import Counter
3from math import gcd
4from functools import reduce
5
6def hasGroupsSizeX(deck):
7    count = Counter(deck)
8    freq = list(count.values())
9    overall_gcd = reduce(gcd, freq)
10    return overall_gcd > 1

ℹ

Complexity note: The time complexity is O(n) because we count the frequencies in a single pass and compute the GCD in linear time relative to the number of unique card values.

1The problem can be reduced to finding the GCD of card frequencies.
2If the GCD is greater than 1, valid groupings are possible.

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