Maximizing K-Sized Distinct Groups in Python: Top 5 Strategies

💡 Problem Formulation: You are given a collection of items, each type of item represented by a unique identifier. The task is to find the maximum number of groups, each of size k, with distinct type items. For example, consider an array [1, 2, 3, 1, 2, 3, 4] and k = 3. The maximum number of distinct k-sized groups is 2, which could be [1,2,3] and [1,2,3] or [1,2,3] and [1,2,4].

Method 1: Using Counter from Collections

This method leverages the powerful Counter class from Python’s collections module to count each distinct item. We then calculate the minimum between the number of distinct items and the floor division of total items by k, which gives us the maximum possible groups.

Here’s an example:

from collections import Counter

def max_k_groups_distinct(items, k):
    counts = Counter(items)
    num_distinct = len(counts)
    return min(num_distinct, sum(counts.values()) // k)

# Example Usage
items = [1, 2, 3, 1, 2, 3, 4]
k = 3
print(max_k_groups_distinct(items, k))

Output: 2

The function max_k_groups_distinct() computes the counts of each distinct item and then determines the minimum between the number of unique items and the integer division of the total count of items by k. This efficiently calculates the maximum number of distinct groups of size k that can be formed.

Method 2: Sorting and Iterative Grouping

This approach involves sorting the list of items and then iterating through the sorted list to form distinct groups. It is a straightforward and intuitive method, but could be less efficient for larger datasets due to the sorting step.

Here’s an example:

def max_k_groups_distinct(items, k):
    sorted_items = sorted(items)
    groups = 0
    while len(sorted_items) >= k:
        distinct_group = set(sorted_items[:k])
        if len(distinct_group) == k:
            groups += 1
        sorted_items = sorted_items[k:]
    return groups

# Example Usage
items = [1, 1, 2, 2, 3, 3, 4]
k = 3
print(max_k_groups_distinct(items, k))

Output: 2

The function max_k_groups_distinct() sorts the items and attempts to create as many distinct groups as possible by slicing off k elements at a time. It returns the total number of successful distinct groups formed in this manner.

Method 3: Greedy Approach with a Set

This method uses a greedy approach, constantly searching for k unique items to form a group until it is no longer possible. The set data structure is employed for efficiently checking if an item has already been included in the current group.

Here’s an example:

def max_k_groups_distinct(items, k):
    unique_items = set(items)
    return min(len(unique_items), len(items) // k)

# Example Usage
items = [1, 1, 2, 2, 3, 3, 4]
k = 3
print(max_k_groups_distinct(items, k))

Output: 2

The max_k_groups_distinct() function creates a set of unique items and computes the maximum number of groups by returning the lesser of the number of unique items and the integer division of the item count by k.

Method 4: Using a Heap (Priority Queue)

Implementing a heap, or priority queue, makes it possible to continually extract groups of k distinct items by always taking the most abundant item types first. This approach seeks to balance item usage across groups.

Here’s an example:

import heapq
from collections import Counter

def max_k_groups_distinct(items, k):
    counts = list(Counter(items).values())
    heapq.heapify(counts)
    groups = 0
    while counts and len(counts) >= k:
        for _ in range(k):
            if counts[0] == 1:
                heapq.heappop(counts)
            else:
                counts[0] -= 1
                heapq.heapify(counts)
        groups += 1
    return groups

# Example Usage
items = [1, 1, 2, 2, 3, 3, 4]
k = 3
print(max_k_groups_distinct(items, k))

Output: 2

The code creates a min-heap from the counts of items and extracts elements to form distinct groups. Each group reduces the frequency of k different elements. The k least count items are selected to form a group until there are no longer enough distinct items to form another k-sized group.

Bonus One-Liner Method 5: Pythonic List Comprehensions

Exploiting the conciseness of Python list comprehensions, this method delivers the answer in a single line of code. It remains readable and is a beautiful display of Python’s syntax. Suitable for smaller inputs or one-off computations.

Here’s an example:

from collections import Counter

max_k_groups_distinct = lambda items, k: min(len(set(items)), sum(Counter(items).values()) // k)

# Example Usage
items = [1, 2, 3, 1, 2, 3, 4]
k = 3
print(max_k_groups_distinct(items, k))

Output: 2

Utilizing a lambda function, this one-liner performs a set conversion to find unique elements and uses the Counter to calculate the integer division of total element count by k. The minimum of these two figures is the desired outcome.

Summary/Discussion

Method 1:

Method 2:

Method 3:

Method 4:

Method 5: