Distribute Candies

Alice is allowed to eat n/2 candies and wants to eat as many different types of candies as possible. We will find the number of unique types of candies and then return the minimum of that number and n/2.

We’ll follow these steps to accomplish that:

Use a set to find the number of unique types of candies in the given list.
Return the minimum of n/2 and the number of unique types.

Here’s the implementation:

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class Solution:
    def distributeCandies(self, candyType: List[int]) -> int:
        unique_types = len(set(candyType))
        return min(unique_types, len(candyType) // 2)

This code first calculates the number of unique types of candies by converting the candyType list into a set and then calculating its length. Then it returns the minimum of this number and n/2, ensuring that Alice eats only the allowed number of candies and as many different types as possible.

“Distribute Candies” involves understanding of arrays and hash tables. Here are some problems of lesser complexity before tackling this problem:

“Single Number” (LeetCode 136): This problem helps understand how to use hash tables to count occurrences.
“Intersection of Two Arrays II” (LeetCode 350): This problem is about finding common elements in two arrays, which is a good practice for dealing with array manipulation and hash table.
“Contains Duplicate” (LeetCode 217): This problem will help you get familiar with the concept of checking for duplicates in an array.
“Two Sum” (LeetCode 1): This is a basic problem involving array manipulation and using hash tables to find matching pairs.
“Majority Element” (LeetCode 169): This problem is also about counting the frequency of elements in an array.
“Valid Anagram” (LeetCode 242): This problem involves checking the count of characters in two strings.
“Find All Numbers Disappeared in an Array” (LeetCode 448): This problem will help you understand how to manipulate arrays and use information from the array itself.
“Missing Number” (LeetCode 268): This problem will help you understand how to use the properties of arrays to find missing elements.
“First Unique Character in a String” (LeetCode 387): This problem also uses the concept of frequency counts to identify unique characters in a string.
“Sort Array By Parity” (LeetCode 905): This problem deals with the reordering of an array based on some condition, which can be useful for understanding how to distribute elements.

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def distributeCandies(self, candyType: List[int]) -> int:
        candy_len = int(len(candyType)/2)

        unique_candy_len = len(set(candyType))
        return min(candy_len,unique_candy_len)

Problem Classification

The problem is in the sub-domain of Array Manipulation and Optimisation.

The “What” components from the problem are:

Alice has n candies of different types. The type of each candy is given by an array candyType[i].
Alice can only eat n / 2 candies due to her doctor’s advice.
Alice wishes to maximize the variety of candies she eats, i.e., she wants to eat as many different types of candies as possible.
The task is to find the maximum number of different types of candies Alice can eat, given the constraint that she can only eat n / 2 candies.

Problem Type: This is an Optimization Problem as the goal is to find the maximum number of different types of candies Alice can eat. We need to find the optimal distribution of candy types that Alice should eat.
Data Structures: Array (to hold the type of candies)
Techniques involved: Set Operations, Greedy Algorithms. The problem involves finding a subset of the candies (which is essentially a Set Operation) such that the number of different types is maximized (a hallmark of Greedy Algorithms).

Identifying Problem Isomorphism

“Distribute Candies” can be mapped to “Water Bottles.”

Reasoning:

Both problems involve distributing items in a specific manner, following certain constraints and rules.
In “Distribute Candies,” the goal is to distribute candies between siblings equally, and you need to find the maximum number of different types of candies a sibling can get. The constraint here relates to the available types of candies and their distribution among siblings.
In “Water Bottles,” the aim is to maximize the amount of water that can be drunk from full water bottles, given that you can exchange empty bottles for new full ones. The constraint here involves the number of empty bottles required for an exchange and the initial number of full bottles.

While the problems are not exactly the same, they share the theme of maximizing something (types of candies or amount of water) under certain constraints, and the logic to solve them revolves around simple arithmetic calculations involving division and modulus operations.

“Distribute Candies” is simpler as it mostly involves finding a unique way of distribution, whereas “Water Bottles” adds an additional layer of complexity by introducing the exchange mechanism.

Language Agnostic Coding Drills

Dissect the Code:
The given Python code is a function that takes in a list of integers (representing the types of candies) and returns an integer (representing the maximum number of different types of candies Alice can eat). The function involves the following distinct concepts:
- List operation: The len function is used to determine the number of elements in the list candyType.
- Division operation: The number of elements in candyType is divided by 2, to get the number of candies Alice is allowed to eat.
- Set operation: The set function is used to convert the list candyType into a set, eliminating duplicate values (if any) and hence giving us the unique candy types.
- Minimum operation: The min function is used to find the minimum between two numbers - the number of candies Alice can eat, and the number of unique candy types.
List of Concepts:
Here are the coding concepts or drills identified in increasing order of difficulty:
- Arithmetic Operations: The code involves basic arithmetic operation (division by 2). This is the simplest concept as it is fundamental to most programming tasks.
- List Operations: Understanding how to work with lists in Python is a crucial concept. In this case, the len function is used to find the number of elements in a list.
- Set Operations: The code converts a list to a set, which is a slightly more advanced concept. Understanding how to manipulate sets, and the fact that sets contain unique elements, is important for solving many types of problems.
- Built-in Functions: The code uses built-in Python functions (len, set, min). Understanding built-in functions can make your code more efficient and concise.
Problem-solving Approach:
- The first step is understanding the problem and noting that Alice can eat only half of the total number of candies she has (n/2). This is calculated using the length of the list and the division operation.
- The second step is determining the total number of unique types of candies that Alice has. This is achieved by converting the list of candy types to a set, which automatically removes any duplicates.
- The final step is realizing that the maximum number of different types of candies Alice can eat is either the total number of unique candy types (if this number is less than or equal to n/2) or n/2 (if the number of unique types is greater than n/2). This is determined using the min function.
Each of these drills (calculating n/2, determining the number of unique types, and finding the minimum of two numbers) contributes to the final solution, which is why understanding each one is important for solving the problem.

Targeted Drills in Python

Python Coding Drills

Arithmetic Operations:

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# Given two integers, perform division
a = 10
b = 2
result = a / b
print(result)  # Output: 5.0

List Operations:

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# Given a list, find its length
list_numbers = [1, 2, 3, 4, 5]
list_len = len(list_numbers)
print(list_len)  # Output: 5

Set Operations:

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# Given a list, convert it to a set to find unique elements
list_numbers = [1, 2, 2, 3, 4, 4, 5, 5]
unique_numbers = set(list_numbers)
print(unique_numbers)  # Output: {1, 2, 3, 4, 5}

Built-in Functions:

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# Given two numbers, find the minimum using the min function
a = 5
b = 10
minimum = min(a, b)
print(minimum)  # Output: 5

Problem-specific Drills
There doesn’t seem to be any problem-specific concepts that need separate drills in this case. All the identified concepts and drills are general Python concepts that are used to solve this specific problem.
Integration of Drills
The final solution can be assembled by integrating the above drills in a particular sequence:
- The length of the list candyType is calculated. Half of this length represents the maximum number of candies Alice can eat.
- The list candyType is converted to a set, which removes any duplicates and hence gives us the number of unique types of candies.
- The minimum between the number of candies Alice can eat and the number of unique types of candies is then calculated. This gives us the maximum number of different types of candies Alice can eat if she only eats n / 2 of them.
Each of these steps corresponds to one of the identified drills, and implementing them in this order solves the problem as per the given problem statement.