## Table of content

- Introduction
- Importance of Problem-Solving Skills
- Picking Numbers Problem Overview
- Solution Approach 1: Brute Force Method
- Solution Approach 2: Optimized Approach Using Hash Map
- Solution Approach 3: Pythonic Way Using List Comprehension
- Conclusion

### Introduction

When it comes to programming, problem-solving skills are essential. They are what separates a good programmer from a great one. Picking numbers problems are a common type of problem in programming, and they can be challenging to solve. However, with some ingenuity and the right tools, you can easily solve these problems. That's where HackerRank comes in. HackerRank is a platform that provides programming challenges that are designed to test your problem-solving skills. In this article, we will look at some of the ingenious picking numbers solutions from HackerRank that you can use to improve your programming skills. We will focus on Python programming, but the concepts discussed can be applied to other programming languages as well. So whether you are a beginner or an experienced programmer, this article will provide you with valuable insights into how to solve picking numbers problems efficiently.

### Importance of Problem-Solving Skills

Problem-solving skills are essential for success in any field, especially in the world of programming. As a programmer, you need to be able to think logically, break down complex problems into smaller, more manageable tasks, and come up with innovative solutions that are efficient and effective. A strong problem-solving mindset enables you to approach challenges with confidence, and to find solutions that others might not see.

In the context of Python programming, problem-solving skills are particularly important because Python is a versatile and powerful language that can be used in a wide variety of applications. Whether you are building software, analyzing data, or creating web applications, you will encounter complex challenges that require creative solutions. By developing your problem-solving skills, you can unlock your full potential as a Python programmer and become an invaluable asset to any team.

One way to enhance your problem-solving skills is by practicing with coding challenges, such as those offered by Hackerrank. These challenges offer a variety of problems that can be solved using Python, allowing you to work on your skills and build your confidence. The more you practice, the better you will become at breaking down problems, identifying patterns, and finding innovative solutions. With the right mindset and approach, you can become a skilled problem solver in Python and beyond.

### Picking Numbers Problem Overview

The Picking Numbers problem is a popular coding challenge featured on HackerRank. The problem requires the programmer to find the maximum length of a subarray where the absolute difference between any two elements is no greater than 1.

In more technical terms, the problem involves finding the length of the longest subarray of a given array where the difference between any two elements within the subarray is less than or equal to 1. For instance, if the input array is [4, 6, 5, 3, 3, 1], the longest subarray that satisfies this condition is [4, 5, 3, 3], which has a length of 4.

The Picking Numbers problem requires the programmer to use a combination of sorting and looping techniques to solve the problem efficiently. Sorting the array makes it easier to identify subarrays with elements that have a maximum difference of 1, while a loop is used to process the sorted array to identify the longest subarray.

There are several approaches to solving the Picking Numbers problem, ranging from simple brute-force solutions to more complex algorithms involving hash maps and frequency counters. The choice of approach depends on the size of the input array and the time and space constraints of the problem.

Overall, the Picking Numbers problem is an excellent challenge for programmers looking to hone their problem-solving skills, and its popularity on platforms like HackerRank makes it a worthwhile exercise for anyone interested in Python programming.

### Solution Approach 1: Brute Force Method

The Brute Force method is a popular solution approach to solve picking number problems on Hackerrank. This approach involves checking each possible subset of the given set of numbers, calculating its length, and storing the maximum length found so far. The time complexity of this approach is O(n^2), where n is the length of the given set of numbers.

To implement this approach in Python, we begin by reading in the set of numbers from the standard input or a given file. We can then initialize a variable to store the maximum length found so far, and a loop to iterate through all possible subsets of the given set of numbers. To generate all possible subsets, we can use the itertools module in Python.

For each subset generated, we calculate its length and compare it to the maximum length found so far. If the length of the current subset is greater than the maximum length found so far, we update the maximum length variable. After iterating through all possible subsets, we return the maximum length found.

While the Brute Force method is a simple and straightforward approach, it may not be the most efficient solution for large sets of numbers. In such cases, other more optimized solution approaches such as using hash maps or sliding windows may be more appropriate. However, for smaller sets of numbers, the Brute Force method is a reliable solution to picking number problems on Hackerrank.

### Solution Approach 2: Optimized Approach Using Hash Map

Another approach to solving the Picking Numbers problem on HackerRank is to use a hash map, which allows for faster lookups and better efficiency when dealing with large amounts of data. This approach involves iterating through the array and storing the frequency of each unique number in the array in a hash map.

Here's an example code snippet that demonstrates this approach:

```
def pickingNumbers(a):
max_count = 0
num_freq = {}
for num in a:
if num not in num_freq:
num_freq[num] = 1
else:
num_freq[num] += 1
for num in num_freq:
count = num_freq[num]
if num + 1 in num_freq:
count += num_freq[num+1]
if count > max_count:
max_count = count
return max_count
```

In this solution, we first initialize a hash map called `num_freq`

, which will store the frequency of each unique number in the array `a`

. We then loop through each element in `a`

, and for each element, we check whether it is already in `num_freq`

.

If the element is not in `num_freq`

, we add it to the hash map with a frequency of 1. If the element is already in `num_freq`

, we increment its frequency by 1. After this loop completes, we have a hash map that stores the frequency of each unique number in `a`

.

We then iterate through each unique number in `num_freq`

, and for each number, we compute the maximum count of numbers that can be selected from `a`

. To do this, we first set `count`

equal to the frequency of the current number. We then check whether the next consecutive number (i.e., `num+1`

) is in `num_freq`

, and if it is, we add its frequency to `count`

.

Finally, we check whether `count`

is greater than `max_count`

, and if it is, we update `max_count`

. After looping through all unique numbers in `num_freq`

, we return `max_count`

, which represents the maximum count of numbers that can be selected from `a`

such that the absolute difference between any two selected numbers is no more than 1.

### Solution Approach 3: Pythonic Way Using List Comprehension

List comprehension is a concise way of creating a list in Python. It is a Pythonic way of performing some operation on a list or creating a new list from an existing one. The syntax for list comprehension is [expression for item in list].

This approach can be applied to picking number problems by filtering out the numbers that meet certain criteria. For example, to find all the even numbers in a list using list comprehension, we can write [num for num in list if num%2==0].

Similarly, to find all the numbers that are divisible by 3 and 5 in a given range, we can use [num for num in range(start, end+1) if num%3==0 and num%5==0].

List comprehension provides a Pythonic and elegant solution to picking number problems, making the code shorter and easier to read. However, it may not always be the most efficient solution, particularly for large datasets. It is important to weigh the advantages and disadvantages of list comprehension before using it in your code.

### Conclusion

In , picking numbers is a common problem-solving scenario in the world of programming. The solutions discussed above provide some ingenious ways to tackle these problems, making it easier to solve complex problems with ease. Using Python programming, developers can come up with various efficient ways to solve picking numbers problems.

By utilizing efficient data structures such as sets and hash tables, developers can efficiently solve these problems, which may save time when dealing with large datasets. The solutions presented above are beginner-friendly and can be improved further as one advances their programming skills.

In summary, picking numbers is a common mathematical problem that can be solved using Python programming. With the right techniques, developers can solve these problems more efficiently by utilizing data structures such as sets and hash tables. As a result, developers can improve their problem-solving skills and simplify their programming tasks.