Problem Description
You will find yourself in situations where you need to sort a large number of numbers for some time. Understanding and implementing commonly used sorting algorithms is an essential skill in coding tests.
The problem presented here is to sort a given list of numbers in ascending order.
Problem:
Write a program that sorts and outputs the given n integers in ascending order.
Input:
The first line contains an integer n (1 ≤ n ≤ 100,000). The next n lines each contain one integer.
These integers will not exceed an absolute value of 1,000,000.
Output:
Print each of the sorted numbers on a new line.
Problem Solving Process
Step 1: Understanding the Problem
To understand the problem, let’s first recall the definition and importance of sorting. Sorting refers to organizing data according to specific criteria in data structures.
In this case, we need to organize the data in ascending order. Advanced algorithms such as binary search and merge sort can be applied based on sorted data.
Step 2: Selecting an Algorithm
Commonly used sorting algorithms include bubble sort, selection sort, insertion sort, quick sort, and merge sort.
Given that the input size can be as large as 100,000, it is recommended to use an algorithm with a time complexity of O(n log n), such as quick sort or merge sort.
In Python, you can easily solve this problem using the built-in function sorted() or the list method sort().
Step 3: Writing the Code
Below is the code to solve this problem.
def sort_numbers(numbers):
return sorted(numbers)
# Input
n = int(input())
numbers = [int(input()) for _ in range(n)]
# Output the sorted result
sorted_numbers = sort_numbers(numbers)
for number in sorted_numbers:
print(number)
In the above code, the sort_numbers function sorts the input list and returns it. It uses list comprehension to receive n integers entered by the user.
Finally, it prints the sorted list line by line.
Step 4: Running the Code and Checking Results
To test the above code, we prepare the following input:
5
3
1
4
1
5
With the above input, the program should output as follows:
1
1
3
4
5
Algorithm Complexity Analysis
Time Complexity: O(n log n)
The built-in sorting function used in this problem is very efficient and has an average time complexity of O(n log n).
Space Complexity: O(n)
Since we need to store n integers, the space complexity is O(n).
Other Considerations
The reason for using Python’s built-in function for sorting is due to its simplicity in implementation and performance advantages.
However, understanding the basic sorting algorithms will allow you to demonstrate your foundational skills in important exams or interviews.
Additionally, it is beneficial to understand and memorize the characteristics, time, and space complexity differences of each sorting algorithm.