Category: C++ Coding Test Tutorials

Problem Description:
“The problem of sorting numbers 3” is a problem of sorting given numbers, in which the range of input numbers is limited. In particular, the range of inputs for this problem is integers from 1 to 10000, and each integer can be very numerous. Therefore, instead of using a simple sorting algorithm, we need to seek a more efficient method. This problem can be solved using the Counting Sort algorithm.

Problem Conditions

• Number of input numbers: N (1 ≤ N ≤ 100000)
• Range of numbers: 1 ≤ number ≤ 10000

Algorithm Explanation

The Counting Sort algorithm creates an array based on the range of given values to sort integer values and counts their occurrences to organize them. The process is as follows:

1. Create an array based on the maximum value of the input numbers. In this case, the maximum value is 10000.
2. Repeat for N number of inputs, storing the count of each number in the counting array.
3. Utilize the counting array to print each number as many times as its count.

This method has a time complexity of O(N + K), where K is the range of the numbers (in this case, 10000). Therefore, it can efficiently handle even large input data.

Problem Solving Process

1. Include the necessary header files to receive input.
2. Input the number N of numbers to be sorted.
3. Declare a counting array to store the number of occurrences and initialize it to 0.
4. Create a loop to input N numbers, incrementing the index of the corresponding number in the counting array to count.
5. Create a loop to reference the counted array and print each number as many times as its count.

C++ Code

#include <iostream>
#include <vector>

using namespace std;

int main() {
    int n;
    cin >> n; // Input the number of numbers
    vector count(10001, 0); // Array to store the count of numbers from 1 to 10000

    // Count the input numbers
    for (int i = 0; i < n; i++) {
        int num;
        cin >> num;
        count[num]++;
    }

    // Output sorted numbers based on the counted array
    for (int i = 1; i <= 10000; i++) {
        while (count[i] > 0) {
            cout << i << '\n';
            count[i]--;
        }
    }

    return 0;
}

Explanation of the Above Code

1. Input: Input the number N of numbers to be sorted and N integers from the user.

2. Create Counting Array: Create a vector of size 10001 for Counting Sort. The index of this array represents the input numbers, and the value at each index stores the count of that number.

3. Counting Numbers: Repeat for N numbers to increment the corresponding index in the counting array. This counts the frequency of each number.

4. Output: Based on the counted results, output each number according to its frequency. In this process, the index of each number identifies that number.

Efficiency Analysis

This algorithm has excellent time efficiency, capable of handling datasets with up to 100000 numbers without issues. In terms of memory, the counting array has a fixed size of 10001, so it does not consume additional memory, resulting in overall good performance.

Summary

The process of solving the “Sorting Numbers 3” problem using Counting Sort is clearly efficient, especially given the limited range of input values which emphasizes the usefulness of this method. This problem allows for a solid understanding of the concept of Counting Sort, and it also provides an opportunity to learn how to combine data structures and algorithms using C++ vectors.

Advanced Content and Applications

While Counting Sort is very efficient in specific situations, it is important to remember that it is not suitable for all sorting problems. This algorithm can only be used for sorting integers or enumerated data, and when dealing with broader data types such as floats, it is advisable to consider other algorithms (e.g., Quick Sort, Merge Sort, etc.).

Additionally, Counting Sort possesses its greatest advantages when the range of numbers is small, so it should always be considered among sorting algorithms for problems with such characteristics.

Conclusion: The “Sorting Numbers 3” problem is an example that can be easily solved using Counting Sort. I hope this course helps you further enhance your C++ coding skills!