Example: Counting Sort Implementation in C++

// Counting Sort Implementation
#include <iostream>
#include <vector>
#include <algorithm> // Required for std::max_element

using namespace std;

void countingSort(vector<int>& arr) {
    if (arr.empty()) {
        return; // Nothing to sort
    }

    // Step 1: Find the maximum element in the input array
    // This determines the size of the count array.
    int max_val = *max_element(arr.begin(), arr.end());

    // Step 2: Create a count array to store frequency of each element
    // The size of count_array will be max_val + 1 to accommodate 0 to max_val.
    vector<int> count(max_val + 1, 0);

    // Step 3: Populate the count array
    // count[i] will store the number of occurrences of i in arr.
    for (int x : arr) {
        count[x]++;
    }

    // Step 4: Modify the count array to store cumulative counts
    // count[i] will now store the number of elements less than or equal to i.
    for (int i = 1; i <= max_val; i++) {
        count[i] += count[i - 1];
    }

    // Step 5: Create an output array to store the sorted elements
    // This array will have the same size as the input array.
    vector<int> output(arr.size());

    // Step 6: Iterate through the input array from right to left
    // Place each element into its correct sorted position in the output array.
    // Decrement the count for that element to handle duplicates correctly.
    for (int i = arr.size() - 1; i >= 0; i--) {
        // The correct position for arr[i] is count[arr[i]] - 1
        output[count[arr[i]] - 1] = arr[i];
        count[arr[i]]--; // Decrement count for stability and duplicate handling
    }

    // Step 7: Copy the sorted elements from the output array back to the original array
    arr = output;
}

int main() {
    // Step 1: Initialize an unsorted array
    vector<int> arr = {4, 2, 2, 8, 3, 3, 1};

    cout << "Original array: ";
    for (int x : arr) {
        cout << x << " ";
    }
    cout << endl;

    // Step 2: Call the countingSort function
    countingSort(arr);

    cout << "Sorted array: ";
    for (int x : arr) {
        cout << x << " ";
    }
    cout << endl;

    // Example with another array
    vector<int> arr2 = {10, 4, 1, 4, 2, 10, 7};
    cout << "\nOriginal array 2: ";
    for (int x : arr2) {
        cout << x << " ";
    }
    cout << endl;
    countingSort(arr2);
    cout << "Sorted array 2: ";
    for (int x : arr2) {
        cout << x << " ";
    }
    cout << endl;

    return 0;
}