Find the kth Largest Element in an Unsorted Array

#!cpp
#include <iostream>

using namespace std;

/**
 * the partition function borrowed from quicksort. See also CLRS.
 * time complexity O(n)
 **/
int partition(int arr[], int left, int right) {
    int x = arr[right];
    int i = left - 1;

    for (int j = left; j < right; j++) {
        if (arr[j] <= x) {
            i++;
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }
    arr[right] = arr[i+1];
    arr[i+1] = x;
    return i + 1;
}

/**
 * find the kth largest ele. O(logk) * O(n) = O(nlogk)
 **/
int find_k(int arr[], int left, int right, int k) {
    int mid = partition(arr, left, right);
    int pos = right - mid + 1;
    if (pos == k) {
        return arr[mid];
    } else if (pos > k) {
        return find_k(arr, mid + 1, right, k);
    } else {
        return find_k(arr, left, mid - 1, k - pos);
    }
}

int main() {
    const int M = 10;
    const int K = 2;
    int arr[M] = {6, 4, 9, 12, 18, 13, 5, 1, 3, 10};
    for (int k = 1; k <= M; k++) {
        cout << find_k(arr, 0, M-1, k) << endl;
    }
    //cout << find_k(arr, 0, M - 1, K) << endl;

    return 0;
}