The code is pretty self-explained enough...
When it comes to the Kth smallest:

algorithm2.png

algorithm.png

Note that the choosing of the pivot value is up to the programmer

class Solution {
public:
    bool flag = false;

    int findKthLargest(vector<int>& nums, int k) {
        if (flag == false) {
            k -= 1;
            flag = true;
        }
        int pivot, pivotindex;
        vector<int> larger, equal, smaller;
        pivotindex = nums.size()/2; // generate a random number between 0 ~ num.size()
        pivot = nums[pivotindex];
        for (auto i : nums) {
            if (i < pivot) {
                smaller.push_back(i);
            }
            else if (i == pivot) {
                equal.push_back(i);
            }
            else if (i > pivot) {
                larger.push_back(i);
            }
        }
        if (k < larger.size())
            return findKthLargest(larger, k);
        else if (k >= larger.size() && k < larger.size() + equal.size()) {
            return pivot;
            flag = false;
        }
        else if (k >= larger.size() + equal.size())
            return findKthLargest(smaller, k-larger.size()-equal.size());
    }
};