Kth Largest Element in an Array — C++

// Time:  O(n) on average, using Median of Medians could achieve O(n) (Intro Select)
// Space: O(1)

// optimized for duplicated nums
class Solution {
public:
    int findKthLargest(vector<int>& nums, int k) {
        nth_element(nums, k - 1);
        return nums[k - 1];
    }
    
private:
    void nth_element(vector<int>& nums, int n) {
        int left = 0, right = size(nums) - 1;
        default_random_engine gen((random_device())());
        while (left <= right) {
            // Generates a random int in [left, right].
            uniform_int_distribution<int> dis(left, right);
            int pivot_idx = dis(gen);
            const auto& [pivot_left, pivot_right] = TriPartition(left, right, nums[pivot_idx], &nums);
            if (pivot_left <= n && n <= pivot_right) {
                return;
            } else if (pivot_left > n) {
                right = pivot_left - 1;
            } else {  // pivot_right < n.
                left = pivot_right + 1;
            }
        }
    }
    
    pair<int, int> TriPartition(int left, int right, int target, vector<int> *nums) {
        for (int mid = left; mid <= right;) {
            if ((*nums)[mid] == target) {
                ++mid;
            } else if ((*nums)[mid] > target) {
                swap((*nums)[left++], (*nums)[mid]);
                ++mid;
            } else {
                swap((*nums)[mid], (*nums)[right--]);
            }
        }
        return {left, right};
    }
};

// Time:  O(n) on average, using Median of Medians could achieve O(n) (Intro Select)
// Space: O(1)
class Solution2 {
public:
    int findKthLargest(vector<int>& nums, int k) {
        int left = 0, right = nums.size() - 1;
        default_random_engine gen((random_device())());
        while (left <= right) {
            // Generates a random int in [left, right].
            uniform_int_distribution<int> dis(left, right);
            int pivot_idx = dis(gen);
            int new_pivot_idx = PartitionAroundPivot(left, right, pivot_idx, &nums);
            if (new_pivot_idx == k - 1) {
                break;
            } else if (new_pivot_idx > k - 1) {
                right = new_pivot_idx - 1;
            } else {  // new_pivot_idx < k - 1.
                left = new_pivot_idx + 1;
            }
        }
        return nums[k - 1];
    }
    
    int PartitionAroundPivot(int left, int right, int pivot_idx, vector<int>* nums) {
        auto& nums_ref = *nums;
        int pivot_value = nums_ref[pivot_idx];
        int new_pivot_idx = left;
        swap(nums_ref[pivot_idx], nums_ref[right]);
        for (int i = left; i < right; ++i) {
            if (nums_ref[i] > pivot_value) {
                swap(nums_ref[i], nums_ref[new_pivot_idx++]);
            }
        }
        swap(nums_ref[right], nums_ref[new_pivot_idx]);
        return new_pivot_idx;
    }
};

// Time:  O(n) ~ O(n^2)
// Space: O(1)
class Solution3 {
public:
    int findKthLargest(vector<int>& nums, int k) {
        nth_element(nums.begin(), next(nums.begin(), k - 1), nums.end(), greater<int>());
        return *next(nums.begin(), k - 1);
    }
};