Is the Time Complexity of this code O(N)?

Question

Is the Time Complexity of this code O(N) ? (in this code I want to find Kth largest element of array)

class Solution {
    public:
        int findKthLargest(vector<int>& nums, int k) {
            make_heap(nums.begin(), nums.end());
            for (int i = 0; i < k - 1; i ++) {
                pop_heap(nums.begin(), nums.end());
                nums.pop_back();
            }
            return nums.front();
        }
    };

Answer 1

Depends.

Because make_heap is already at O(n), and each loop is at O(log n), the total time complexity for your algorithm is O(n + k log n) . With a small k or a "good" set of data, the result is roughly O(n) and the constant behind the O() mark, but with a large k (near or surpassing n/2) or random data, it's O(n log n).

Also I'd like to point out that this code is modifying the original array (using reference for passing arguments), which isn't often a good practice.

^{log is 2-based in this post}