Is the time complexity of this function O(log n)?

Question

I am trying to do this problem on LeetCode , and the following is the solution I came up with:

 var findKthLargest = function(nums, k) { //var tmp = nums.slice(); var iteration = 0; while (iteration < k) { var max = -Infinity; for (var i = 0; i < nums.length; i++) { var cut; if (nums[i] > max) { max = nums[i]; cut = i; } } nums.splice(cut, 1); iteration++; } return max; }; 

Now, I believe this is a log n solution because what I'm basically doing is removing the largest value in the array, which decreases my number of comparisons. However, it only beats 59% of the JavaScript solutions, which makes me think I might not have the right complexity.

Answer 1

There are k iterations of the while() loop (which, I think, would be more idiomatically written as for(var j = 0; j < k; j++) ).

The first iteration then performs n iterations of the for loop, and nums.splice(cut, 1) is O(n) because it has to shift all the array elements from cut to n . O(2n) is the same as O(n) because constant factors are ignored in big-O calculation.

The second iteration performs n-1 iterations. This is also O(n) because we ignore constant adjustments in big-O notation. The same goes for the splice .

So the final result is that it's O(k * n) , since you have k iterations of the outer loop, and the inner loops are each O(n) . The worst case, when k >= n , is O(n^2)