Kth Largest - Implementation

Here's the solution:

function findKthLargest(nums, k)
    heap := empty min-heap

    for each num in nums
        if size of heap < k
            insert num into heap
        else if num > root of heap
            extract min from heap
            insert num into heap

    return root of heap

Time: $O(n \log k)$. Space: $O(k)$.

You'll find this better than sorting when $k$ is small relative to $n$.