Kth Largest Element in a Stream

Numbers arrive one at a time, like the scores of a game coming in live, and after each one you must say which number is in k-th place: the k-th largest of all the numbers so far. Equal numbers count separately: in [8, 7, 7, 5] the 2nd largest is 7, and so is the 3rd.

Implement the class KthLargest:

• KthLargest(k, nums) creates the object with the integer k and the numbers nums that have arrived already.
• add(val) adds the number val and returns the k-th largest of all the numbers so far.

The input describes one new KthLargest and a list of add calls, applied in order. The output lists what the add calls return, in order. The starter code spells these names the way your language does.

Example 1:

Input:
    KthLargest(3, [4, 5, 8, 2])
    add(3)
    add(5)
    add(10)
    add(9)
    add(4)
Output: 4 5 5 8 8
Explanation:
After add(3) the numbers are [2, 3, 4, 5, 8]: the three largest are 8, 5 and 4, so the 3rd largest is 4.
After add(5): 8, 5, 5 are the three largest, so the answer is 5.
After add(10): 10, 8, 5, answer 5. After add(9): 10, 9, 8, answer 8.
add(4) changes nothing at the top: 4 is smaller than the 3rd largest, so the answer stays 8.

Example 2:

Input:
    KthLargest(1, [])
    add(-3)
    add(-2)
    add(-4)
    add(0)
    add(4)
Output: -3 -2 -2 0 4
Explanation: With k = 1, add returns the largest number so far. No numbers have arrived when the object is created, so after the first add, -3 is the only one, and the largest.

Example 3:

Input:
    KthLargest(4, [7, 7, 7, 7, 8, 3])
    add(2)
    add(10)
    add(9)
    add(9)
Output: 7 7 7 8
Explanation: Equal numbers count separately: in [8, 7, 7, 7, 7, 3, 2] the 4th largest is the third 7. After 10 and 9 arrive the four largest are 10, 9, 8, 7. The second 9 pushes the last 7 out: 10, 9, 9, 8, so the answer becomes 8.

Constraints:

• 1 <= k <= 105
• 0 <= nums.length <= 105
• -104 <= nums[i], val <= 104
• At most 105 calls are made to add.
• When add returns, at least k numbers have arrived, so the k-th largest always exists.