# 703. Kth Largest Element in a Stream

#### Easy

***

Design a class to find the `kth` largest element in a stream. Note that it is the `kth` largest element in the sorted order, not the `kth` distinct element.

Implement `KthLargest` class:

* `KthLargest(int k, int[] nums)` Initializes the object with the integer `k` and the stream of integers `nums`.
* `int add(int val)` Appends the integer `val` to the stream and returns the element representing the `kth` largest element in the stream.

 

**Example 1:**

```
Input
["KthLargest", "add", "add", "add", "add", "add"]
[[3, [4, 5, 8, 2]], [3], [5], [10], [9], [4]]
Output
[null, 4, 5, 5, 8, 8]

Explanation
KthLargest kthLargest = new KthLargest(3, [4, 5, 8, 2]);
kthLargest.add(3);   // return 4
kthLargest.add(5);   // return 5
kthLargest.add(10);  // return 5
kthLargest.add(9);   // return 8
kthLargest.add(4);   // return 8
```

 

**Constraints:**

* `1 <= k <= 104`
* `0 <= nums.length <= 104`
* `-104 <= nums[i] <= 104`
* `-104 <= val <= 104`
* At most `104` calls will be made to `add`.
* It is guaranteed that there will be at least `k` elements in the array when you search for the `kth` element.

#### Fast Solution : O(nlogn)

```python
class KthLargest:

    def __init__(self, k: int, nums: List[int]):
        self.k = k
        self.nums = nums
        heapq.heapify(self.nums)

    def add(self, val: int) -> int:
        heapq.heappush(self.nums, val)
        while len(self.nums) > self.k:
            heapq.heappop(self.nums)
        return self.nums[0]


# Your KthLargest object will be instantiated and called as such:
# obj = KthLargest(k, nums)
# param_1 = obj.add(val)
```

#### Slow Solution O(n^2)

```python
class KthLargest:

    def __init__(self, k: int, nums: List[int]):
        self.k = k
        self.nums = nums

    def add(self, val: int) -> int:
        self.nums.append(val)
        self.nums.sort()
        num = self.nums[-self.k]
        return num


# Your KthLargest object will be instantiated and called as such:
# obj = KthLargest(k, nums)
# param_1 = obj.add(val)
```