703. Kth Largest Element in a Stream
Difficulty: Easy
Topics: Tree
, Design
, Binary Search Tree
, Heap (Priority Queue)
, Binary Tree
, Data Stream
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 integerk
and the stream of integersnums
. -
int add(int val)
Appends the integerval
to the stream and returns the element representing thekth
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
Example 2:
- Input:
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- Output:
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Constraints:
1 <= k <= 104
0 <= nums.length <= 104
-104 <= nums[i] <= 104
-104 <= val <= 104
- At most
104
calls will be made toadd
. - It is guaranteed that there will be at least
k
elements in the array when you search for thekth
element.
Solution:
We can use a min-heap data structure. Here’s a step-by-step guide to implementing the KthLargest
class using PHP:
Min-Heap Data Structure: We will maintain a min-heap (priority queue) of size
k
. The root of this heap will always give us the k-th largest element.Initialization: During initialization, we will add the first
k
elements of the stream to the min-heap. For any additional elements, we will compare each new element with the smallest element in the heap (the root). If the new element is larger, we replace the smallest element with this new element and adjust the heap to maintain the k size.Adding Elements: Each time an element is added to the stream, we use the same process of comparing and possibly replacing elements in the heap.
Here’s the PHP code to implement the KthLargest
class: 703. Kth Largest Element in a Stream
Explanation:
-
Class Constructor:
- Initializes a min-heap to keep track of the top k elements.
- Inserts each element from the initial
nums
array into the heap using theadd
method.
-
add
Method:- If the heap contains fewer than
k
elements, the new value is simply inserted. - If the heap already contains
k
elements, compare the new value with the smallest value (root) in the heap:- If the new value is greater, remove the smallest value and insert the new value.
- Finally, return the smallest value in the heap, which is the k-th largest element.
- If the heap contains fewer than
This approach ensures that we efficiently keep track of the k-th largest element with each insertion into the stream, maintaining an O(log k) complexity for insertion operations due to heap operations.
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