LeetCode-in-All

295. Find Median from Data Stream

Hard

The median is the middle value in an ordered integer list. If the size of the list is even, there is no middle value and the median is the mean of the two middle values.

• For example, for arr = [2,3,4], the median is 3.
• For example, for arr = [2,3], the median is (2 + 3) / 2 = 2.5.

Implement the MedianFinder class:

• MedianFinder() initializes the MedianFinder object.
• void addNum(int num) adds the integer num from the data stream to the data structure.
• double findMedian() returns the median of all elements so far. Answers within 10-5 of the actual answer will be accepted.

Example 1:

Input

["MedianFinder", "addNum", "addNum", "findMedian", "addNum", "findMedian"]
[[], [1], [2], [], [3], []]

Output: [null, null, null, 1.5, null, 2.0]

Explanation:

MedianFinder medianFinder = new MedianFinder();
medianFinder.addNum(1); // arr = [1]
medianFinder.addNum(2); // arr = [1, 2]
medianFinder.findMedian(); // return 1.5 (i.e., (1 + 2) / 2)
medianFinder.addNum(3); // arr[1, 2, 3]
medianFinder.findMedian(); // return 2.0 

Constraints:

• -105 <= num <= 105
• There will be at least one element in the data structure before calling findMedian.
• At most 5 * 104 calls will be made to addNum and findMedian.

Follow up:

• If all integer numbers from the stream are in the range [0, 100], how would you optimize your solution?
• If 99% of all integer numbers from the stream are in the range [0, 100], how would you optimize your solution?

Solution

(require data/heap racket/class)

(define median-finder%
  (class object%
    (super-new)
    
    ;; Max heap (stores smaller half, max at the top)
    (define max-heap (make-heap >))
    ;; Min heap (stores larger half, min at the top)
    (define min-heap (make-heap <))

    ;; add-num : exact-integer? -> void?
    (define/public (add-num num)
      (heap-add! max-heap num)                      ; Add to max-heap
      (heap-add! min-heap (heap-min max-heap))      ; Move max-heap root to min-heap
      (heap-remove-min! max-heap)                   ; Remove moved element

      ;; Balance: Ensure max-heap has at least as many elements as min-heap
      (when (> (heap-count min-heap) (heap-count max-heap))
        (heap-add! max-heap (heap-min min-heap))
        (heap-remove-min! min-heap)))

    ;; find-median : -> flonum?
    (define/public (find-median)
      (if (> (heap-count max-heap) (heap-count min-heap))
          (exact->inexact (heap-min max-heap))
          (/ (+ (heap-min max-heap) (heap-min min-heap)) 2.0)))))

;; Your median-finder% object will be instantiated and called as such:
;; (define obj (new median-finder%))
;; (send obj add-num num)
;; (define param_2 (send obj find-median))

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