Leetcode 295. Find Median from Data Stream

[hard]

Find Median from Data Stream - LeetCode

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?

[Java]

1. use two priority queue to keep track the closest nums to median.
2. default priority queue is sorted from from small to large. -> put all large number in this PQ; use (Collections.reverseOrder()) in smaller PQ, so that the number sort from large to small
3. If it’s even, we add number in large PQ, and poll the smallest from large-PQ to small-PQ; else is odd, wee add number in small-PQ, and poll the largest from small-PQ to large-PQ
4. After one iteration, change the boolean of “even”
5. If we have odd numbers, we can peek small-PQ to find the median; if we have the even number, we can use two PQ peek numbers / 2.0