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Median is the middle value in an ordered integer list. If the size of the list is even, there is no middle value. So the median is the mean of the two middle value. Examples: [2,3,4] , the median is 3 [2,3], the median is (2 + 3) / 2 = 2.5 Design a data structure that supports the following two operations: void addNum(int num) - Add a integer number from the data stream to the data structure. double findMedian() - Return the median of all elements so far. For example: add(1) add(2) findMedian() -> 1.5 add(3) findMedian() -> 2
时间 O(NlogN) 空间 O(N)
维护一个最大堆,一个最小堆。最大堆存的是到目前为止较小的那一半数,最小堆存的是到目前为止较大的那一半数,这样中位数只有可能是堆顶或者堆顶两个数的均值。而维护两个堆的技巧在于判断堆顶数和新来的数的大小关系,还有两个堆的大小关系。我们始终维护MaxHeap>=MinHeap
我的solution:
1 class MedianFinder { 2 PriorityQueue<Integer> maxHeap; 3 PriorityQueue<Integer> minHeap; 4 int count; 5 6 public MedianFinder() { 7 this.minHeap = new PriorityQueue<Integer>(); 8 this.maxHeap = new PriorityQueue<Integer>(11, new Comparator<Integer>() { 9 public int compare(Integer i1, Integer i2) { 10 return i2-i1; 11 } 12 }); 13 this.count = 0; 14 } 15 16 17 // Adds a number into the data structure. 18 public void addNum(int num) { 19 if (count%2 == 0) { 20 if (count == 0) maxHeap.offer(num); 21 else if (num <= minHeap.peek()) maxHeap.offer(num); 22 else { // num > minHeap.peek() 23 maxHeap.offer(minHeap.poll()); 24 minHeap.offer(num); 25 } 26 } 27 else { //count%2 == 1 28 if (count == 1) { 29 if (num < maxHeap.peek()) { 30 minHeap.offer(maxHeap.poll()); 31 maxHeap.offer(num); 32 } 33 else minHeap.offer(num); 34 } 35 else if (num >= maxHeap.peek()) minHeap.offer(num); 36 else { //num < maxHeap.peek() 37 minHeap.offer(maxHeap.poll()); 38 maxHeap.offer(num); 39 } 40 41 } 42 count++; 43 } 44 45 // Returns the median of current data stream 46 public double findMedian() { 47 if (count%2 == 1) return (double)maxHeap.peek(); 48 else return (double)(maxHeap.peek() + minHeap.peek())/2.0; 49 } 50 }; 51 52 // Your MedianFinder object will be instantiated and called as such: 53 // MedianFinder mf = new MedianFinder(); 54 // mf.addNum(1); 55 // mf.findMedian();
简洁方法参考:http://segmentfault.com/a/1190000003709954
1 class MedianFinder { 2 3 PriorityQueue<Integer> maxheap = new PriorityQueue<Integer>(); 4 PriorityQueue<Integer> minheap = new PriorityQueue<Integer>(Collections.reverseOrder()); 5 6 // Adds a number into the data structure. 7 public void addNum(int num) { 8 maxheap.offer(num); 9 minheap.offer(maxheap.poll()); 10 if(maxheap.size() < minheap.size()){ 11 maxheap.offer(minheap.poll()); 12 } 13 } 14 15 // Returns the median of current data stream 16 public double findMedian() { 17 return maxheap.size() == minheap.size() ? (double)(maxheap.peek() + minheap.peek()) / 2.0 : maxheap.peek(); 18 } 19 };
Leetcode: Find Median from Data Stream
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原文地址:http://www.cnblogs.com/EdwardLiu/p/5081437.html