leetcode -- Find Median from Data Stream

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

【解題思路】

最簡單的作法是直接把數據放到ArrayList中，每次計算Median時先對ArrayList排序，而後計算Median

 1 class MedianFinder {
 2 
 3     private ArrayList<Integer> nums = new ArrayList<Integer>();
 4 
 5     // Adds a number into the data structure.
 6     public void addNum(int num) {
 7         nums.add(num);
 8     }
 9 
10     // Returns the median of current data stream
11     public double findMedian() {
12         Collections.sort(nums);
13         
14         int count = nums.size();
15         
16         if (count % 2 == 0) {
17             // even
18             int index2 = count / 2;
19             int index1 = index2 - 1;
20             
21             return (nums.get(index1) + nums.get(index2)) / 2.0;
22         } else {
23             // odd
24             int index = count / 2;
25             
26             return nums.get(index);
27         }
28     }
29 }

代碼提交後，結果顯示超時。

看了下超時測試用例，有2w多addNum操做，每一個addNum操做後面緊跟着一個findMedian操做，每次findMedian須要對數組從新排序，事件複雜度爲O(nlgn)

稍微優化點的作法是，在addNum時就讓數組有序，每次插入的時間複雜度爲O(n)，再次運行仍然TOL

 1 public static void addNum(int num) {
 2         
 3         int indexOfNumBiggerThanInput = 0;
 4         int i = 0;
 5         for (; i < nums.size(); i ++) {
 6             if (num < nums.get(i)) {
 7                 indexOfNumBiggerThanInput = i;
 8                 break;
 9             }
10         }
11         
12         if (indexOfNumBiggerThanInput != i) {
13             nums.add(i, num);
14         } else {
15             nums.add(indexOfNumBiggerThanInput, num);
16         }
17     }

addNum若是一直有序採用二分插入會提升效率，時間複雜度O(lgn)