如何得到一个数据流中的中位数？如果从数据流中读出奇数个数值，那么中位数就是所有数值排序之后位于中间的数值。如果从数据流中读出偶数个数值，那么中位数就是所有数值排序之后中间两个数的平均值。
例如，
[2,3,4] 的中位数是 3
[2,3] 的中位数是 (2 + 3) / 2 = 2.5
设计一个支持以下两种操作的数据结构：
- void addNum(int num) - 从数据流中添加一个整数到数据结构中。
- double findMedian() - 返回目前所有元素的中位数。
示例 1：
输入： ["MedianFinder","addNum","addNum","findMedian","addNum","findMedian"] [[],[1],[2],[],[3],[]] 输出：[null,null,null,1.50000,null,2.00000]
示例 2：
输入： ["MedianFinder","addNum","findMedian","addNum","findMedian"] [[],[2],[],[3],[]] 输出：[null,null,2.00000,null,2.50000]
限制：
- 最多会对
addNum、findMedian进行50000次调用。
注意：本题与主站 295 题相同：https://leetcode.cn/problems/find-median-from-data-stream/
- 创建大根堆、小根堆，其中：大根堆存放较小的一半元素，小根堆存放较大的一半元素。
- 添加元素时，若两堆元素个数相等，放入小根堆（使得小根堆个数多 1）；若不等，放入大根堆（使得大小根堆元素个数相等）
- 取中位数时，若两堆元素个数相等，取两堆顶求平均值；若不等，取小根堆堆顶。
class MedianFinder:
def __init__(self):
"""
initialize your data structure here.
"""
self.max_heap = []
self.min_heap = []
def addNum(self, num: int) -> None:
if len(self.max_heap) == len(self.min_heap):
heappush(self.min_heap, -heappushpop(self.max_heap, -num))
else:
heappush(self.max_heap, -heappushpop(self.min_heap, num))
def findMedian(self) -> float:
return (-self.max_heap[0] + self.min_heap[0]) / 2 if len(self.max_heap) == len(self.min_heap) else self.min_heap[0]
# Your MedianFinder object will be instantiated and called as such:
# obj = MedianFinder()
# obj.addNum(num)
# param_2 = obj.findMedian()class MedianFinder {
Queue<Integer> minHeap;
Queue<Integer> maxHeap;
/** initialize your data structure here. */
public MedianFinder() {
minHeap = new PriorityQueue<>();
maxHeap = new PriorityQueue<>((a, b) -> b - a);
}
public void addNum(int num) {
if (maxHeap.size() == minHeap.size()) {
maxHeap.offer(num);
// 放入小根堆(小根堆多1)
minHeap.offer(maxHeap.poll());
} else {
minHeap.offer(num);
// 放入大根堆(大小堆数量相等)
maxHeap.offer(minHeap.poll());
}
}
public double findMedian() {
if (((maxHeap.size() + minHeap.size()) & 1) == 0) {
// 偶数个，取两个堆顶平均值
return (maxHeap.peek() + minHeap.peek()) / 2.0;
}
return minHeap.peek();
}
}
/**
* Your MedianFinder object will be instantiated and called as such:
* MedianFinder obj = new MedianFinder();
* obj.addNum(num);
* double param_2 = obj.findMedian();
*//**
* initialize your data structure here.
*/
var MedianFinder = function () {
this.val = [];
};
/**
* @param {number} num
* @return {void}
*/
MedianFinder.prototype.addNum = function (num) {
let left = 0;
let right = this.val.length;
while (left < right) {
let mid = left + ~~((right - left) / 2);
if (num > this.val[mid]) {
left = mid + 1;
} else {
right = mid;
}
}
this.val.splice(left, 0, num);
};
/**
* @return {number}
*/
MedianFinder.prototype.findMedian = function () {
let mid = ~~(this.val.length / 2);
return this.val.length % 2
? this.val[mid]
: (this.val[mid - 1] + this.val[mid]) / 2;
};class MedianFinder {
public:
/** initialize your data structure here. */
MedianFinder() {
}
void addNum(int num) {
if (maxHeap.size() == minHeap.size()) {
maxHeap.push(num);
int temp = maxHeap.top();
maxHeap.pop();
minHeap.push(temp);
} else {
minHeap.push(num);
int temp = minHeap.top();
minHeap.pop();
maxHeap.push(temp);
}
}
double findMedian() {
if (maxHeap.size() == minHeap.size()) {
return (maxHeap.top() + minHeap.top()) / 2.0;
}
return minHeap.top();
}
private:
priority_queue<int> maxHeap;
priority_queue<int, vector<int>, greater<int>> minHeap;
};class MedianFinder {
private nums: number[];
constructor() {
this.nums = [];
}
addNum(num: number): void {
const { nums } = this;
let l = 0;
let r = nums.length;
while (l < r) {
const mid = (l + r) >>> 1;
if (nums[mid] < num) {
l = mid + 1;
} else {
r = mid;
}
}
nums.splice(l, 0, num);
}
findMedian(): number {
const { nums } = this;
const n = nums.length;
if ((n & 1) === 1) {
return nums[n >> 1];
}
return (nums[n >> 1] + nums[(n >> 1) - 1]) / 2;
}
}
/**
* Your MedianFinder object will be instantiated and called as such:
* var obj = new MedianFinder()
* obj.addNum(num)
* var param_2 = obj.findMedian()
*/struct MedianFinder {
nums: Vec<i32>,
}
/**
* `&self` means the method takes an immutable reference.
* If you need a mutable reference, change it to `&mut self` instead.
*/
impl MedianFinder {
/** initialize your data structure here. */
fn new() -> Self {
Self { nums: Vec::new() }
}
fn add_num(&mut self, num: i32) {
let mut l = 0;
let mut r = self.nums.len();
while l < r {
let mid = l + r >> 1;
if self.nums[mid] < num {
l = mid + 1;
} else {
r = mid;
}
}
self.nums.insert(l, num);
}
fn find_median(&self) -> f64 {
let n = self.nums.len();
if (n & 1) == 1 {
return f64::from(self.nums[n >> 1]);
}
f64::from(self.nums[n >> 1] + self.nums[(n >> 1) - 1]) / 2.0
}
}
/**
* Your MedianFinder object will be instantiated and called as such:
* let obj = MedianFinder::new();
* obj.add_num(num);
* let ret_2: f64 = obj.find_median();
*/public class MedianFinder {
private List<int> nums;
private int curIndex;
/** initialize your data structure here. */
public MedianFinder() {
nums = new List<int>();
}
private int FindIndex(int val) {
int left = 0;
int right = nums.Count - 1;
while (left <= right) {
int mid = left + (right - left) / 2;
if (val > nums[mid]) {
left = mid + 1;
} else {
right = mid - 1;
}
}
return left;
}
public void AddNum(int num) {
if (nums.Count == 0) {
nums.Add(num);
curIndex = 0;
} else {
curIndex = FindIndex(num);
if (curIndex == nums.Count) {
nums.Add(num);
} else {
nums.Insert(curIndex, num);
}
}
}
public double FindMedian() {
if (nums.Count % 2 == 1) {
return (double)nums[nums.Count / 2];
} else {
if (nums.Count == 0) {
return 0;
} else {
return (double) (nums[nums.Count / 2 - 1] + nums[nums.Count / 2]) / 2;
}
}
}
}
/**
* Your MedianFinder object will be instantiated and called as such:
* MedianFinder obj = new MedianFinder();
* obj.AddNum(num);
* double param_2 = obj.FindMedian();
*/