Question

295. Find Median from Data Stream

中文文档

Description

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?

Solutions

Solution 1

class MedianFinder:
  def __init__(self):
    """
    initialize your data structure here.
    """
    self.h1 = []
    self.h2 = []

  def addNum(self, num: int) -> None:
    heappush(self.h1, num)
    heappush(self.h2, -heappop(self.h1))
    if len(self.h2) - len(self.h1) > 1:
      heappush(self.h1, -heappop(self.h2))

  def findMedian(self) -> float:
    if len(self.h2) > len(self.h1):
      return -self.h2[0]
    return (self.h1[0] - self.h2[0]) / 2


# Your MedianFinder object will be instantiated and called as such:
# obj = MedianFinder()
# obj.addNum(num)
# param_2 = obj.findMedian()

class MedianFinder {
  private PriorityQueue<Integer> q1 = new PriorityQueue<>();
  private PriorityQueue<Integer> q2 = new PriorityQueue<>(Collections.reverseOrder());

  /** initialize your data structure here. */
  public MedianFinder() {
  }

  public void addNum(int num) {
    q1.offer(num);
    q2.offer(q1.poll());
    if (q2.size() - q1.size() > 1) {
      q1.offer(q2.poll());
    }
  }

  public double findMedian() {
    if (q2.size() > q1.size()) {
      return q2.peek();
    }
    return (q1.peek() + q2.peek()) * 1.0 / 2;
  }
}

/**
 * Your MedianFinder object will be instantiated and called as such:
 * MedianFinder obj = new MedianFinder();
 * obj.addNum(num);
 * double param_2 = obj.findMedian();
 */

class MedianFinder {
public:
  /** initialize your data structure here. */
  MedianFinder() {
  }

  void addNum(int num) {
    q1.push(num);
    q2.push(q1.top());
    q1.pop();
    if (q2.size() - q1.size() > 1) {
      q1.push(q2.top());
      q2.pop();
    }
  }

  double findMedian() {
    if (q2.size() > q1.size()) {
      return q2.top();
    }
    return (double) (q1.top() + q2.top()) / 2;
  }

private:
  priority_queue<int, vector<int>, greater<int>> q1;
  priority_queue<int> q2;
};

/**
 * Your MedianFinder object will be instantiated and called as such:
 * MedianFinder* obj = new MedianFinder();
 * obj->addNum(num);
 * double param_2 = obj->findMedian();
 */

type MedianFinder struct {
  q1 hp
  q2 hp
}

/** initialize your data structure here. */
func Constructor() MedianFinder {
  return MedianFinder{hp{}, hp{}}
}

func (this *MedianFinder) AddNum(num int) {
  heap.Push(&this.q1, num)
  heap.Push(&this.q2, -heap.Pop(&this.q1).(int))
  if this.q2.Len()-this.q1.Len() > 1 {
    heap.Push(&this.q1, -heap.Pop(&this.q2).(int))
  }
}

func (this *MedianFinder) FindMedian() float64 {
  if this.q2.Len() > this.q1.Len() {
    return -float64(this.q2.IntSlice[0])
  }
  return float64(this.q1.IntSlice[0]-this.q2.IntSlice[0]) / 2.0
}

/**
 * Your MedianFinder object will be instantiated and called as such:
 * obj := Constructor();
 * obj.AddNum(num);
 * param_2 := obj.FindMedian();
 */

type hp struct{ sort.IntSlice }

func (h hp) Less(i, j int) bool { return h.IntSlice[i] < h.IntSlice[j] }
func (h *hp) Push(v any)    { h.IntSlice = append(h.IntSlice, v.(int)) }
func (h *hp) Pop() any {
  a := h.IntSlice
  v := a[len(a)-1]
  h.IntSlice = a[:len(a)-1]
  return v
}

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();
 */

/**
 * 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;
};

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();
 */