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/**
 * Binary Search Insertion Approach
 * Time Complexity: O(n) for addNum, O(1) for findMedian
 * Space Complexity: O(n) - We need to store all elements
 */
class MedianFinderBinarySearch {
  constructor() {
    this.nums = [];
  }
 
  /**
   * Adds a number to the data structure.
   * @param {number} num - The number to add
   * @return {void}
   */
  addNum(num) {
    // Use binary search to find the insertion position
    let left = 0;
    let right = this.nums.length;
 
    while (left < right) {
      const mid = Math.floor((left + right) / 2);
      if (this.nums[mid] < num) {
        left = mid + 1;
      } else {
        right = mid;
      }
    }
 
    // Insert the number at the correct position
    this.nums.splice(left, 0, num);
  }
 
  /**
   * Returns the median of all numbers added so far.
   * @return {number} - The median
   */
  findMedian() {
    const n = this.nums.length;
    if (n % 2 === 1) {
      // Odd number of elements
      return this.nums[Math.floor(n / 2)];
    } else {
      // Even number of elements
      return (this.nums[n / 2 - 1] + this.nums[n / 2]) / 2;
    }
  }
}
 
/**
 * Two Heaps Approach
 * Time Complexity: O(log n) for addNum, O(1) for findMedian
 * Space Complexity: O(n) - We need to store all elements
 */
class MedianFinder {
  constructor() {
    // Max heap for the smaller half
    this.smallerHalf = new MaxHeap();
    // Min heap for the larger half
    this.largerHalf = new MinHeap();
  }
 
  /**
   * Adds a number to the data structure.
   * @param {number} num - The number to add
   * @return {void}
   */
  addNum(num) {
    // Add the number to the appropriate heap
    if (this.smallerHalf.size() === 0 || num <= this.smallerHalf.peek()) {
      this.smallerHalf.add(num);
    } else {
      this.largerHalf.add(num);
    }
 
    // Balance the heaps
    if (this.smallerHalf.size() > this.largerHalf.size() + 1) {
      this.largerHalf.add(this.smallerHalf.poll());
    } else if (this.largerHalf.size() > this.smallerHalf.size()) {
      this.smallerHalf.add(this.largerHalf.poll());
    }
  }
 
  /**
   * Returns the median of all numbers added so far.
   * @return {number} - The median
   */
  findMedian() {
    if (this.smallerHalf.size() > this.largerHalf.size()) {
      // Odd number of elements, smallerHalf has one more element
      return this.smallerHalf.peek();
    } else {
      // Even number of elements, both heaps have the same size
      return (this.smallerHalf.peek() + this.largerHalf.peek()) / 2;
    }
  }
}
 
/**
 * Max Heap implementation
 */
class MaxHeap {
  constructor() {
    this.heap = [];
  }
 
  size() {
    return this.heap.length;
  }
 
  isEmpty() {
    return this.size() === 0;
  }
 
  peek() {
    return this.heap[0];
  }
 
  add(val) {
    this.heap.push(val);
    this.siftUp(this.heap.length - 1);
  }
 
  poll() {
    if (this.isEmpty()) {
      return null;
    }
 
    const max = this.heap[0];
    const last = this.heap.pop();
 
    if (this.heap.length > 0) {
      this.heap[0] = last;
      this.siftDown(0);
    }
 
    return max;
  }
 
  siftUp(index) {
    let parent = Math.floor((index - 1) / 2);
 
    while (index > 0 && this.heap[parent] < this.heap[index]) {
      [this.heap[parent], this.heap[index]] = [this.heap[index], this.heap[parent]];
      index = parent;
      parent = Math.floor((index - 1) / 2);
    }
  }
 
  siftDown(index) {
    const left = 2 * index + 1;
    const right = 2 * index + 2;
    let largest = index;
 
    if (left < this.heap.length && this.heap[left] > this.heap[largest]) {
      largest = left;
    }
 
    if (right < this.heap.length && this.heap[right] > this.heap[largest]) {
      largest = right;
    }
 
    if (largest !== index) {
      [this.heap[index], this.heap[largest]] = [this.heap[largest], this.heap[index]];
      this.siftDown(largest);
    }
  }
}
 
/**
 * Min Heap implementation
 */
class MinHeap {
  constructor() {
    this.heap = [];
  }
 
  size() {
    return this.heap.length;
  }
 
  isEmpty() {
    return this.size() === 0;
  }
 
  peek() {
    return this.heap[0];
  }
 
  add(val) {
    this.heap.push(val);
    this.siftUp(this.heap.length - 1);
  }
 
  poll() {
    if (this.isEmpty()) {
      return null;
    }
 
    const min = this.heap[0];
    const last = this.heap.pop();
 
    if (this.heap.length > 0) {
      this.heap[0] = last;
      this.siftDown(0);
    }
 
    return min;
  }
 
  siftUp(index) {
    let parent = Math.floor((index - 1) / 2);
 
    while (index > 0 && this.heap[parent] > this.heap[index]) {
      [this.heap[parent], this.heap[index]] = [this.heap[index], this.heap[parent]];
      index = parent;
      parent = Math.floor((index - 1) / 2);
    }
  }
 
  siftDown(index) {
    const left = 2 * index + 1;
    const right = 2 * index + 2;
    let smallest = index;
 
    if (left < this.heap.length && this.heap[left] < this.heap[smallest]) {
      smallest = left;
    }
 
    if (right < this.heap.length && this.heap[right] < this.heap[smallest]) {
      smallest = right;
    }
 
    if (smallest !== index) {
      [this.heap[index], this.heap[smallest]] = [this.heap[smallest], this.heap[index]];
      this.siftDown(smallest);
    }
  }
}