355. Design Twitter☆

class MedianFinder {
  // low = max-heap (smaller half), high = min-heap (larger half).
  // We keep |low| === |high|, or |low| === |high| + 1.
  private low: MaxHeap = new MaxHeap();
  private high: MinHeap = new MinHeap();

  addNum(num: number): void {
    // 1. Route by value so low always holds the smaller numbers.
    if (this.low.size === 0 || num <= this.low.peek()) this.low.push(num);
    else this.high.push(num);

    // 2. Rebalance so the two sizes differ by at most one.
    if (this.low.size > this.high.size + 1) {
      this.high.push(this.low.pop());
    } else if (this.high.size > this.low.size) {
      this.low.push(this.high.pop());
    }
  }

  findMedian(): number {
    if (this.low.size === this.high.size) {
      // Even count: average the two middle elements (the heap tops).
      return (this.low.peek() + this.high.peek()) / 2;
    }
    // Odd count: low carries the extra element, so its top IS the median.
    return this.low.peek();
  }
}

class Twitter {
  private static ts = 0;                      // global monotonic timestamp
  private tweets = new Map<number, { tweetId: number; time: number }[]>();
  private following = new Map<number, Set<number>>();

  postTweet(userId: number, tweetId: number): void {
    if (!this.tweets.has(userId)) this.tweets.set(userId, []);
    this.tweets.get(userId)!.push({ tweetId, time: Twitter.ts++ });
  }

  getNewsFeed(userId: number): number[] {
    // Collect latest tweet from every followee (plus self)
    const peers = new Set([userId, ...(this.following.get(userId) ?? [])]);
    // Min-heap keyed by time (max-10 merge via a max-heap simulation)
    // We use a simple sorted merge of per-user pointers for clarity.
    type Cursor = { list: { tweetId: number; time: number }[]; idx: number };
    const cursors: Cursor[] = [];
    for (const uid of peers) {
      const list = this.tweets.get(uid) ?? [];
      if (list.length > 0) cursors.push({ list, idx: list.length - 1 });
    }

    const result: number[] = [];
    while (result.length < 10 && cursors.length > 0) {
      // pick the cursor with the largest time (max-heap by time)
      let best = 0;
      for (let i = 1; i < cursors.length; i++) {
        if (cursors[i].list[cursors[i].idx].time >
            cursors[best].list[cursors[best].idx].time) {
          best = i;
        }
      }
      const cur = cursors[best];
      result.push(cur.list[cur.idx].tweetId);
      if (cur.idx === 0) {
        cursors.splice(best, 1);   // exhausted this user's list
      } else {
        cur.idx--;
      }
    }
    return result;
  }

  follow(followerId: number, followeeId: number): void {
    if (!this.following.has(followerId)) this.following.set(followerId, new Set());
    this.following.get(followerId)!.add(followeeId);
  }

  unfollow(followerId: number, followeeId: number): void {
    this.following.get(followerId)?.delete(followeeId);
  }
}

function kClosest(points: number[][], k: number): number[][] {
  // Max-heap stored as an array: root holds the FARTHEST point among our k best.
  const heap: number[][] = [];

  const dist2 = (p: number[]) => p[0] * p[0] + p[1] * p[1];

  const swap = (i: number, j: number) => {
    [heap[i], heap[j]] = [heap[j], heap[i]];
  };

  const siftUp = (i: number) => {
    while (i > 0) {
      const parent = Math.floor((i - 1) / 2);
      if (dist2(heap[parent]) < dist2(heap[i])) {
        swap(parent, i);
        i = parent;
      } else break;
    }
  };

  const siftDown = (i: number, size: number) => {
    while (true) {
      let largest = i;
      const l = 2 * i + 1, r = 2 * i + 2;
      if (l < size && dist2(heap[l]) > dist2(heap[largest])) largest = l;
      if (r < size && dist2(heap[r]) > dist2(heap[largest])) largest = r;
      if (largest === i) break;
      swap(i, largest);
      i = largest;
    }
  };

  for (const p of points) {
    heap.push(p);
    siftUp(heap.length - 1);

    if (heap.length > k) {
      // Root is the farthest; replace it with the last element and sift down.
      heap[0] = heap.pop()!;
      siftDown(0, heap.length);
    }
  }

  return heap;
}

function topKFrequent(nums: number[], k: number): number[] {
  // 1) Count every value in one pass.
  const freq = new Map<number, number>();
  for (const n of nums) {
    freq.set(n, (freq.get(n) ?? 0) + 1);
  }

  // 2) Bucket sort: buckets[c] = all values seen exactly c times.
  //    A value's count is at most nums.length, so we need that many slots.
  const buckets: number[][] = Array.from({ length: nums.length + 1 }, () => []);
  for (const [val, count] of freq) {
    buckets[count].push(val);
  }

  // 3) Walk buckets from the highest count down, collecting k values.
  const res: number[] = [];
  for (let c = buckets.length - 1; c >= 1 && res.length < k; c--) {
    for (const val of buckets[c]) {
      res.push(val);
      if (res.length === k) return res;
    }
  }
  return res;
}