Stream Cluster Max and Median

Process an integer data stream whose values are assigned to stored clusters. A cluster's representative is its first value and never changes.
ADD value: among representatives within maxDistance of value, choose the closest; break a distance tie by the smaller zero-based cluster identifier. If none qualifies, create a new cluster. Append the assigned cluster identifier.
MAX clusterId: append that cluster's maximum value, or INVALID for an unknown identifier.
MEDIAN clusterId: append the exact median, using an integer or an x.5 string, or INVALID for an unknown identifier.
Return one string for every operation in order.

Function
processClusterStream(maxDistance: int, operations: String[]) → String[]

Examples
Example 1
maxDistance = 3
operations = ["ADD 10","ADD 12","ADD 20","ADD 17","MAX 0","MEDIAN 0","MAX 1","MEDIAN 1"]
return = ["0","0","1","1","12","11","20","18.5"]
Ten and twelve form cluster 0. Twenty starts cluster 1, and seventeen joins it at distance three from its representative.
Example 2
maxDistance = 5
operations = ["ADD 0","ADD 10","ADD 5","MEDIAN 0","MEDIAN 1","MAX 4"]
return = ["0","1","0","2.5","10","INVALID"]
Value five ties both representatives and joins the smaller cluster identifier.

Constraints
0 <= maxDistance <= 10^9.
1 <= operations.length <= 5000.
Added values are signed 32-bit integers.
Every operation has one of the exact forms above.

Two separate problems live here. First, assignment: scan all representatives, keep those within maxDistance, pick the smallest distance, and break ties by the lower cluster id. With at most 5000 operations, a linear scan per ADD is fine, so don't overbuild it. Second, per-cluster stats. Keep a max-heap for the lower half and a min-heap for the upper half in each cluster, plus a running max value. Rebalance after each insert so sizes differ by at most one. Median is the top of the larger heap if the count is odd, otherwise the average of both tops. Pitfalls: averaging can give x.5, so format it as a string and avoid float drift. Use 64-bit sums for 32-bit values. Distance should also be computed in 64-bit. Return INVALID for ids that don't exist yet. StealthCoder is the hedge if the heap rebalancing slips away mid-OA.

If this hits your live OA and you blank, StealthCoder solves it in seconds, invisible to the proctor.