SQL for the pair of traders with nearest median P&L

Two tables are available:

• traders(id INTEGER, name VARCHAR)
• trades(id INTEGER, trader_id INTEGER, profit FLOAT)

Considering only traders who have made at least one trade, write a SQL query that finds the two traders whose median profit per trade are closest to each other. Return their names and the absolute gap between the medians, as columns trader1_name, trader2_name, median_profit_diff.

Median per trader, self-join on pairs, keep the smallest gap. In a CTE, inner-join traders to trades and compute PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY profit) grouped by trader (the inner join drops traders with no trades). Join the CTE to itself with a.id < b.id so each pair appears once, compute ABS(a.median - b.median), order ascending and LIMIT 1. The pairing step is $O(n^2)$ in the number of traders.