Overall Technical Foundation and Potential Questions

WITH recent_events AS (
  SELECT
    e.*,
    ROW_NUMBER() OVER (PARTITION BY e.user_id ORDER BY e.event_time ASC, e.event_id ASC)  AS rn_first,
    ROW_NUMBER() OVER (PARTITION BY e.user_id ORDER BY e.event_time DESC, e.event_id DESC) AS rn_last
  FROM events e
  WHERE e.event_time >= (now() - INTERVAL '365 days')
)
SELECT
  u.user_id,
  u.name,
  fe.event_time AS first_event_time,
  fe.event_type AS first_event_type,
  le.event_time AS last_event_time,
  le.event_type AS last_event_type
FROM users u
JOIN (
  SELECT user_id, event_time, event_type FROM recent_events WHERE rn_first = 1
) fe ON fe.user_id = u.user_id
JOIN (
  SELECT user_id, event_time, event_type FROM recent_events WHERE rn_last = 1
) le ON le.user_id = u.user_id;

def coin_change_combinations(coins, N):
    """
    Returns number of ways to make amount N using unlimited coins in 'coins'.
    Order of coins does not matter (combinations).
    Time: O(len(coins) * N), Space: O(N)
    """
    dp = [0] * (N + 1)
    dp[0] = 1  # one way to make 0: choose nothing

    for coin in coins:
        for amount in range(coin, N + 1):
            dp[amount] += dp[amount - coin]

    return dp[N]