Game play analysis v

# Table: Activity
# 
# +--------------+---------+
# | Column Name  | Type    |
# +--------------+---------+
# | player_id    | int     |
# | device_id    | int     |
# | event_date   | date    |
# | games_played | int     |
# +--------------+---------+
# (player_id, event_date) is the primary key (combination of columns with unique values) of this table.
# This table shows the activity of players of some games.
# Each row is a record of a player who logged in and played a number of games (possibly 0) before logging out on someday using some device.
# 
#  
# 
# The install date of a player is the first login day of that player.
# 
# We define day one retention of some date x to be the number of players whose install date is x and they logged back in on the day right after x, divided by the number of players whose install date is x, rounded to 2 decimal places.
# 
# Write a solution to report for each install date, the number of players that installed the game on that day, and the day one retention.
# 
# Return the result table in any order.
# 
# The result format is in the following example.
#
# Example 1:
# Input:
# Activity table:
# +-----------+-----------+------------+--------------+
# | player_id | device_id | event_date | games_played |
# +-----------+-----------+------------+--------------+
# | 1         | 2         | 2016-03-01 | 5            |
# | 1         | 2         | 2016-03-02 | 6            |
# | 2         | 3         | 2017-06-25 | 1            |
# | 3         | 1         | 2016-03-01 | 0            |
# | 3         | 4         | 2016-07-03 | 5            |
# +-----------+-----------+------------+--------------+
# Output:
# +------------+----------+----------------+
# | install_dt | installs | Day1_retention |
# +------------+----------+----------------+
# | 2016-03-01 | 2        | 0.50           |
# | 2017-06-25 | 1        | 0.00           |
# +------------+----------+----------------+
# Explanation:
# Player 1 and 3 installed the game on 2016-03-01 but only player 1 logged back in on 2016-03-02 so the day 1 retention of 2016-03-01 is 1 / 2 = 0.50
# Player 2 installed the game on 2017-06-25 but didn't log back in on 2017-06-26 so the day 1 retention of 2017-06-25 is 0 / 1 = 0.00

import math
import pandas as pd

def gameplay_analysis(activity: pd.DataFrame) -> pd.DataFrame:
  activity['event_date'] = pd.to_datetime(activity['event_date'])
  install = activity.groupby('player_id')['event_date'].min().reset_index()
  install.columns = ['player_id', 'install_dt']
  install['next_day'] = install['install_dt'] + pd.Timedelta(days=1)
  merged = install.merge(activity, left_on=['player_id', 'next_day'], right_on=['player_id', 'event_date'], how='left')
  merged['retained'] = merged['event_date'].notna().astype(int)
  result = install.groupby('install_dt').size().reset_index(name='installs')
  retention = merged.groupby('install_dt')['retained'].mean().apply(
    lambda x: math.floor(x * 100 + 0.5) / 100
  ).reset_index(name='Day1_retention')
  result = result.merge(retention, on='install_dt')
  result['install_dt'] = result['install_dt'].dt.strftime('%Y-%m-%d')
  return result