Calculate trapping rain water

# Table: Heights
# 
# +-------------+------+
# | Column Name | Type |
# +-------------+------+
# | id          | int  |
# | height      | int  |
# +-------------+------+
# id is the primary key (column with unique values) for this table, and it is guaranteed to be in sequential order.
# Each row of this table contains an id and height.
# 
# Write a solution to calculate the amount of rainwater can be trapped between the bars in the landscape, considering that each bar has a width of 1 unit.
# 
# Return the result table in any order.
# 
# The result format is in the following example.
#
# Example 1:
# Input:
# Heights table:
# +-----+--------+
# | id  | height |
# +-----+--------+
# | 1   | 0      |
# | 2   | 1      |
# | 3   | 0      |
# | 4   | 2      |
# | 5   | 1      |
# | 6   | 0      |
# | 7   | 1      |
# | 8   | 3      |
# | 9   | 2      |
# | 10  | 1      |
# | 11  | 2      |
# | 12  | 1      |
# +-----+--------+
# Output:
# +---------------------+
# | total_trapped_water |
# +---------------------+
# | 6                   |
# +---------------------+
# Explanation:
# 
# The elevation map depicted above (in the black section) is graphically represented with the x-axis denoting the id and the y-axis representing the heights [0,1,0,2,1,0,1,3,2,1,2,1]. In this scenario, 6 units of rainwater are trapped within the blue section.

import pandas as pd

def calculate_trapped_rain_water(heights: pd.DataFrame) -> pd.DataFrame:
  heights = heights.sort_values('id').reset_index(drop=True)
  h = heights['height'].tolist()
  n = len(h)
  if n < 3:
    return pd.DataFrame({'total_trapped_water': [0]})
  left_max = [0] * n
  right_max = [0] * n
  left_max[0] = h[0]
  for i in range(1, n):
    left_max[i] = max(left_max[i-1], h[i])
  right_max[n-1] = h[n-1]
  for i in range(n-2, -1, -1):
    right_max[i] = max(right_max[i+1], h[i])
  total = sum(min(left_max[i], right_max[i]) - h[i] for i in range(n))
  return pd.DataFrame({'total_trapped_water': [total]})