# 3061. Calculate Trapping Rain Water

## Description

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.


## Solutions

### Solution 1: Window Function + Summation

We use the window function MAX(height) OVER (ORDER BY id) to calculate the maximum height for each position and its left side, and use MAX(height) OVER (ORDER BY id DESC) to calculate the maximum height for each position and its right side, denoted as l and r respectively. Then, the amount of water stored at each position is min(l, r) - height. Finally, we sum them up.

• import pandas as pd

def calculate_trapped_rain_water(heights: pd.DataFrame) -> pd.DataFrame:
heights["l"] = heights["height"].cummax()
heights["r"] = heights["height"][::-1].cummax()[::-1]
heights["trapped_water"] = heights[["l", "r"]].min(axis=1) - heights["height"]
return pd.DataFrame({"total_trapped_water": [heights["trapped_water"].sum()]})


• # Write your MySQL query statement below
WITH
T AS (
SELECT
*,
MAX(height) OVER (ORDER BY id) AS l,
MAX(height) OVER (ORDER BY id DESC) AS r
FROM Heights
)
SELECT SUM(LEAST(l, r) - height) AS total_trapped_water
FROM T;