Leetcode #407: Trapping Rain Water II
In this guide, we solve Leetcode #407 Trapping Rain Water II in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given an m x n integer matrix heightMap representing the height of each unit cell in a 2D elevation map, return the volume of water it can trap after raining. Example 1: Input: heightMap = [[1,4,3,1,3,2],[3,2,1,3,2,4],[2,3,3,2,3,1]] Output: 4 Explanation: After the rain, water is trapped between the blocks.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Breadth-First Search, Array, Matrix, Heap (Priority Queue)
Intuition
We need to repeatedly access the smallest or largest element as the input changes.
A heap provides fast insertions and removals while keeping order.
Approach
Push candidates into the heap as you scan, and pop when you need the best element.
Keep the heap size bounded if the problem requires a top-k structure.
Steps:
- Push candidates into a heap.
- Pop the best candidate when needed.
- Maintain heap size or invariants.
Example
Input: heightMap = [[1,4,3,1,3,2],[3,2,1,3,2,4],[2,3,3,2,3,1]]
Output: 4
Explanation: After the rain, water is trapped between the blocks.
We have two small ponds 1 and 3 units trapped.
The total volume of water trapped is 4.
Python Solution
class Solution:
def trapRainWater(self, heightMap: List[List[int]]) -> int:
m, n = len(heightMap), len(heightMap[0])
vis = [[False] * n for _ in range(m)]
pq = []
for i in range(m):
for j in range(n):
if i == 0 or i == m - 1 or j == 0 or j == n - 1:
heappush(pq, (heightMap[i][j], i, j))
vis[i][j] = True
ans = 0
dirs = (-1, 0, 1, 0, -1)
while pq:
h, i, j = heappop(pq)
for a, b in pairwise(dirs):
x, y = i + a, j + b
if x >= 0 and x < m and y >= 0 and y < n and not vis[x][y]:
ans += max(0, h - heightMap[x][y])
vis[x][y] = True
heappush(pq, (max(h, heightMap[x][y]), x, y))
return ans
Complexity
The time complexity is , and the space complexity is , where and are the number of rows and columns in the matrix, respectively. The space complexity is , where and are the number of rows and columns in the matrix, respectively.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.