Leetcode #305: Number of Islands II
In this guide, we solve Leetcode #305 Number of Islands 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
You are given an empty 2D binary grid grid of size m x n. The grid represents a map where 0's represent water and 1's represent land.
Quick Facts
- Difficulty: Hard
- Premium: Yes
- Tags: Union Find, Array, Hash Table
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: m = 3, n = 3, positions = [[0,0],[0,1],[1,2],[2,1]]
Output: [1,1,2,3]
Explanation:
Initially, the 2d grid is filled with water.
- Operation #1: addLand(0, 0) turns the water at grid[0][0] into a land. We have 1 island.
- Operation #2: addLand(0, 1) turns the water at grid[0][1] into a land. We still have 1 island.
- Operation #3: addLand(1, 2) turns the water at grid[1][2] into a land. We have 2 islands.
- Operation #4: addLand(2, 1) turns the water at grid[2][1] into a land. We have 3 islands.
Python Solution
class UnionFind:
def __init__(self, n: int):
self.p = list(range(n))
self.size = [1] * n
def find(self, x: int):
if self.p[x] != x:
self.p[x] = self.find(self.p[x])
return self.p[x]
def union(self, a: int, b: int) -> bool:
pa, pb = self.find(a - 1), self.find(b - 1)
if pa == pb:
return False
if self.size[pa] > self.size[pb]:
self.p[pb] = pa
self.size[pa] += self.size[pb]
else:
self.p[pa] = pb
self.size[pb] += self.size[pa]
return True
class Solution:
def numIslands2(self, m: int, n: int, positions: List[List[int]]) -> List[int]:
uf = UnionFind(m * n)
grid = [[0] * n for _ in range(m)]
ans = []
dirs = (-1, 0, 1, 0, -1)
cnt = 0
for i, j in positions:
if grid[i][j]:
ans.append(cnt)
continue
grid[i][j] = 1
cnt += 1
for a, b in pairwise(dirs):
x, y = i + a, j + b
if (
0 <= x < m
and 0 <= y < n
and grid[x][y]
and uf.union(i * n + j, x * n + y)
):
cnt -= 1
ans.append(cnt)
return ans
Complexity
The time complexity is or , where is the length of , and is the inverse function of the Ackermann function. The space complexity is O(n).
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.