Leetcode #666: Path Sum IV
In this guide, we solve Leetcode #666 Path Sum IV 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
If the depth of a tree is smaller than 5, then this tree can be represented by an array of three-digit integers. You are given an ascending array nums consisting of three-digit integers representing a binary tree with a depth smaller than 5, where for each integer: The hundreds digit represents the depth d of this node, where 1 <= d <= 4.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Tree, Depth-First Search, Array, Hash Table, Binary Tree
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.
Python Solution
class Solution:
def pathSum(self, nums: List[int]) -> int:
def dfs(node, t):
if node not in mp:
return
t += mp[node]
d, p = divmod(node, 10)
l = (d + 1) * 10 + (p * 2) - 1
r = l + 1
nonlocal ans
if l not in mp and r not in mp:
ans += t
return
dfs(l, t)
dfs(r, t)
ans = 0
mp = {num // 10: num % 10 for num in nums}
dfs(11, 0)
return ans
Complexity
The time complexity is O(n). 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.