Leetcode #1964: Find the Longest Valid Obstacle Course at Each Position
In this guide, we solve Leetcode #1964 Find the Longest Valid Obstacle Course at Each Position 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 want to build some obstacle courses. You are given a 0-indexed integer array obstacles of length n, where obstacles[i] describes the height of the ith obstacle.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Binary Indexed Tree, Array, Binary Search
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: obstacles = [1,2,3,2]
Output: [1,2,3,3]
Explanation: The longest valid obstacle course at each position is:
- i = 0: [1], [1] has length 1.
- i = 1: [1,2], [1,2] has length 2.
- i = 2: [1,2,3], [1,2,3] has length 3.
- i = 3: [1,2,3,2], [1,2,2] has length 3.
Python Solution
class BinaryIndexedTree:
__slots__ = ["n", "c"]
def __init__(self, n: int):
self.n = n
self.c = [0] * (n + 1)
def update(self, x: int, v: int):
while x <= self.n:
self.c[x] = max(self.c[x], v)
x += x & -x
def query(self, x: int) -> int:
s = 0
while x:
s = max(s, self.c[x])
x -= x & -x
return s
class Solution:
def longestObstacleCourseAtEachPosition(self, obstacles: List[int]) -> List[int]:
nums = sorted(set(obstacles))
n = len(nums)
tree = BinaryIndexedTree(n)
ans = []
for x in obstacles:
i = bisect_left(nums, x) + 1
ans.append(tree.query(i) + 1)
tree.update(i, ans[-1])
return ans
Complexity
The time complexity is , and the space complexity is . The space complexity is .
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.