Leetcode #1776: Car Fleet II
In this guide, we solve Leetcode #1776 Car Fleet 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
There are n cars traveling at different speeds in the same direction along a one-lane road. You are given an array cars of length n, where cars[i] = [positioni, speedi] represents: positioni is the distance between the ith car and the beginning of the road in meters.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Stack, Array, Math, Monotonic Stack, 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: cars = [[1,2],[2,1],[4,3],[7,2]]
Output: [1.00000,-1.00000,3.00000,-1.00000]
Explanation: After exactly one second, the first car will collide with the second car, and form a car fleet with speed 1 m/s. After exactly 3 seconds, the third car will collide with the fourth car, and form a car fleet with speed 2 m/s.
Python Solution
class Solution:
def getCollisionTimes(self, cars: List[List[int]]) -> List[float]:
stk = []
n = len(cars)
ans = [-1] * n
for i in range(n - 1, -1, -1):
while stk:
j = stk[-1]
if cars[i][1] > cars[j][1]:
t = (cars[j][0] - cars[i][0]) / (cars[i][1] - cars[j][1])
if ans[j] == -1 or t <= ans[j]:
ans[i] = t
break
stk.pop()
stk.append(i)
return ans
Complexity
The time complexity is O(n log 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.