car fleet

Author: always-maap

853.CarFleet.py

@@ -0,0 +1,67 @@
+"""
+853. Car Fleet
+Medium
+Array | Stack | Sorting | Monotonic Stack
+---
+There are n cars going to the same destination along a one-lane road. The destination is target miles away.
+
+You are given two integer array position and speed, both of length n,
+ where position[i] is the position of the ith car and speed[i] is the speed of the ith car (in miles per hour).
+
+A car can never pass another car ahead of it, but it can catch up to it and drive bumper to bumper at the same speed.
+ The faster car will slow down to match the slower car's speed.
+   The distance between these two cars is ignored (i.e., they are assumed to have the same position).
+
+A car fleet is some non-empty set of cars driving at the same position and same speed.
+ Note that a single car is also a car fleet.
+
+If a car catches up to a car fleet right at the destination point, it will still be considered as one car fleet.
+
+Return the number of car fleets that will arrive at the destination.
+
+Example 1:
+Input: target = 12, position = [10,8,0,5,3], speed = [2,4,1,1,3]
+Output: 3
+Explanation:
+The cars starting at 10 (speed 2) and 8 (speed 4) become a fleet, meeting each other at 12.
+The car starting at 0 does not catch up to any other car, so it is a fleet by itself.
+The cars starting at 5 (speed 1) and 3 (speed 3) become a fleet, meeting each other at 6. The fleet moves at speed 1 until it reaches target.
+Note that no other cars meet these fleets before the destination, so the answer is 3.
+
+Example 2:
+Input: target = 10, position = [3], speed = [3]
+Output: 1
+Explanation: There is only one car, hence there is only one fleet.
+
+Example 3:
+Input: target = 100, position = [0,2,4], speed = [4,2,1]
+Output: 1
+Explanation:
+The cars starting at 0 (speed 4) and 2 (speed 2) become a fleet, meeting each other at 4. The fleet moves at speed 2.
+Then, the fleet (speed 2) and the car starting at 4 (speed 1) become one fleet, meeting each other at 6. The fleet moves at speed 1 until it reaches target.
+
+Constraints:
+n == position.length == speed.length
+1 <= n <= 105
+0 < target <= 106
+0 <= position[i] < target
+All the values of position are unique.
+0 < speed[i] <= 106
+"""
+
+from typing import List
+
+
+# O(n log n) time | O(n) space
+class Solution:
+    def carFleet(self, target: int, position: List[int], speed: List[int]) -> int:
+        stack = []
+
+        for pos, spd in sorted(zip(position, speed), reverse=True):
+            time = (target - pos) / spd
+            if not stack:
+                stack.append(time)
+            elif time > stack[-1]:
+                stack.append(time)
+
+        return len(stack)