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Tested Python solution for LeetCode 1359 with 13 pytest cases. Generate a practice environment with lcpy.
lcpy gen -n 1359 # by problem number
lcpy gen -s count_all_valid_pickup_and_delivery_options # by problem name
Input: n = 1
Output: 1
Explanation: Unique order (P1, D1), Delivery 1 always is after of Pickup 1.
Input: n = 2
Output: 6
Explanation: All possible orders:
(P1,P2,D1,D2), (P1,P2,D2,D1), (P1,D1,P2,D2), (P2,P1,D1,D2), (P2,P1,D2,D1) and (P2,D2,P1,D1).
This is an invalid order (P1,D2,P2,D1) because Pickup 2 is after of Delivery 2.
Input: n = 3
Output: 90
class Solution:
# Time: O(n)
# Space: O(1)
def count_orders(self, n: int) -> int:
# Inserting the i-th order into a valid sequence of i-1 orders:
# place pickup_i in one of 2i-1 gaps, then delivery_i in one of
# the remaining 2i positions -> factor of (2i - 1) * i.
mod = 1_000_000_007
result = 1
for i in range(2, n + 1):
result = result * (2 * i - 1) % mod * i % mod
return result
| Time | Space |
|---|---|
| O(n) | O(1) |