Count All Valid Pickup and Delivery Options - LeetCode
Given n orders, each order consist in pickup and delivery services. Count all valid pickup/delivery possible sequences such that delivery(i) is always after of pickup(i). Since the answer may be too large, return it modulo 10^9 + 7.
Example 1: Input: n = 1 Output: 1 Explanation: Unique order (P1, D1), Delivery 1 always is after of Pickup 1. Example 2: 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. Example 3: Input: n = 3 Output: 90
Constraints:
1 <= n <= 500
- code
class Solution:
def countOrders(self, n: int) -> int:
res = 1
for i in range(1, n+1):
res *= i * (2 * i - 1)
res %= 1e9 + 7
return int(res)