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1359. Count All Valid Pickup and Delivery Options

Difficulty Topics

Description

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

Solution

count-all-valid-pickup-and-delivery-options.py
class Solution:
    def countOrders(self, n: int) -> int:
        M = 10 ** 9 + 7
        res = 1

        for i in range(2, n + 1):
            res *= i * (i * 2 - 1)
            res %= M

        return res