1359 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

所有的 pickup 有 n! 种排列。

当 pickup 排好后，最后一个 pickup 的 delivery 只有 1 种选择，倒数第 2 个有 3 种选择，倒数第 n 个有 2n-1 种选择

public int countOrders(int n) {
    long res=1;
    long mod=1000000007;
    for(int i=1;i<=n;++i){
        res*=i;
        res=res%mod;
        res*=2*i-1;
        res=res%mod;
    }
    return (int)res;
}