README_EN.md

1359. Count All Valid Pickup and Delivery Options

中文文档

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

Solutions

Python3

class Solution:
    def countOrders(self, n: int) -> int:
        mod = 10**9 + 7
        f = 1
        for i in range(2, n + 1):
            f = (f * i * (2 * i - 1)) % mod
        return f

Java

class Solution {
    public int countOrders(int n) {
        final int mod = (int) 1e9 + 7;
        long f = 1;
        for (int i = 2; i <= n; ++i) {
            f = f * i * (2 * i - 1) % mod;
        }
        return (int) f;
    }
}

C++

class Solution {
public:
    int countOrders(int n) {
        const int mod = 1e9 + 7;
        long long f = 1;
        for (int i = 2; i <= n; ++i) {
            f = f * i * (2 * i - 1) % mod;
        }
        return f;
    }
};

Go

func countOrders(n int) int {
	const mod = 1e9 + 7
	f := 1
	for i := 2; i <= n; i++ {
		f = f * i * (2*i - 1) % mod
	}
	return f
}

...