Leetcode #1359: Count All Valid Pickup and Delivery Options
In this guide, we solve Leetcode #1359 Count All Valid Pickup and Delivery Options in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given n orders, each order consists of a pickup and a delivery service. Count all valid pickup/delivery possible sequences such that delivery(i) is always after of pickup(i).
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Math, Dynamic Programming, Combinatorics
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: n = 1
Output: 1
Explanation: Unique order (P1, D1), Delivery 1 always is after of Pickup 1.
Python Solution
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
Complexity
The time complexity is , where is the number of orders. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.