From 72acda89728d6bd8267c39594c7e1138f4a49fa4 Mon Sep 17 00:00:00 2001 From: tom4649 Date: Sun, 5 Jul 2026 07:04:36 +0900 Subject: [PATCH] step1,2 --- .../memo.md | 30 ++++++++++++++++ .../step1.py | 11 ++++++ .../step1_backtrack.py | 36 +++++++++++++++++++ .../step2_math.py | 8 +++++ .../step2_recursion.py | 14 ++++++++ 5 files changed, 99 insertions(+) create mode 100644 1359.Count-All-Valid-Pickup-and-Delivery-Options/memo.md create mode 100644 1359.Count-All-Valid-Pickup-and-Delivery-Options/step1.py create mode 100644 1359.Count-All-Valid-Pickup-and-Delivery-Options/step1_backtrack.py create mode 100644 1359.Count-All-Valid-Pickup-and-Delivery-Options/step2_math.py create mode 100644 1359.Count-All-Valid-Pickup-and-Delivery-Options/step2_recursion.py diff --git a/1359.Count-All-Valid-Pickup-and-Delivery-Options/memo.md b/1359.Count-All-Valid-Pickup-and-Delivery-Options/memo.md new file mode 100644 index 0000000..0792fab --- /dev/null +++ b/1359.Count-All-Valid-Pickup-and-Delivery-Options/memo.md @@ -0,0 +1,30 @@ +# 1359. Count All Valid Pickup and Delivery Options + +## step1 +算数だと思って解いた。9mほど。 + +modulo定数はSolution固有だと考えてクラス内に定義する。グローバル変数にしても良いと思う。 + +バックトラックがキーワードにあるので書くがTLEした。他の書き方があるのか？ + +## 他の解法 +https://leetcode.com/problems/count-all-valid-pickup-and-delivery-options/solutions/4024280/9957-dp-math-recursion-by-vanamsen-qd4r/ + +再帰と直接計算する方法 + +https://docs.python.org/ja/3/library/functions.html#pow + +> If mod is present and exp is negative, base must be relatively prime to mod. In that case, pow(inv_base, -exp, mod) is returned, where inv_base is an inverse to base modulo mod. + +逆元の計算をpowで行える + +https://leetcode.com/problems/count-all-valid-pickup-and-delivery-options/solutions/3223439/2-python-solutions-with-explanation-using-dp-and-backtracking/ + +バックトラックはほとんど自分と同じ解法なので、TLEを避ける方法はなさそう？ + +https://discord.com/channels/1084280443945353267/1196498607977799853/1358454829005144125 + +> Count All Valid Pickup and Delivery Options ... Math・Dynamic Programming・Combinatorics に分類される問題に、ソフトウェアエンジニアとしての教育効果がどれくらいあるのか分かりませんでした。最近の入社試験で出題されるということであり、かつ入社試験に向けた練習をするのであれば、入れたほうがよいと思います。 + +## step3 +省略 diff --git a/1359.Count-All-Valid-Pickup-and-Delivery-Options/step1.py b/1359.Count-All-Valid-Pickup-and-Delivery-Options/step1.py new file mode 100644 index 0000000..76c11b0 --- /dev/null +++ b/1359.Count-All-Valid-Pickup-and-Delivery-Options/step1.py @@ -0,0 +1,11 @@ +class Solution: + MODULO = 10 ** 9 + 7 + def countOrders(self, n: int) -> int: + count = 1 + for i in range(n): + num_order = i * 2 + num_insertion = (num_order + 1) * (num_order + 2) // 2 # 1 + 2 + ... (num_order + 1) + count *= num_insertion % self.MODULO + count %= self.MODULO + + return count diff --git a/1359.Count-All-Valid-Pickup-and-Delivery-Options/step1_backtrack.py b/1359.Count-All-Valid-Pickup-and-Delivery-Options/step1_backtrack.py new file mode 100644 index 0000000..d3a61bc --- /dev/null +++ b/1359.Count-All-Valid-Pickup-and-Delivery-Options/step1_backtrack.py @@ -0,0 +1,36 @@ +from enum import IntEnum + +class OrderStatus(IntEnum): + WAITING = 0 + PICKED_UP = 1 + DELIVERED = 2 + +class Solution: + MODULO = 10 ** 9 + 7 + def countOrders(self, n: int) -> int: + order_statuses = [OrderStatus.WAITING] * n + count = 0 + + def update_order_status(i): + nonlocal count + if i == 2 * n: + count += 1 + count %= self.MODULO + return + + for j in range(n): + if order_statuses[j] == OrderStatus.DELIVERED: + continue + + if order_statuses[j] == OrderStatus.WAITING: + order_statuses[j] = OrderStatus.PICKED_UP + update_order_status(i + 1) + order_statuses[j] = OrderStatus.WAITING + continue + + order_statuses[j] = OrderStatus.DELIVERED + update_order_status(i + 1) + order_statuses[j] = OrderStatus.PICKED_UP + + update_order_status(0) + return count diff --git a/1359.Count-All-Valid-Pickup-and-Delivery-Options/step2_math.py b/1359.Count-All-Valid-Pickup-and-Delivery-Options/step2_math.py new file mode 100644 index 0000000..b9b96f1 --- /dev/null +++ b/1359.Count-All-Valid-Pickup-and-Delivery-Options/step2_math.py @@ -0,0 +1,8 @@ +import math + +class Solution: + MODULO = 10 ** 9 + 7 + def countOrders(self, n: int) -> int: + numerator = math.factorial(2 * n) % self.MODULO + denominator = pow(2, n, self.MODULO) + return numerator * pow(denominator, -1, self.MODULO) % self.MODULO diff --git a/1359.Count-All-Valid-Pickup-and-Delivery-Options/step2_recursion.py b/1359.Count-All-Valid-Pickup-and-Delivery-Options/step2_recursion.py new file mode 100644 index 0000000..ffd00d5 --- /dev/null +++ b/1359.Count-All-Valid-Pickup-and-Delivery-Options/step2_recursion.py @@ -0,0 +1,14 @@ +import functools +class Solution: + MODULO = 10 ** 9 + 7 + def countOrders(self, n: int) -> int: + + @functools.cache + def count_orders_helper(n): + if n == 1: + return 1 + + count = (self.countOrders(n - 1) * (2 * n - 1) * n) % self.MODULO + return count + + return count_orders_helper(n)