1011. Capacity To Ship Packages Within D Days

1011/memo.md

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+# 1011. Capacity To Ship Packages Within D Days
+
+https://leetcode.com/problems/capacity-to-ship-packages-within-d-days/description/
+
+TODO: 二分探索を自分で書く
+
+- capacityを指定すればそれが可能かはO(N)で判定できる
+- 上限をどのように定めるかが問題。単純にsum(weights)としたとき220ms、minを使ったとき119msとなった。
+- 問題のWeight上限を使う方法は正攻法なのだろうか
+- 自力で解法を思いついたが、二分探索のヒントがあったから
+
+n = len(weights), M = maximum_valueとすると
+- 時間計算量: O(n*log(M))
+- 空間計算量: O(1) (入力は含めない)
+
+
+コメント集に該当箇所はない
+
+https://github.com/naoto-iwase/leetcode/pull/27/changes
+
+capacityの下限はmax(weights)とできるのか
+- これを反映してsol2.pyとしたが、149msとなり逆に遅くなった
+- maxをとるO(n)の操作に余分な時間がかかるケースが多いのだろう。二分探索は途中で打ち切られるのでそれほど重くない。
+
+
+https://github.com/mamo3gr/arai60/blob/1011_capacity-to-ship-packages-within-d-days/1011_capacity-to-ship-packages-within-d-days/memo.md
+
+色々なコードがまとめられている
+
+https://github.com/h1rosaka/arai60/pull/46/changes
+
+上でも述べられているけど、 `for _ in range(days):` で書くこともできるのは思いつかなかった

1011/sol1.py

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+import bisect
+
+MAXIMUM_WEIGHT = 500
+
+
+class Solution:
+    def shipWithinDays(self, weights: list[int], days: int) -> int:
+        def can_ship(capacity):
+            used_days = 1
+            shipped_weight_on_current_day = 0
+            for weight in weights:
+                if shipped_weight_on_current_day + weight <= capacity:
+                    shipped_weight_on_current_day += weight
+                    continue
+                used_days += 1
+                if used_days > days or weight > capacity:
+                    return False
+                shipped_weight_on_current_day = weight
+            return True
+
+        maximum_value = min(sum(weights), MAXIMUM_WEIGHT * (len(weights) // days + 1))
+
+        return bisect.bisect_left(range(1, maximum_value), True, key=can_ship) + 1

1011/sol2.py

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+import bisect
+
+
+class Solution:
+    def shipWithinDays(self, weights: list[int], days: int) -> int:
+        def can_ship(capacity):
+            used_days = 1
+            shipped_weight_on_current_day = 0
+            for weight in weights:
+                if shipped_weight_on_current_day + weight <= capacity:
+                    shipped_weight_on_current_day += weight
+                    continue
+                used_days += 1
+                if used_days > days or weight > capacity:
+                    return False
+                shipped_weight_on_current_day = weight
+            return True
+
+        minimum_value = max(weights)
+        maximum_value = sum(weights)
+
+        return (
+            bisect.bisect_left(range(minimum_value, maximum_value), True, key=can_ship)
+            + minimum_value
+        )

1011/sol2_revised.py

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+import bisect
+
+
+class Solution:
+    def shipWithinDays(self, weights: list[int], days: int) -> int:
+        def can_ship(capacity):
+            used_days = 1
+            total_weight = 0
+            for weight in weights:
+                if total_weight + weight <= capacity:
+                    total_weight += weight
+                    continue
+                used_days += 1
+                if used_days > days or weight > capacity:
+                    return False
+                total_weight = weight
+            return True
+
+        minimum_value = max(weights)
+        maximum_value = sum(weights)
+
+        return (
+            bisect.bisect_left(range(minimum_value, maximum_value), True, key=can_ship)
+            + minimum_value
+        )