1011 capacity to ship packages within d days medium

1011_capacity_to_ship_packages_within_d_days_medium/README.md

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+# 問題へのリンク
+[Capacity To Ship Packages Within D Days](https://leetcode.com/problems/capacity-to-ship-packages-within-d-days/)
+
+# 言語
+Python
+
+
+# 自分の解法
+
+## step1
+
+```python
+class Solution:
+    def shipWithinDays(self, weights: list[int], days: int) -> int:
+        if not weights:
+            return 0
+
+        def can_ship_within_days(days: int, capacity: int) -> bool:
+            cargo_weight = 0
+            days_required = 1
+            for weight in weights:
+                if weight > capacity:
+                    return False
+                if cargo_weight + weight > capacity:
+                    cargo_weight = 0
+                    days_required += 1
+                cargo_weight += weight
+            return days_required <= days
+
+        # 0 < capacity <= sum weights
+        left = 0
+        right = sum(weights)
+        while right - left > 1:
+            mid = (right + left) // 2
+            if can_ship_within_days(days, mid):
+                right = mid
+            else:
+                left = mid
+        return right
+```
+
+- 単調性あるところに二分探索あり。
+- `(left, right]`の範囲で二分探索するパターン。
+- `can_ship_within_days`関数内で`weight > capacity`のチェックをしているが、はじめは抜けていた上、なかなか気づきづらい。
+    - `left`の初期値を`0`にしていたが、`max(weights)`などにすればこのチェックは不要になる。その場合、二分探索も変わる。
+    - そうはいっても、そもそも`if max(weights) > capacity: return False`とすべき。
+    - 例えば`weights = [100,]`のとき、can_ship_within_days(2, 50)は`False`を返すべきだが、上記のコードでは`True`を返してしまう。これは2日に分ければ大きな荷物も運べるということになってしまうため。
+- `cargo_weight`は複数の荷物をまとめた重さを表す変数としているが、`current_weight`の方がわかりやすいと思った
+- `can_ship_within_days`という名前の関数で`days`が引数にないのは違和感があるので、`days`を引数にした。が、`can_ship`にリネームして`days`をキャプチャする形にしたほうが自然だと思った。
+
+`weights`の要素数を`N`、`weights`の要素の和を`S`とすると、
+- 時間計算量：`O(N log(S))`
+- 空間計算量：`O(N)`
+
+## step2
+
+```python
+class Solution:
+    def shipWithinDays(self, weights: list[int], days: int) -> int:
+        if not weights:
+            return 0
+
+        def can_ship(capacity: int) -> bool:
+            current_weight = 0
+            days_required = 1
+            for weight in weights:
+                if current_weight + weight > capacity:
+                    current_weight = 0
+                    days_required += 1
+                current_weight += weight
+            return days_required <= days
+
+        # max weight <= capacity <= sum weights
+        left = max(weights) - 1
+        right = sum(weights)
+        while right - left > 1:
+            mid = (right + left) // 2
+            if can_ship(mid):
+                right = mid
+            else:
+                left = mid
+        return right
+```
+- `can_ship_within_days`関数を`can_ship`にリネーム
+
+
+## step3
+```python
+class Solution:
+    def shipWithinDays(self, weights: list[int], days: int) -> int:
+        # for given capacity, we can check if we can ship all the packages with it
+        def can_ship(capacity: int) -> bool:
+            if max(weights) > capacity:
+                return False
+
+            current_weight = 0
+            days_required = 1
+            for weight in weights:
+                current_weight += weight
+                if current_weight > capacity:
+                    current_weight = weight
+                    days_required += 1
+            return days_required <= days
+
+        left = 0
+        right = sum(weights)
+        while right - left > 1:
+            mid = (right + left) // 2
+            if can_ship(mid):
+                right = mid
+            else:
+                left = mid
+
+        return right
+```
+
+## step4 (FB)
+- 二分探索の `left`/`right`という変数名を問題に適した名前に変える。これで不変条件がわかりやすくなる。
+    - `left` -> `insufficient_capacity`
+    - `right` -> `sufficient_capacity`
+
+
+# 別解・模範解答
+`bisect`モジュールを使う方法
+
+```python
+import bisect
+
+
+class Solution:
+    def shipWithinDays(self, weights: list[int], days: int) -> int:
+        def can_ship(capacity: int) -> bool:
+            if max(weights) > capacity:
+                return False
+            current_weight = 0
+            days_required = 1
+            for weight in weights:
+                current_weight += weight
+                if current_weight > capacity:
+                    days_required += 1
+                    current_weight = weight
+            return days_required <= days
+
+        return bisect.bisect_left(range(sum(weights) + 1), True, key=can_ship)
+```
+
+- 二分探索を自分で書く前に、まずは`bisect`モジュールを使って通るかを見るのが良い。
+- `bisect`モジュールでは`key`引数が使えるので、`can_ship`関数をそのまま渡せる。
+- ソート済みのリストを用意する必要があるが、`range`で用意できる。`bool`の配列ではソートすると`False`が先に来るので、`True`が初めて出現するインデックスを求めることになる。
+- `bisect`に渡せる配列は`SupportsLenAndGetItem`プロトコルを満たしていれば良いので、`__len__`と`__getitem__`を実装したクラスならば良い。
+
+```python
+import bisect
+
+class MyRange:
+    def __init__(self):
+        self.length = 5
+
+    def __len__(self):
+        return self.length
+
+    def __getitem__(self, key: int) -> int:
+        return 2 * key
+
+
+g = MyRange()  # [0, 2, 4, 6, 8]
+bisect.bisect_left(g, 3) # 2
+```
+
+
+# 次に解く問題の予告
+- [Unique Paths II](https://leetcode.com/problems/unique-paths-ii/)
+- [Longest Increasing Subsequence](https://leetcode.com/problems/longest-increasing-subsequence/)

1011_capacity_to_ship_packages_within_d_days_medium/step1.py

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+#
+# @lc app=leetcode id=1011 lang=python3
+#
+# [1011] Capacity To Ship Packages Within D Days
+#
+
+# @lc code=start
+class Solution:
+    def shipWithinDays(self, weights: list[int], days: int) -> int:
+        if not weights:
+            return 0
+
+        def can_ship_within_days(days: int, capacity: int) -> bool:
+            cargo_weight = 0
+            days_required = 1
+            for weight in weights:
+                if weight > capacity:
+                    return False
+                if cargo_weight + weight > capacity:
+                    cargo_weight = 0
+                    days_required += 1
+                cargo_weight += weight
+            return days_required <= days
+
+        # 0 < capacity <= sum weights
+        left = 0
+        right = sum(weights)
+        while right - left > 1:
+            mid = (right + left) // 2
+            if can_ship_within_days(days, mid):
+                right = mid
+            else:
+                left = mid
+        return right
+
+
+# @lc code=end

1011_capacity_to_ship_packages_within_d_days_medium/step2.py

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+#
+# @lc app=leetcode id=1011 lang=python3
+#
+# [1011] Capacity To Ship Packages Within D Days
+#
+
+# @lc code=start
+class Solution:
+    def shipWithinDays(self, weights: list[int], days: int) -> int:
+        if not weights:
+            return 0
+
+        def can_ship(capacity: int) -> bool:
+            if max(weights) > capacity:
+                return False
+            current_weight = 0
+            days_required = 1
+            for weight in weights:
+                if current_weight + weight > capacity:
+                    current_weight = 0
+                    days_required += 1
+                current_weight += weight
+            return days_required <= days
+
+        # max weight <= capacity <= sum weights
+        left = 0
+        right = sum(weights)
+        while right - left > 1:
+            mid = (right + left) // 2
+            if can_ship(mid):
+                right = mid
+            else:
+                left = mid
+        return right
+
+
+# @lc code=end

1011_capacity_to_ship_packages_within_d_days_medium/step3.py

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+#
+# @lc app=leetcode id=1011 lang=python3
+#
+# [1011] Capacity To Ship Packages Within D Days
+#
+
+# @lc code=start
+class Solution:
+    def shipWithinDays(self, weights: list[int], days: int) -> int:
+        # for given capacity, we can check if we can ship all the packages with it
+        def can_ship(capacity: int) -> bool:
+            if max(weights) > capacity:
+                return False
+
+            current_weight = 0
+            days_required = 1
+            for weight in weights:
+                current_weight += weight
+                if current_weight > capacity:
+                    current_weight = weight
+                    days_required += 1
+            return days_required <= days
+
+        left = 0
+        right = sum(weights)
+        while right - left > 1:
+            mid = (right + left) // 2
+            if can_ship(mid):
+                right = mid
+            else:
+                left = mid
+
+        return right
+
+
+# @lc code=end

1011_capacity_to_ship_packages_within_d_days_medium/use_bisect.py

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+#
+# @lc app=leetcode id=1011 lang=python3
+#
+# [1011] Capacity To Ship Packages Within D Days
+#
+
+# @lc code=start
+
+import bisect
+
+
+class Solution:
+    def shipWithinDays(self, weights: list[int], days: int) -> int:
+        def can_ship(capacity: int) -> bool:
+            if max(weights) > capacity:
+                return False
+            current_weight = 0
+            days_required = 1
+            for weight in weights:
+                current_weight += weight
+                if current_weight > capacity:
+                    days_required += 1
+                    current_weight = weight
+            return days_required <= days
+
+        return bisect.bisect_left(range(sum(weights) + 1), True, key=can_ship)
+
+
+# @lc code=end