From 48ed268adefcf0653b315ba20f0bc94f6d535f14 Mon Sep 17 00:00:00 2001
From: tokuhirat <54652919+tokuhirat@users.noreply.github.com>
Date: Sun, 17 Aug 2025 13:03:31 +0900
Subject: [PATCH] Create 39. Combination Sum.md

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 39. Combination Sum/39. Combination Sum.md | 130 +++++++++++++++++++++
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+# 39. Combination Sum
+## STEP1
+- 何も見ずに解いてみる
+- 78\. Subsets では各要素を使う使わないの2通りだったが、この問題は各要素を使えるだけ使って良い。
+```python
+class Solution:
+    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
+        results = []
+
+        def generate_combination(index: int, combination: list[int]) -> None:
+            total = sum(combination)
+            if total == target:
+                results.append(combination)
+                return
+            if index == len(candidates):
+                return
+
+            generate_combination(index + 1, combination[:])
+            num = candidates[index]
+            while total + num <= target:
+                combination = combination + [num]
+                total += num
+                generate_combination(index + 1, combination)
+
+        generate_combination(0, [])
+        return results
+```
+- generate_combination の引数 combination は毎回異なるオブジェクトを指すようにした。コピーしない場合は while:pop みたいなことをする必要があり煩雑になると思った。
+- generate_combination 内で if total > target: return を書くか迷った。
+- generate_combination の呼び出しをまとめようとすると以下になる。こちらの方がすこしわかりやすいかもしれない。
+```python
+            next_combination = combination[:]
+            num = candidates[index]
+            while total <= target:
+                generate_combination(index + 1, next_combination)
+                next_combination = next_combination + [num]
+                total += num
+```
+
+- DP でも書いてみた。
+```python
+class Solution:
+    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
+        sum_to_combinations = [[] for _ in range(target + 1)]
+        sum_to_combinations[0].append([])
+        for sum_ in range(target + 1):
+            if not sum_to_combinations[sum_]:
+                continue
+            for combination in sum_to_combinations[sum_]:
+                for num in candidates:
+                    if combination and combination[-1] >= num:
+                        continue
+                    for i in range(1, (target - sum_) // num + 1):            
+                        sum_to_combinations[sum_ + num * i].append(
+                            combination + [num] * i
+                        )
+        return sum_to_combinations[target]
+```
+- if not sum_to_combinations[sum_]:continue は不要でした。
+
+## STEP2
+### プルリクやドキュメントを参照
+- https://github.com/olsen-blue/Arai60/pull/53/files
+    - 解法1 が結構読みにくかった。traverse_candidates が index を進めない場合があることを最初読めていなくて、index == len(candidates) を先に確認したらダメなのではないかと考えてしまった。
+    - シンプルに DP を実装している。
+        - 一番外側で使える数字ごとにループを回すと、重複を考慮しないで済む。
+```python
+class Solution:
+    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
+        sum_to_combinations = [[] for _ in range(target + 1)]
+        sum_to_combinations[0].append([])
+        for candidate in candidates:
+            for sum_ in range(candidate, target + 1):
+                for combination in sum_to_combinations[sum_ - candidate]:
+                    sum_to_combinations[sum_].append(combination + [candidate])
+        return sum_to_combinations[target]
+``` 
+- https://discord.com/channels/1084280443945353267/1235829049511903273/1265717341178822787
+    - 分岐の分類。色々ありますね。
+- stack でも書いてみる。
+```python
+class Solution:
+    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
+        results = []
+        combination_and_index = [([], 0)]
+
+        while combination_and_index:
+            combination, index = combination_and_index.pop()
+            if sum(combination) == target:
+                results.append(combination)
+                continue
+            if index >= len(candidates):
+                continue
+            
+            num = candidates[index]
+            sum_ = sum(combination)
+            new_combination = combination[:]
+            while sum_ <= target:
+                combination_and_index.append((new_combination[:], index + 1))
+                sum_ += num
+                new_combination.append(num)            
+        return results
+```
+## STEP3
+### 3回ミスなく書く
+```python
+class Solution:
+    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
+        results = []
+
+        def generate_combination(index: int, combination: list[int]) -> None:
+            if sum(combination) == target:
+                results.append(combination)
+                return
+            if index >= len(candidates):
+                return
+            
+            sum_ = sum(combination)
+            num = candidates[index]
+            new_combination = combination[:]
+            while sum_ <= target:
+                generate_combination(index + 1, new_combination[:])
+                sum_ += num
+                new_combination.append(num)
+        
+        generate_combination(0, [])
+        return results
+```
+
+3分,3分,3分で3回Accept