322. Coin Change

322_coin_change/problem.md

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+## 問題: [322. Coin Change](https://leetcode.com/problems/coin-change/description/)

322_coin_change/step1.md

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+# Step 1
+
+- 部分問題を解く
+  - base case: amountが0のときに必要なコインの枚数は0
+  - $dp[amount]=min(dp[amount], 1 + dp[amount - coin])$
+  - amountにするのに必要な最小のコインの枚数は、amountからコインを引いた分にするのに必要な最小のコインの枚数に1を足したものである
+
+```python
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        dp = [float('inf')] * (amount + 1)
+        dp[0] = 0
+
+        for i in range(1, amount + 1):
+            for coin in coins:
+                if i - coin >= 0:
+                    dp[i] = min(dp[i], 1 + dp[i - coin])
+
+        return dp[amount] if dp[amount] != float('inf') else -1
+```
+
+時間計算量: $O(nm)$
+
+空間計算量: $O(m)$
+
+$n$: $coins$のサイズ
+
+$m$: $amount$の大きさ

322_coin_change/step2.md

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+# Step 2
+
+```python
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        min_coins = [float('inf')] * (amount + 1)
+        min_coins[0] = 0
+
+        for sub_amount in range(1, amount + 1):
+            for coin in coins:
+                if sub_amount - coin >= 0:
+                    min_coins[sub_amount] = min(min_coins[sub_amount], 1 + min_coins[sub_amount - coin])
+
+        return min_coins[amount] if min_coins[amount] != float('inf') else -1
+```
+
+時間計算量: $O(nm)$
+
+空間計算量: $O(m)$

322_coin_change/step3.md

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+# Step 3
+
+```python
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        min_coins = [float('inf')] * (amount + 1)
+        min_coins[0] = 0
+
+        for sub_amount in range(1, amount + 1):
+            for coin in coins:
+                if sub_amount - coin >= 0:
+                    min_coins[sub_amount] = min(min_coins[sub_amount], 1 + min_coins[sub_amount - coin])
+
+        return min_coins[amount] if min_coins[amount] != float('inf') else -1
+```
+
+1回目: 2分　48秒
+
+2回目: 2分　41秒
+
+3回目: 1分　49秒