From f4b65b300ecd5c533a30598e519a18e47d692b9e Mon Sep 17 00:00:00 2001
From: Hiro Funatsuka <hiro.funatsuka@gmail.com>
Date: Sat, 16 May 2026 22:59:35 +0900
Subject: [PATCH] Solve coin change

---
 322_coin_change/problem.md |  1 +
 322_coin_change/step1.md   | 28 ++++++++++++++++++++++++++++
 322_coin_change/step2.md   | 19 +++++++++++++++++++
 322_coin_change/step3.md   | 21 +++++++++++++++++++++
 4 files changed, 69 insertions(+)
 create mode 100644 322_coin_change/problem.md
 create mode 100644 322_coin_change/step1.md
 create mode 100644 322_coin_change/step2.md
 create mode 100644 322_coin_change/step3.md

diff --git a/322_coin_change/problem.md b/322_coin_change/problem.md
new file mode 100644
index 0000000..48b0fda
--- /dev/null
+++ b/322_coin_change/problem.md
@@ -0,0 +1 @@
+## 問題: [322. Coin Change](https://leetcode.com/problems/coin-change/description/)
diff --git a/322_coin_change/step1.md b/322_coin_change/step1.md
new file mode 100644
index 0000000..0378ef1
--- /dev/null
+++ b/322_coin_change/step1.md
@@ -0,0 +1,28 @@
+# 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
diff --git a/322_coin_change/step2.md b/322_coin_change/step2.md
new file mode 100644
index 0000000..aba3e26
--- /dev/null
+++ b/322_coin_change/step2.md
@@ -0,0 +1,19 @@
+# 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: $O(m)$
diff --git a/322_coin_change/step3.md b/322_coin_change/step3.md
new file mode 100644
index 0000000..d5ba684
--- /dev/null
+++ b/322_coin_change/step3.md
@@ -0,0 +1,21 @@
+# 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