Create 2025-05-10-Leetcode-322.md

Author: hyeonukim

_posts/Leetcode/DP/2025-05-10-Leetcode-322.md

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+---
+title: Leetcode 322. Coin Change
+description: Explanation for  Dynamic Programming, Medium, and its solution in Python.
+date: 2025-05-10
+categories: [Leetcode, Dynamic Programming, Medium]
+tags: [Leetcode, Python, Study, Dynamic Programming, Medium]
+math: true
+---
+
+## Problem
+[ Dynamic Programming, Medium](https://leetcode.com/problems/coin-change/description/)
+
+Example:
+```
+Input: coins = [1,2,5], amount = 11
+Output: 3
+Explanation: 11 = 5 + 5 + 1
+
+Input: coins = [2], amount = 3
+Output: -1
+
+Input: coins = [1], amount = 0
+Output: 0
+```
+
+## Approach
+
+Using dynamic programming, we can solve for the counts by storing all the coin values in dp array
+
+Here is the Python code for the solution:
+```python
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        dp = [float('inf')] * (amount+1)
+        dp[0] = 0
+
+        for a in range(amount):
+            for c in coins:
+                if a-c >= 0:
+                    dp[a] = min(dp[a], 1+dp[a-c])
+
+        return dp[amonut] if dp[amount] != float('inf') else return -1    
+    
+```
+## Time Complexity and Space Complexity
+
+Time Complexity: $O(n * t)$ where $n$ is length of coins $t$ is amount
+
+Space Complexity: $O(t)$