Add Coin Change Dynamic Programming Algorithm with Doctests and Type Hints

dynamic_programming/coin_change.py

@@ -0,0 +1,43 @@
+"""
+Coin Change Problem - Dynamic Programming Approach
+--------------------------------------------------
+
+Given a list of coin denominations and a target amount,
+this function returns the minimum number of coins needed
+to make up that amount. If it's not possible, returns -1.
+
+Example:
+    >>> coin_change([1, 2, 5], 11)
+    3
+    # Explanation: 11 = 5 + 5 + 1
+"""
+
+from typing import List
+
+
+def coin_change(coins: List[int], amount: int) -> int:
+    """
+    Calculate the minimum number of coins required
+    to make up the given amount using dynamic programming.
+
+    Args:
+        coins (List[int]): List of coin denominations.
+        amount (int): The target amount.
+
+    Returns:
+        int: Minimum number of coins required, or -1 if not possible.
+    """
+    dp = [float("inf")] * (amount + 1)
+    dp[0] = 0
+
+    for coin in coins:
+        for i in range(coin, amount + 1):
+            dp[i] = min(dp[i], dp[i - coin] + 1)
+
+    return dp[amount] if dp[amount] != float("inf") else -1
+
+
+if __name__ == "__main__":
+    coins = [1, 2, 5]
+    amount = 11
+    print(f"Minimum coins required: {coin_change(coins, amount)}")