Create inverse_coin_change.py

backtracking/inverse_coin_change.py

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+def inverse_coin_change(amount, coins):
+    """
+    Finds all combinations of coins that sum up to the given amount.
+    
+    :param amount: Target amount
+    :param coins: List of coin denominations
+    :return: List of combinations (each combination is a list of coins)
+    """
+    results = []
+
+    def backtrack(remaining, combo, start):
+        if remaining == 0:
+            results.append(list(combo))
+            return
+        for i in range(start, len(coins)):
+            coin = coins[i]
+            if coin <= remaining:
+                combo.append(coin)
+                backtrack(remaining - coin, combo, i)  # allow reuse
+                combo.pop()
+
+    coins.sort()
+    backtrack(amount, [], 0)
+    return results
+
+
+def main():
+    import argparse
+
+    parser = argparse.ArgumentParser(description="Inverse Coin Change Solver")
+    parser.add_argument("--amount", type=int, required=True, help="Target amount to reach")
+    parser.add_argument("--coins", type=int, nargs="+", required=True, help="List of coin denominations")
+
+    args = parser.parse_args()
+
+    solutions = inverse_coin_change(args.amount, args.coins)
+
+    if not solutions:
+        print(f"No combinations found to make {args.amount} using coins {args.coins}")
+    else:
+        print(f"Combinations to make {args.amount} using coins {args.coins}:")
+        for combo in solutions:
+            print(combo)
+
+
+if __name__ == "__main__":
+    main()