From 5b66a24b4ad535778fa407aec56b41659f688e89 Mon Sep 17 00:00:00 2001
From: pawareliza14 <135448125+pawareliza14@users.noreply.github.com>
Date: Tue, 7 Oct 2025 01:00:05 +0530
Subject: [PATCH 1/2] Create inverse_coin_change.py

---
 backtracking/inverse_coin_change.py | 47 +++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)
 create mode 100644 backtracking/inverse_coin_change.py

diff --git a/backtracking/inverse_coin_change.py b/backtracking/inverse_coin_change.py
new file mode 100644
index 000000000000..440804026a02
--- /dev/null
+++ b/backtracking/inverse_coin_change.py
@@ -0,0 +1,47 @@
+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()

From 41bb691c7c46400f433ac67d93be09e427861f85 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Mon, 6 Oct 2025 19:41:17 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 backtracking/inverse_coin_change.py | 10 +++++++---
 1 file changed, 7 insertions(+), 3 deletions(-)

diff --git a/backtracking/inverse_coin_change.py b/backtracking/inverse_coin_change.py
index 440804026a02..f5c30ebcec64 100644
--- a/backtracking/inverse_coin_change.py
+++ b/backtracking/inverse_coin_change.py
@@ -1,7 +1,7 @@
 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)
@@ -28,8 +28,12 @@ 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")
+    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()