Add solution for Issue #2605: Fresh Donuts

Author: Dev-06-06

exercises/1000_programs/medium/1815_fresh_donuts.py

@@ -0,0 +1,55 @@
+from functools import lru_cache
+
+def maxHappyGroups(batchSize, groups):
+    # Time Complexity: O(k^m) where k is batchSize and m is number of groups
+    # Space Complexity: O(batchSize)
+    
+    # 1. Simplify groups by taking modulo
+    remainder_counts = [0] * batchSize
+    happy_groups = 0
+    
+    for g in groups:
+        rem = g % batchSize
+        if rem == 0:
+            happy_groups += 1
+        else:
+            remainder_counts[rem] += 1
+            
+    # 2. Match complements (e.g., remainder 1 and batchSize-1)
+    for i in range(1, batchSize // 2 + 1):
+        if i == batchSize - i:
+            happy_groups += remainder_counts[i] // 2
+            remainder_counts[i] %= 2
+        else:
+            pairs = min(remainder_counts[i], remainder_counts[batchSize - i])
+            happy_groups += pairs
+            remainder_counts[i] -= pairs
+            remainder_counts[batchSize - i] -= pairs
+
+    # 3. DFS to optimize remaining groups
+    @lru_cache(None)
+    def dfs(current_rem, counts):
+        max_val = 0
+        total_remaining = sum(counts)
+        
+        if total_remaining == 0:
+            return 0
+            
+        for i in range(1, batchSize):
+            if counts[i] > 0:
+                new_counts = list(counts)
+                new_counts[i] -= 1
+                
+                is_happy = 1 if current_rem == 0 else 0
+                res = is_happy + dfs((current_rem + i) % batchSize, tuple(new_counts))
+                max_val = max(max_val, res)
+                
+        return max_val
+
+    happy_groups += dfs(0, tuple(remainder_counts))
+    return happy_groups
+
+# Driver Code
+if __name__ == "__main__":
+    print(f"Test 1: {maxHappyGroups(3, [1,2,3,4,5,6])}") # Expected: 4
+    print(f"Test 2: {maxHappyGroups(4, [1,3,2,5,2,2,1,6])}") # Expected: 4