Update app.py

app.py

@@ -234,6 +234,24 @@ def is_semipositive_definite(matrix):
 
     # Check if all eigenvalues are non-negative
     return all(val >= 0 for val in eigenvalues)
+""",
+"""
+def key_exists(data, key_to_find):
+    # Base case: If data is not a dictionary, return False
+    if not isinstance(data, dict):
+        return False
+
+    # If the key is in the dictionary, return True
+    if key_to_find in data:
+        return True
+
+    # Otherwise, recurse into each nested dictionary
+    for key, value in data.items():
+        if key_exists(value, key_to_find):
+            return True
+
+    # If the key was not found in this dictionary or any sub-dictionary, return False
+    return False
 """
     ]
 example = examples[0]