GH-49385: Clarify empty schema contract on stream_reader

cpp/src/parquet/stream_reader.cc

@@ -50,6 +50,9 @@ StreamReader::StreamReader(std::unique_ptr<ParquetFileReader> reader)
   auto schema = file_metadata_->schema();
   auto group_node = schema->group_node();
 
+  if (schema->num_columns() == 0) {
+    throw ParquetException("StreamReader does not support empty schemas.");
+  }
   nodes_.resize(schema->num_columns());
 
   for (auto i = 0; i < schema->num_columns(); ++i) {

cpp/src/parquet/stream_reader.h

@@ -65,6 +65,7 @@ class PARQUET_EXPORT StreamReader {
   //      assigned afterwards.
   StreamReader() = default;
 
+  /// Reader must have at least one field defined in its schema.
   explicit StreamReader(std::unique_ptr<ParquetFileReader> reader);
 
   ~StreamReader() = default;

cpp/src/parquet/stream_reader_test.cc

@@ -24,8 +24,10 @@
 #include <memory>
 
 #include "arrow/io/file.h"
+#include "arrow/io/memory.h"
 #include "arrow/util/decimal.h"
 #include "parquet/exception.h"
+#include "parquet/file_writer.h"
 #include "parquet/test_util.h"
 
 namespace parquet {
@@ -251,6 +253,22 @@ TEST_F(TestStreamReader, DefaultConstructed) {
   EXPECT_EQ(0, os.SkipRows(100));
 }
 
+TEST(StreamReaderEmptySchema, ThrowsOnConstruction) {
+  PARQUET_ASSIGN_OR_THROW(auto buffer_os, ::arrow::io::BufferOutputStream::Create());
+
+  auto empty_schema = std::static_pointer_cast<schema::GroupNode>(
+      schema::GroupNode::Make("schema", Repetition::REQUIRED, schema::NodeVector{}));
+
+  auto file_writer = ParquetFileWriter::Open(buffer_os, empty_schema);
+  file_writer->Close();
+
+  PARQUET_ASSIGN_OR_THROW(auto buffer, buffer_os->Finish());
+  auto buffer_reader = std::make_shared<::arrow::io::BufferReader>(buffer);
+  auto file_reader = ParquetFileReader::Open(buffer_reader);
+
+  EXPECT_THROW(StreamReader{std::move(file_reader)}, ParquetException);
+}
+
 TEST_F(TestStreamReader, TypeChecking) {
   bool b;
   std::string s;