feat: Add partition_stats() for EmptyExec (apache#20203)

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- Part of apache#15873 .

## Rationale for this change
Add partition stats for `EmptyExec`. 
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## What changes are included in this PR?

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## Are these changes tested?
Added integration test.

Author: jonathanc-n

datafusion/core/tests/physical_optimizer/partition_statistics.rs

@@ -1294,4 +1294,64 @@ mod test {
 
         Ok(())
     }
+
+    #[tokio::test]
+    async fn test_statistics_by_partition_of_empty_exec() -> Result<()> {
+        let schema = Arc::new(Schema::new(vec![
+            Field::new("id", DataType::Int32, false),
+            Field::new("name", DataType::Utf8, true),
+        ]));
+
+        // Try to test with single partition
+        let empty_single = Arc::new(EmptyExec::new(Arc::clone(&schema)));
+
+        let stats = empty_single.partition_statistics(Some(0))?;
+        assert_eq!(stats.num_rows, Precision::Exact(0));
+        assert_eq!(stats.total_byte_size, Precision::Exact(0));
+        assert_eq!(stats.column_statistics.len(), 2);
+
+        for col_stat in &stats.column_statistics {
+            assert_eq!(col_stat.null_count, Precision::Exact(0));
+            assert_eq!(col_stat.distinct_count, Precision::Exact(0));
+            assert_eq!(col_stat.byte_size, Precision::Exact(0));
+            assert_eq!(col_stat.min_value, Precision::<ScalarValue>::Absent);
+            assert_eq!(col_stat.max_value, Precision::<ScalarValue>::Absent);
+            assert_eq!(col_stat.sum_value, Precision::<ScalarValue>::Absent);
+            assert_eq!(col_stat.byte_size, Precision::Exact(0));
+        }
+
+        let overall_stats = empty_single.partition_statistics(None)?;
+        assert_eq!(stats, overall_stats);
+
+        validate_statistics_with_data(empty_single, vec![ExpectedStatistics::Empty], 0)
+            .await?;
+
+        // Test with multiple partitions
+        let empty_multi: Arc<dyn ExecutionPlan> =
+            Arc::new(EmptyExec::new(Arc::clone(&schema)).with_partitions(3));
+
+        let statistics = (0..empty_multi.output_partitioning().partition_count())
+            .map(|idx| empty_multi.partition_statistics(Some(idx)))
+            .collect::<Result<Vec<_>>>()?;
+
+        assert_eq!(statistics.len(), 3);
+
+        for stat in &statistics {
+            assert_eq!(stat.num_rows, Precision::Exact(0));
+            assert_eq!(stat.total_byte_size, Precision::Exact(0));
+        }
+
+        validate_statistics_with_data(
+            empty_multi,
+            vec![
+                ExpectedStatistics::Empty,
+                ExpectedStatistics::Empty,
+                ExpectedStatistics::Empty,
+            ],
+            0,
+        )
+        .await?;
+
+        Ok(())
+    }
 }

datafusion/physical-plan/src/empty.rs

@@ -21,15 +21,16 @@ use std::any::Any;
 use std::sync::Arc;
 
 use crate::memory::MemoryStream;
-use crate::{DisplayAs, PlanProperties, SendableRecordBatchStream, Statistics, common};
+use crate::{DisplayAs, PlanProperties, SendableRecordBatchStream, Statistics};
 use crate::{
     DisplayFormatType, ExecutionPlan, Partitioning,
     execution_plan::{Boundedness, EmissionType},
 };
 
 use arrow::datatypes::SchemaRef;
 use arrow::record_batch::RecordBatch;
-use datafusion_common::{Result, assert_or_internal_err};
+use datafusion_common::stats::Precision;
+use datafusion_common::{ColumnStatistics, Result, ScalarValue, assert_or_internal_err};
 use datafusion_execution::TaskContext;
 use datafusion_physical_expr::EquivalenceProperties;
 
@@ -169,20 +170,31 @@ impl ExecutionPlan for EmptyExec {
             );
         }
 
-        let batch = self
-            .data()
-            .expect("Create empty RecordBatch should not fail");
-        Ok(common::compute_record_batch_statistics(
-            &[batch],
-            &self.schema,
-            None,
-        ))
+        // Build explicit stats: exact zero rows and bytes, with explicit known column stats
+        let mut stats = Statistics::default()
+            .with_num_rows(Precision::Exact(0))
+            .with_total_byte_size(Precision::Exact(0));
+
+        // Add explicit column stats for each field in schema
+        for _ in self.schema.fields() {
+            stats = stats.add_column_statistics(ColumnStatistics {
+                null_count: Precision::Exact(0),
+                distinct_count: Precision::Exact(0),
+                min_value: Precision::<ScalarValue>::Absent,
+                max_value: Precision::<ScalarValue>::Absent,
+                sum_value: Precision::<ScalarValue>::Absent,
+                byte_size: Precision::Exact(0),
+            });
+        }
+
+        Ok(stats)
     }
 }
 
 #[cfg(test)]
 mod tests {
     use super::*;
+    use crate::common;
     use crate::test;
     use crate::with_new_children_if_necessary;