[C++][Acero] Fix key hashers for tables with differently ordered sche…

…mas than the output

cpp/src/arrow/acero/asof_join_node.cc

@@ -1098,7 +1098,7 @@ class AsofJoinNode : public ExecNode {
     auto inputs = this->inputs();
     for (size_t i = 0; i < inputs.size(); i++) {
       RETURN_NOT_OK(key_hashers_[i]->Init(plan()->query_context()->exec_context(),
-                                          output_schema()));
+                                          inputs[i]->output_schema()));
       ARROW_ASSIGN_OR_RAISE(
           auto input_state,
           InputState::Make(i, tolerance_, must_hash_, may_rehash_, key_hashers_[i].get(),

cpp/src/arrow/acero/asof_join_node_test.cc

@@ -16,6 +16,7 @@
 // under the License.
 
 #include <gmock/gmock-matchers.h>
+#include <iostream>  // nocommit
 
 #include <chrono>
 #include <memory>
@@ -1582,6 +1583,66 @@ TEST(AsofJoinTest, BatchSequencing) {
   return TestSequencing(MakeIntegerBatches, /*num_batches=*/32, /*batch_size=*/1);
 }
 
+template <typename BatchesMaker>
+void TestSchemaResolution(BatchesMaker maker, int num_batches, int batch_size) {
+  auto l_schema =
+      schema({field("time", int32()), field("key", int32()), field("l_value", int32())});
+  auto r_schema =
+      schema({field("time", int32()), field("key", int32()), field("r0_value", int32())});
+
+  auto make_shift = [&maker, num_batches, batch_size](
+                        const std::shared_ptr<Schema>& schema, int shift) {
+    return maker({[](int row) -> int64_t { return row; },
+                  [num_batches](int row) -> int64_t { return row / num_batches; },
+                  [shift](int row) -> int64_t { return row * 10 + shift; }},
+                 schema, num_batches, batch_size);
+  };
+  ASSERT_OK_AND_ASSIGN(auto l_batches, make_shift(l_schema, 0));
+  ASSERT_OK_AND_ASSIGN(auto r_batches, make_shift(r_schema, 1));
+
+  Declaration l_src = {"source",
+                       SourceNodeOptions(l_schema, l_batches.gen(false, false))};
+  Declaration r_src = {"source",
+                       SourceNodeOptions(r_schema, r_batches.gen(false, false))};
+  Declaration l_project = {
+      "project",
+      {std::move(l_src)},
+      ProjectNodeOptions({compute::field_ref("time"),
+                          compute::call("cast", {compute::field_ref("key")},
+                                        compute::CastOptions::Safe(utf8())),
+                          compute::field_ref("l_value")},
+                         {"time", "key", "l_value"})};
+  Declaration r_project = {
+      "project",
+      {std::move(r_src)},
+      ProjectNodeOptions({compute::call("cast", {compute::field_ref("key")},
+                                        compute::CastOptions::Safe(utf8())),
+                          compute::field_ref("r0_value"), compute::field_ref("time")},
+                         {"key", "r0_value", "time"})};
+
+  Declaration asofjoin = {
+      "asofjoin", {l_project, r_project}, GetRepeatedOptions(2, "time", {"key"}, 1000)};
+
+  QueryOptions query_options;
+  query_options.use_threads = false;
+  ASSERT_OK_AND_ASSIGN(auto table, DeclarationToTable(asofjoin, query_options));
+
+  Int32Builder expected_r0_b;
+  for (int i = 1; i <= 91; i += 10) {
+    ASSERT_OK(expected_r0_b.Append(i));
+  }
+  ASSERT_OK_AND_ASSIGN(auto expected_r0, expected_r0_b.Finish());
+
+  auto actual_r0 = table->GetColumnByName("r0_value");
+  std::vector<std::shared_ptr<arrow::Array>> chunks = {expected_r0};
+  auto expected_r0_chunked = std::make_shared<arrow::ChunkedArray>(chunks);
+  ASSERT_TRUE(actual_r0->Equals(expected_r0_chunked));
+}
+
+TEST(AsofJoinTest, OutputSchemaResolution) {
+  return TestSchemaResolution(MakeIntegerBatches, /*num_batches=*/1, /*batch_size=*/10);
+}
+
 namespace {
 
 Result<AsyncGenerator<std::optional<ExecBatch>>> MakeIntegerBatchGenForTest(