[opt](cache elimation) using step decending method to elimiate cache

be/src/util/algorithm_util.h

@@ -0,0 +1,44 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+#pragma once
+
+#include <cstdint>
+#include <utility>
+
+#include "common/status.h"
+namespace doris {
+class AlgoUtil {
+    // descent the value step by step not linear continuity
+    double descent_by_step(int step_num, int64_t low_bound, int64_t high_bound, int64_t current) {
+        if (current <= low_bound) {
+            return 1;
+        }
+        if (current >= high_bound) {
+            return 0;
+        }
+        if (high_bound <= low_bound) {
+            // Invalid
+            return 0;
+        }
+        int64_t step_size = (int64_t)std::floor((high_bound - low_bound) / step_num);
+        int64_t used_step = (int64_t)std::ceil((current - low_bound) / step_size);
+        int64_t left_step = step_num - used_step;
+        return left_step / step_num;
+    }
+};
+} // namespace doris

be/test/util/algo_util_test.cpp

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+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you under the Apache License, Version 2.0 (the
+// "License"); you may not use this file except in compliance
+// with the License.  You may obtain a copy of the License at
+//
+//   http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing,
+// software distributed under the License is distributed on an
+// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, either express or implied.  See the License for the
+// specific language governing permissions and limitations
+// under the License.
+
+#include <gtest/gtest-message.h>
+#include <gtest/gtest-test-part.h>
+
+#include <boost/utility/binary.hpp>
+#include <memory>
+
+#include "gtest/gtest_pred_impl.h"
+#include "util/algorithm_util.h"
+
+namespace doris {
+
+TEST(TestAlgoUtil, DescentByStep) {
+    // double descent_by_step(int step_num, int64_t low_bound, int64_t high_bound, int64_t current)
+    EXPECT_EQ(AlgoUtil::descent_by_step(10, 100, 200, 101), 0.9);
+    EXPECT_EQ(AlgoUtil::descent_by_step(10, 100, 200, 99), 1);
+    EXPECT_EQ(AlgoUtil::descent_by_step(10, 200, 100, 101), 0);
+    EXPECT_EQ(AlgoUtil::descent_by_step(10, 100, 200, 111), 0.8);
+    EXPECT_EQ(AlgoUtil::descent_by_step(10, 100, 200, 188), 0.1);
+    EXPECT_EQ(AlgoUtil::descent_by_step(10, 100, 200, 100), 1);
+    EXPECT_EQ(AlgoUtil::descent_by_step(10, 100, 200, 200), 0);
+    EXPECT_EQ(AlgoUtil::descent_by_step(10, 100, 200, 300), 0);
+}
+
+} // namespace doris