diff --git a/pkg/expression/constant_propagation.go b/pkg/expression/constant_propagation.go
index 38c4cf3790a63..41ad3637308ed 100644
--- a/pkg/expression/constant_propagation.go
+++ b/pkg/expression/constant_propagation.go
@@ -32,10 +32,10 @@ var MaxPropagateColsCnt = 100
 
 // nolint:structcheck
 type basePropConstSolver struct {
-	colMapper map[int64]int       // colMapper maps column to its index
-	eqList    []*Constant         // if eqList[i] != nil, it means col_i = eqList[i]
-	unionSet  *disjointset.IntSet // unionSet stores the relations like col_i = col_j
-	columns   []*Column           // columns stores all columns appearing in the conditions
+	colMapper map[int64]int             // colMapper maps column to its index
+	eqList    []*Constant               // if eqList[i] != nil, it means col_i = eqList[i]
+	unionSet  *disjointset.SimpleIntSet // unionSet stores the relations like col_i = col_j
+	columns   []*Column                 // columns stores all columns appearing in the conditions
 	ctx       exprctx.ExprContext
 }
 
diff --git a/pkg/util/disjointset/BUILD.bazel b/pkg/util/disjointset/BUILD.bazel
index 941410ed9d54b..8578cbc54206b 100644
--- a/pkg/util/disjointset/BUILD.bazel
+++ b/pkg/util/disjointset/BUILD.bazel
@@ -2,7 +2,10 @@ load("@io_bazel_rules_go//go:def.bzl", "go_library", "go_test")
 
 go_library(
     name = "disjointset",
-    srcs = ["int_set.go"],
+    srcs = [
+        "int_set.go",
+        "set.go",
+    ],
     importpath = "github.com/pingcap/tidb/pkg/util/disjointset",
     visibility = ["//visibility:public"],
 )
@@ -13,6 +16,7 @@ go_test(
     srcs = [
         "int_set_test.go",
         "main_test.go",
+        "set_test.go",
     ],
     embed = [":disjointset"],
     flaky = True,
diff --git a/pkg/util/disjointset/int_set.go b/pkg/util/disjointset/int_set.go
index 05846e3840850..a53b7e6d0a44a 100644
--- a/pkg/util/disjointset/int_set.go
+++ b/pkg/util/disjointset/int_set.go
@@ -14,27 +14,29 @@
 
 package disjointset
 
-// IntSet is the int disjoint set.
-type IntSet struct {
+// SimpleIntSet is the int disjoint set.
+// It's not designed for sparse case. You should use it when the elements are continuous.
+// Time complexity: the union operation is inverse ackermann function, which is very close to O(1).
+type SimpleIntSet struct {
 	parent []int
 }
 
 // NewIntSet returns a new int disjoint set.
-func NewIntSet(size int) *IntSet {
+func NewIntSet(size int) *SimpleIntSet {
 	p := make([]int, size)
 	for i := range p {
 		p[i] = i
 	}
-	return &IntSet{parent: p}
+	return &SimpleIntSet{parent: p}
 }
 
 // Union unions two sets in int disjoint set.
-func (m *IntSet) Union(a int, b int) {
+func (m *SimpleIntSet) Union(a int, b int) {
 	m.parent[m.FindRoot(a)] = m.FindRoot(b)
 }
 
 // FindRoot finds the representative element of the set that `a` belongs to.
-func (m *IntSet) FindRoot(a int) int {
+func (m *SimpleIntSet) FindRoot(a int) int {
 	if a == m.parent[a] {
 		return a
 	}
diff --git a/pkg/util/disjointset/set.go b/pkg/util/disjointset/set.go
new file mode 100644
index 0000000000000..08b63aec5dd3c
--- /dev/null
+++ b/pkg/util/disjointset/set.go
@@ -0,0 +1,67 @@
+// Copyright 2024 PingCAP, Inc.
+//
+// Licensed 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.
+
+package disjointset
+
+// Set is the universal implementation of a disjoint set.
+// It's designed for sparse cases or non-integer types.
+// If you are dealing with continuous integers, you should use SimpleIntSet to avoid the cost of a hash map.
+// We hash the original value to an integer index and then apply the core disjoint set algorithm.
+// Time complexity: the union operation has an inverse Ackermann function time complexity, which is very close to O(1).
+type Set[T comparable] struct {
+	parent  []int
+	val2Idx map[T]int
+	tailIdx int
+}
+
+// NewSet creates a disjoint set.
+func NewSet[T comparable](size int) *Set[T] {
+	return &Set[T]{
+		parent:  make([]int, 0, size),
+		val2Idx: make(map[T]int, size),
+		tailIdx: 0,
+	}
+}
+func (s *Set[T]) findRootOriginalVal(a T) int {
+	idx, ok := s.val2Idx[a]
+	if !ok {
+		s.parent = append(s.parent, s.tailIdx)
+		s.val2Idx[a] = s.tailIdx
+		s.tailIdx++
+		return s.tailIdx - 1
+	}
+	return s.findRoot(idx)
+}
+
+// findRoot is an internal implementation. Call it inside findRootOriginalVal.
+func (s *Set[T]) findRoot(a int) int {
+	if s.parent[a] != a {
+		s.parent[a] = s.findRoot(s.parent[a])
+	}
+	return s.parent[a]
+}
+
+// InSameGroup checks whether a and b are in the same group.
+func (s *Set[T]) InSameGroup(a, b T) bool {
+	return s.findRootOriginalVal(a) == s.findRootOriginalVal(b)
+}
+
+// Union joins two sets in the disjoint set.
+func (s *Set[T]) Union(a, b T) {
+	rootA := s.findRootOriginalVal(a)
+	rootB := s.findRootOriginalVal(b)
+	if rootA != rootB {
+		s.parent[rootA] = rootB
+	}
+}
diff --git a/pkg/util/disjointset/set_test.go b/pkg/util/disjointset/set_test.go
new file mode 100644
index 0000000000000..ae7cada175845
--- /dev/null
+++ b/pkg/util/disjointset/set_test.go
@@ -0,0 +1,49 @@
+// Copyright 2024 PingCAP, Inc.
+//
+// Licensed 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.
+
+package disjointset
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestDisjointSet(t *testing.T) {
+	set := NewSet[string](10)
+	assert.False(t, set.InSameGroup("a", "b"))
+	assert.Len(t, set.parent, 2)
+	set.Union("a", "b")
+	assert.True(t, set.InSameGroup("a", "b"))
+	assert.False(t, set.InSameGroup("a", "c"))
+	assert.Len(t, set.parent, 3)
+	assert.False(t, set.InSameGroup("b", "c"))
+	assert.Len(t, set.parent, 3)
+	set.Union("b", "c")
+	assert.True(t, set.InSameGroup("a", "c"))
+	assert.True(t, set.InSameGroup("b", "c"))
+	set.Union("d", "e")
+	set.Union("e", "f")
+	set.Union("f", "g")
+	assert.Len(t, set.parent, 7)
+	assert.False(t, set.InSameGroup("a", "d"))
+	assert.True(t, set.InSameGroup("d", "g"))
+	assert.False(t, set.InSameGroup("c", "g"))
+	set.Union("a", "g")
+	assert.True(t, set.InSameGroup("a", "d"))
+	assert.True(t, set.InSameGroup("b", "g"))
+	assert.True(t, set.InSameGroup("c", "f"))
+	assert.True(t, set.InSameGroup("a", "e"))
+	assert.True(t, set.InSameGroup("b", "c"))
+}