Union-Find: add a new module in kernel library

This patch implements a union-find data structure in the kernel library,
which includes operations for allocating nodes, freeing nodes,
finding the root of a node, and merging two nodes.

Signed-off-by: Xavier <xavier_qy@163.com>
Signed-off-by: Tejun Heo <tj@kernel.org>

1 files changed, 102 insertions, 0 deletions

diff --git a/Documentation/core-api/union_find.rst b/Documentation/core-api/union_find.rst
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+.. SPDX-License-Identifier: GPL-2.0
+
+====================
+Union-Find in Linux
+====================
+
+
+:Date: June 21, 2024
+:Author: Xavier <xavier_qy@163.com>
+
+What is union-find, and what is it used for?
+------------------------------------------------
+
+Union-find is a data structure used to handle the merging and querying
+of disjoint sets. The primary operations supported by union-find are:
+
+	Initialization: Resetting each element as an individual set, with
+		each set's initial parent node pointing to itself.
+	Find: Determine which set a particular element belongs to, usually by
+		returning a “representative element” of that set. This operation
+		is used to check if two elements are in the same set.
+	Union: Merge two sets into one.
+
+As a data structure used to maintain sets (groups), union-find is commonly
+utilized to solve problems related to offline queries, dynamic connectivity,
+and graph theory. It is also a key component in Kruskal's algorithm for
+computing the minimum spanning tree, which is crucial in scenarios like
+network routing. Consequently, union-find is widely referenced. Additionally,
+union-find has applications in symbolic computation, register allocation,
+and more.
+
+Space Complexity: O(n), where n is the number of nodes.
+
+Time Complexity: Using path compression can reduce the time complexity of
+the find operation, and using union by rank can reduce the time complexity
+of the union operation. These optimizations reduce the average time
+complexity of each find and union operation to O(α(n)), where α(n) is the
+inverse Ackermann function. This can be roughly considered a constant time
+complexity for practical purposes.
+
+This document covers use of the Linux union-find implementation.  For more
+information on the nature and implementation of union-find,  see:
+
+  Wikipedia entry on union-find
+    https://en.wikipedia.org/wiki/Disjoint-set_data_structure
+
+Linux implementation of union-find
+-----------------------------------
+
+Linux's union-find implementation resides in the file "lib/union_find.c".
+To use it, "#include <linux/union_find.h>".
+
+The union-find data structure is defined as follows::
+
+	struct uf_node {
+		struct uf_node *parent;
+		unsigned int rank;
+	};
+
+In this structure, parent points to the parent node of the current node.
+The rank field represents the height of the current tree. During a union
+operation, the tree with the smaller rank is attached under the tree with the
+larger rank to maintain balance.
+
+Initializing union-find
+--------------------
+
+You can complete the initialization using either static or initialization
+interface. Initialize the parent pointer to point to itself and set the rank
+to 0.
+Example::
+
+	struct uf_node my_node = UF_INIT_NODE(my_node);
+or
+	uf_node_init(&my_node);
+
+Find the Root Node of union-find
+--------------------------------
+
+This operation is mainly used to determine whether two nodes belong to the same
+set in the union-find. If they have the same root, they are in the same set.
+During the find operation, path compression is performed to improve the
+efficiency of subsequent find operations.
+Example::
+
+	int connected;
+	struct uf_node *root1 = uf_find(&node_1);
+	struct uf_node *root2 = uf_find(&node_2);
+	if (root1 == root2)
+		connected = 1;
+	else
+		connected = 0;
+
+Union Two Sets in union-find
+----------------------------
+
+To union two sets in the union-find, you first find their respective root nodes
+and then link the smaller node to the larger node based on the rank of the root
+nodes.
+Example::
+
+	uf_union(&node_1, &node_2);