From 0038d9bd0318c1025b8edd005f3aaa609a308a57 Mon Sep 17 00:00:00 2001
From: Loic GUEGAN <loic.guegan@yahoo.fr>
Date: Mon, 28 Jan 2019 18:21:58 +0100
Subject: [PATCH] Add algo

---
 .gitignore                                    |  2 +
 src/quick-find.lisp                           |  2 +-
 src/quick-union.lisp                          |  2 +-
 ...weighted-quick-union-path-compression.lisp | 59 +++++++++++++++++++
 src/weighted-quick-union.lisp                 |  2 +-
 5 files changed, 64 insertions(+), 3 deletions(-)
 create mode 100644 .gitignore
 create mode 100644 src/weighted-quick-union-path-compression.lisp

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..098114e
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,2 @@
+# Exclude Emacs temporary files
+*~
diff --git a/src/quick-find.lisp b/src/quick-find.lisp
index 21bd6d5..edaa7f0 100644
--- a/src/quick-find.lisp
+++ b/src/quick-find.lisp
@@ -30,7 +30,7 @@
     `(= (elt ,network ,n1) (elt ,network ,n2)))
 
 (defmacro nunion_ (network n1 n2)
-  "A consed version of union_"
+  "A destructive version of union_"
   `(setq ,network (union_ ,network ,n1 ,n2)))
 
 
diff --git a/src/quick-union.lisp b/src/quick-union.lisp
index 9b4e9d8..bf2ff3d 100644
--- a/src/quick-union.lisp
+++ b/src/quick-union.lisp
@@ -37,6 +37,6 @@ the find operation on the Quick Union algorithm"
   `(= (find-root ,network ,n1) (find-root ,network ,n2)))
 
 (defmacro nunion_ (network n1 n2)
-  "A consed version of union_"
+  "A destructive version of union_"
   `(setf ,network (union_ ,network ,n1 ,n2)))
 
diff --git a/src/weighted-quick-union-path-compression.lisp b/src/weighted-quick-union-path-compression.lisp
new file mode 100644
index 0000000..56c80b7
--- /dev/null
+++ b/src/weighted-quick-union-path-compression.lisp
@@ -0,0 +1,59 @@
+;;;; Weighted Quick Union Algorithm With Path Compression
+;;;; This algorithm solve dynamic connectivity
+;;;; problem by providing a way to find if there
+;;;; is a path between two nodes in a dynamic graph.
+;;;; It is an improved version of the Quick Union algorithm
+;;;; by improving the way that the union-tree is constructed
+;;;; The algorithm try to reduce the deepness of the tree in
+;;;; order to optimize the find-root function
+;;;; The path compression is ensure by the find-root function
+;;;; IMPORTANT: find-root is now a destructive function ! Be aware...
+
+;;; Base functions
+
+(defun create-network (n)
+  "Build a quick-find network using a multi-dimensional dynamic vector:\n
+1st dimension = the network\n 2nd dimension = each subtree node quantities"
+  (let ((network (make-array `(2 ,n) :initial-element 1)))
+    (dotimes (id n)
+      (setf (aref network 0 id) id))
+    network))
+
+(defun find-root (network node)
+  "Find the root of a sub-tree in the network. This is a destructive version of find-root that
+include path compression"
+  (do ((id node value)
+       (value (aref network 0 node) (aref network 0 value)))
+      ((= id value) (progn (setf (aref network 0 node) id) ; Path compression
+                           id))))
+
+(defun union_ (network n1 n2)
+  "Connect to sub-tree together. union represent the union operation on the Quick Union algorithm"
+  (let ((new-network (copy-tree network))) ; Duplicate network
+    (let* ((n1-root (find-root new-network n1))
+          (n2-root (find-root new-network n2))
+           (n1-size (aref new-network 1 n1-root))
+           (n2-size (aref new-network 1 n2-root)))
+      (if (>= n1-size n2-size) ; Check which subtree is LARGER (not deeper)
+          (progn (setf (aref new-network 0 n2-root) (aref new-network 0 n1-root)) ; Modify the second node
+                 (setf (aref new-network 1 n1-root) ; Update tree larger
+                       (+ (aref new-network 1 n1-root) (aref new-network 1 n2-root))))
+          (progn (setf (aref new-network 0 n1-root) (aref new-network 0 n2-root)) ; Otherwise modify the first node
+                 (setf (aref new-network 1 n2-root) ; Update tree larger
+                       (+ (aref new-network 1 n2-root) (aref new-network 1 n1-root)))))
+      new-network)))
+
+
+;;; Macro definitions
+
+
+(defmacro connected (network n1 n2)
+  "Return true if n1 and n2 are connected and nil otherwise. connection represent
+the find operation on the Quick Union algorithm"
+  `(= (find-root ,network ,n1) (find-root ,network ,n2)))
+
+(defmacro nunion_ (network n1 n2)
+  "A destructive version of the union function."
+  `(setf ,network (union_ ,network ,n1 ,n2)))
+
+
diff --git a/src/weighted-quick-union.lisp b/src/weighted-quick-union.lisp
index 7a3a3a7..679de80 100644
--- a/src/weighted-quick-union.lisp
+++ b/src/weighted-quick-union.lisp
@@ -49,7 +49,7 @@ the find operation on the Quick Union algorithm"
   `(= (find-root ,network ,n1) (find-root ,network ,n2)))
 
 (defmacro nunion_ (network n1 n2)
-  "A consed version of the union function."
+  "A destructive version of the union function."
   `(setf ,network (union_ ,network ,n1 ,n2)))