From ee5bce70f59bd831ad8521972edc8c4194242e9a Mon Sep 17 00:00:00 2001
From: Loic GUEGAN <loic.guegan@yahoo.fr>
Date: Sun, 27 Jan 2019 19:34:56 +0100
Subject: [PATCH] Add some algo

---
 src/quick-find.lisp           | 30 ++++++++++++++++++++++
 src/quick-union.lisp          | 33 ++++++++++++++++++++++++
 src/weighted-quick-union.lisp | 47 +++++++++++++++++++++++++++++++++++
 3 files changed, 110 insertions(+)
 create mode 100644 src/quick-find.lisp
 create mode 100644 src/quick-union.lisp
 create mode 100644 src/weighted-quick-union.lisp

diff --git a/src/quick-find.lisp b/src/quick-find.lisp
new file mode 100644
index 0000000..dd371b8
--- /dev/null
+++ b/src/quick-find.lisp
@@ -0,0 +1,30 @@
+;; Create network nodes
+(defun create-network (n)
+  "Build a quick-find network using a dynamic vector"
+  (let ((nodes (make-array n :fill-pointer 0)))
+    (dotimes (id n)
+      (vector-push id nodes))
+    nodes))
+
+;; Check if two nodes are connected
+(defmacro connected (network n1 n2)
+  " Return t if there is a path between n1 and n2, nil otherwise. connected represent the find operation of the Quick Find Algorithm"
+    `(= (elt ,network ,n1) (elt ,network ,n2)))
+
+;; Link two nodes in the network
+(defun union_ (network n1 n2)
+  "Link two nodes in the quick-find network. union_ represent the union operation of the Quick Find Algorithm"
+  (let ((v-n1 (elt network n1))
+        (v-n2 (elt network n2))
+        (new-network (copy-seq network)))
+    (dotimes (n (length new-network))
+      (if (= (elt new-network n) v-n2) (setf (elt new-network n) v-n1)))
+    new-network))
+
+;; Union consing version
+(defmacro nunion_ (network n1 n2)
+  "A cosing version of union_"
+  `(setq ,network (union_ ,network ,n1 ,n2)))
+
+
+
diff --git a/src/quick-union.lisp b/src/quick-union.lisp
new file mode 100644
index 0000000..ca61703
--- /dev/null
+++ b/src/quick-union.lisp
@@ -0,0 +1,33 @@
+;; Create network nodes
+(defun create-network (n)
+  "Build a quick-find network using a dynamic vector"
+  (let ((nodes (make-array n :fill-pointer 0)))
+    (dotimes (id n)
+      (vector-push id nodes))
+    nodes))
+
+;; Find the root of a node
+(defun find-root (network node)
+  "Find the root of a sub-tree in the network."
+  (do ((id node value)
+       (value (elt network node) (elt network value)))
+      ((= id value) id)))
+
+;; Check if two nodes are connected
+(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)))
+
+;; Link two nodes together
+(defun union_ (network n1 n2)
+  "Connect to sub-tree together. union represent the union operation on the Quick Union algorithm"
+  (let ((new-network (copy-seq network)))
+    (setf (elt new-network (find-root new-network n1))
+          (find-root new-network n2))
+    new-network))
+
+;; A consed version of union_
+(defmacro nunion_ (network n1 n2)
+  `(setf ,network (union_ ,network ,n1 ,n2)))
+
diff --git a/src/weighted-quick-union.lisp b/src/weighted-quick-union.lisp
new file mode 100644
index 0000000..16b1aa5
--- /dev/null
+++ b/src/weighted-quick-union.lisp
@@ -0,0 +1,47 @@
+;; Create network nodes: A two dimensionnal array.
+;; 1st dimension = the network
+;; 2nd dimension = each subtree node quantities
+(defun create-network (n)
+  "Build a quick-find network using a multi-dimensional dynamic vector"
+  (let ((network (make-array `(2 ,n) :initial-element 1)))
+    (dotimes (id n)
+      (setf (aref network 0 id) id))
+    network))
+
+;; Find the root of a node
+(defun find-root (network node)
+  "Find the root of a sub-tree in the network."
+  (do ((id node value)
+       (value (aref network 0 node) (aref network 0 value)))
+      ((= id value) id)))
+
+;; Check if two nodes are connected
+(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)))
+
+;; Link two nodes together
+(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)))
+
+
+
+;; A consed version of union_
+(defmacro nunion_ (network n1 n2)
+  `(setf ,network (union_ ,network ,n1 ,n2)))
+
+