-
Notifications
You must be signed in to change notification settings - Fork 0
/
algorithm.lisp
217 lines (203 loc) · 7.5 KB
/
algorithm.lisp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
;;; algorithm.lisp ---
;;
;; Filename: algorithm.lisp
;; Description:
;; Author: Liu Enze
;; Maintainer:
;; Created: Fri Nov 28 07:49:16 2014 (+0800)
;; Version:
;; Package-Requires: ()
;; Last-Updated: Fri Nov 28 07:49:16 2014 (+0800)
;; By: Liu Enze
;; Update #: 1
;; URL:
;; Doc URL:
;; Keywords:
;; Compatibility:
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;;; Commentary:
;;
;;
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;;; Change Log:
;;
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;; This program is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation, either version 3 of the License, or (at
;; your option) any later version.
;;
;; This program is distributed in the hope that it will be useful, but
;; WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
;; General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License
;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;;; Code:
;;; algorithm.lisp ---
;;
;; Filename: algorithm.lisp
;; Description:
;; Author: Liu Enze
;; Maintainer:
;; Created: Fri Nov 28 07:49:16 2014 (+0800)
;; Version:
;; Package-Requires: ()
;; Last-Updated: Fri Nov 28 07:49:16 2014 (+0800)
;; By: Liu Enze
;; Update #: 1
;; URL:
;; Doc URL:
;; Keywords:
;; Compatibility:
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;;; Commentary:
;;
;;
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;;; Change Log:
;;
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;; This program is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation, either version 3 of the License, or (at
;; your option) any later version.
;;
;; This program is distributed in the hope that it will be useful, but
;; WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
;; General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License
;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;;; Code:
;KMP string match
(defun kmp (s w)
"input is source string and word,this function is to get index for word in source"
(match_kmp (next w #'char=) s w #'char=))
(defun match_kmp (next s w predicate)
(labels ((match_kmp_r (next s w m i l wl)
(if (= (+ m i) l)
(values l nil)
(if (funcall predicate (char s (+ m i)) (char w i))
(if (= i (1- wl))
(values m t)
(match_kmp_r next s w m (1+ i) l wl))
(if (> (nth i next) -1)
(match_kmp_r next s w (- (1+ m) (nth i next)) (nth i next) l wl)
(match_kmp_r next s w (1+ m) 0 l wl))))))
(match_kmp_r next s w 0 0 (length s) (length w))))
(defun next (w predicate)
(labels ((next_r (next pos cnd w wl)
(if (= pos wl)
next
(cond ((= pos 1)
(progn (setf (nth pos next) 0)
(next_r next (1+ pos) cnd w wl)))
((funcall predicate (char w (1- pos)) (char w cnd))
(progn (setf (nth pos next) (1+ cnd))
(next_r next (1+ pos) (1+ cnd) w wl)))
((> cnd 0) (next_r next pos (nth cnd next) w wl))
(t (progn (setf (nth pos next) 0)
(next_r next (1+ pos) cnd w wl)))))))
(next_r (make-list (length w) :initial-element -1) 1 0 w (length w))))
;Fibnacci in matrix
;f(n)=f(n-1)+f(n-2) (when n >1)
;f(0)=0,f(1)=1;
(defvar *matrix* '(1 1 1 0))
(defvar *0-matrix* '(1 0 0 1))
(defun fib (n)
"using 2d-array [1,1,1,0] to calculate fib n,
reduce this problem from '+' to '*' so that a^n
can be calculated as a^x1*a^x2*a^xn (x1,x2...xn are all 2^n)"
(labels (
(decompose (n) (format nil "~B" n))
(listMulti (l1 l2) (+ (* (nth 0 l1) (nth 0 l2)) (+ (* (nth 1 l1) (nth 1 l2)))))
(multi (m1 m2) (list
(listMulti (list (nth 0 m1) (nth 1 m1))
(list (nth 0 m2) (nth 2 m2)))
(listMulti (list (nth 0 m1) (nth 1 m1))
(list (nth 1 m2) (nth 3 m2)))
(listMulti (list (nth 2 m1) (nth 3 m1))
(list (nth 0 m2) (nth 2 m2)))
(listMulti (list (nth 2 m1) (nth 3 m1))
(list (nth 1 m2) (nth 3 m2)))))
(multiMatrixBase2 (matrix n value)
(cond
((string= value "0") *0-matrix*)
((<= n 1) matrix)
(t (multiMatrixBase2 (multi matrix matrix) (1- n) value))))
(multiMatrix (matrix bits len)
(if (= 0 len)
*0-matrix*
(multi (multiMatrixBase2 matrix len (subseq bits 0 1)) (multiMatrix matrix (subseq bits 1 len) (1- len))))))
(let ((m (multiMatrix *matrix* (decompose (1- n)) (length (decompose (1- n))))))
(cond
((< n 0) "wrong input")
((= n 0) 0)
(t (nth 0 m))))))
;gcd
(defun gcd_m (a b)
"using gcd(x,y) = gcd (x-y,y)"
(if (= 0 b)
a
(gcd b (mod a b))))
;;QUICK SORT
(defun quicksort (seq)
(if (>= 1 (length seq)) seq
(let* ((key (first seq))
(less (remove-if-not (lambda (x) (< x key)) seq))
(more (remove-if-not (lambda (x) (> x key)) seq))
(same (remove-if-not (lambda (x) (= x key)) seq)))
(append (quicksort less) same (quicksort more)))))
(defun quicksort2 (seq)
(if (>= 1 (length seq)) seq
(labels ((partition (seq key)
(loop for x in seq
when (< x key) collect x into less
when (= x key) collect x into same
when (> x key) collect x into more
finally (return (values less same more)))))
(multiple-value-bind (less same more) (partition seq (first seq))
(append (quicksort2 less) same (quicksort2 more))))))
;;HEAP SORT
(defun heapsort (a &optional (count (length a)))
(macrolet ((ref (i) `(aref a ,i))
(swap (i j) `(rotatef (ref ,i) (ref ,j)))
(ref< (i j) `(< (ref ,i) (ref ,j))))
(labels ((sift (root count)
(let ((c1 (+ (* 2 root) 1))
(c2 (+ (* 2 root) 2)))
(when (< c1 count)
(let ((c (if (and (< c2 count) (ref< c1 c2)) c2 c1)))
(when (ref< root c)
(swap root c)
(sift c count)))))))
(loop for start from (1- (floor count 2)) downto 0
do (sift start count))
(loop for end from (1- count) downto 1
do (swap 0 end) (sift 0 end))))
a)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; algorithm.lisp ends here
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; algorithm.lisp ends here