1. 问题描述
马尔可夫链算法用于生成一段随机的英文，其思想非常简单。首先读入数据，然后将读入的数据分成前缀和后缀两部分，通过前缀来随机获取后缀，籍此产生一段可读的随机英文。
为了说明方便，假设我们有如下一段话：
复制代码 代码如下:
Show your flowcharts and conceal your tables and I will be mystified. Show your tables and your flowcharts will be obvious.
假设前缀的长度为2,则我们处理输入以后得到如下数据，我们首先获取一个前缀，然后在前缀的后缀列表中随机选择一个单词，然后改变前缀，重复上述过程，这样，我们产生的句子将是可读的。
下面是处理过的数据：
复制代码 代码如下:
前缀 后缀
show your flowcharts tables
your flowcharts and will
flowcharts and conceal
flowcharts will be
your tables and and
will be mystified. obvious.
be mystified. show
be obvious. (end)
处理这个文本的马尔可夫链算法将首先带引show your,然后随机取出flowcharts 或者table 两个单词，假设选择的是flowcharts, 则新的前缀就是your flowcharts,同理，选择table 时，新的前缀就是your table,有了新的前缀your flowcharts 以后，再次随即选择它的后缀，这次是在and 和 will 中随机选择，重复上述过程，就能够产生一段可读的文本。具体描述如下：
复制代码 代码如下:
设置 w1 和 w2 为文本的前两个词
输出 w1 和 w2
循环：
随机地选出 w3,它是文本中 w1 w2 的后缀中的一个
打印 w3
把 w1 和 w2 分别换成 w2 和 w3
重复循环
2.awk 程序
马尔可夫链算法并不难，我们会在后面看到，用c语言来解决这个问题会相当麻烦，而用awk则只需要5分钟就能搞定。这简直就是一个演示awk优点的问题。
awk 中有关联数组，正好可以用来表示前缀和后缀的关系。程序如下：
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
|
# markov.awk: markov chain algorithm for 2-word prefixesBEGIN { MAXGEN = 10000; NONWORD = "\n"; w1 = w2 = NONWORD }{ for (i = 1; i <= NF; i++) { # read all words statetab[w1,w2,++nsuffix[w1,w2]] = $i w1 = w2 w2 = $i }}END { statetab[w1,w2,++nsuffix[w1,w2]] = NONWORD # add tail w1 = w2 = NONWORD for (i = 0; i < MAXGEN; i++) { # generate r = int(rand()*nsuffix[w1,w2]) + 1 # nsuffix >= 1 p = statetab[w1,w2,r] if (p == NONWORD) exit print p w1 = w2 # advance chain w2 = p }} |
3. C++ 程序
该问题的主要难点就在于通过前缀随机的获取后缀，在C++ 中，我们可以借助map 来实现前缀和后缀的对应关系，以此得到较高的开发效率。
|
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
|
/* Copyright (C) 1999 Lucent Technologies *//* Excerpted from 'The Practice of Programming' *//* by Brian W. Kernighan and Rob Pike */#include <time.h>#include <iostream>#include <string>#include <deque>#include <map>#include <vector>using namespace std;const int NPREF = 2;const char NONWORD[] = "\n"; // cannot appear as real line: we remove newlinesconst int MAXGEN = 10000; // maximum words generatedtypedef deque<string> Prefix;map<Prefix, vector<string> > statetab; // prefix -> suffixesvoid build(Prefix&, istream&);void generate(int nwords);void add(Prefix&, const string&);// markov main: markov-chain random text generationint main(void){ int nwords = MAXGEN; Prefix prefix; // current input prefix srand(time(NULL)); for (int i = 0; i < NPREF; i++) add(prefix, NONWORD); build(prefix, cin); add(prefix, NONWORD); generate(nwords); return 0;}// build: read input words, build state tablevoid build(Prefix& prefix, istream& in){ string buf; while (in >> buf) add(prefix, buf);}// add: add word to suffix deque, update prefixvoid add(Prefix& prefix, const string& s){ if (prefix.size() == NPREF) { statetab[prefix].push_back(s); prefix.pop_front(); } prefix.push_back(s);}// generate: produce output, one word per linevoid generate(int nwords){ Prefix prefix; int i; for (i = 0; i < NPREF; i++) add(prefix, NONWORD); for (i = 0; i < nwords; i++) { vector<string>& suf = statetab[prefix]; const string& w = suf[rand() % suf.size()]; if (w == NONWORD) break; cout << w << "\n"; prefix.pop_front(); // advance prefix.push_back(w); }} |
4. c 程序
如果需要程序运行得足够快，那就只能用较低级的语言来实现了。当我们用c 语言来实现时，就不得不考虑各种各样的问题了。首先，面临的第一个问题就是，如何表示前缀和后缀的关系?
这里采用前缀的key,后缀为value 的方式存储前缀与后缀的关系，我们知道，hash表的查找速度最快，所以，这里采用hash表也是情理之中的事，只是看你能不能想到，用前缀作key,基于上面的思路，再仔细一点，就没有什么大问题了。
|
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
|
/* Copyright (C) 1999 Lucent Technologies *//* Excerpted from 'The Practice of Programming' *//* by Brian W. Kernighan and Rob Pike *//* * Markov chain random text generator. */#include <string.h>#include <stdlib.h>#include <stdio.h>#include <string.h>#include <time.h>#include "eprintf.h"enum { NPREF = 2, /* number of prefix words */ NHASH = 4093, /* size of state hash table array */ MAXGEN = 10000 /* maximum words generated */};typedef struct State State;typedef struct Suffix Suffix;struct State { /* prefix + suffix list */ char *pref[NPREF]; /* prefix words */ Suffix *suf; /* list of suffixes */ State *next; /* next in hash table */};struct Suffix { /* list of suffixes */ char *word; /* suffix */ Suffix *next; /* next in list of suffixes */};State *lookup(char *prefix[], int create);void build(char *prefix[], FILE*);void generate(int nwords);void add(char *prefix[], char *word);State *statetab[NHASH]; /* hash table of states */char NONWORD[] = "\n"; /* cannot appear as real word *//* markov main: markov-chain random text generation */int main(void){ int i, nwords = MAXGEN; char *prefix[NPREF]; /* current input prefix */ int c; long seed; setprogname("markov"); seed = time(NULL); srand(seed); for (i = 0; i < NPREF; i++) /* set up initial prefix */ prefix[i] = NONWORD; build(prefix, stdin); add(prefix, NONWORD); generate(nwords); return 0;} const int MULTIPLIER = 31; /* for hash() *//* hash: compute hash value for array of NPREF strings */unsigned int hash(char *s[NPREF]){ unsigned int h; unsigned char *p; int i; h = 0; for (i = 0; i < NPREF; i++) for (p = (unsigned char *) s[i]; *p != '\0'; p++) h = MULTIPLIER * h + *p; return h % NHASH;}/* lookup: search for prefix; create if requested. *//* returns pointer if present or created; NULL if not. *//* creation doesn't strdup so strings mustn't change later. */State* lookup(char *prefix[NPREF], int create){ int i, h; State *sp; h = hash(prefix); for (sp = statetab[h]; sp != NULL; sp = sp->next) { for (i = 0; i < NPREF; i++) if (strcmp(prefix[i], sp->pref[i]) != 0) break; if (i == NPREF) /* found it */ return sp; } if (create) { sp = (State *) emalloc(sizeof(State)); for (i = 0; i < NPREF; i++) sp->pref[i] = prefix[i]; sp->suf = NULL; sp->next = statetab[h]; statetab[h] = sp; } return sp;}/* addsuffix: add to state. suffix must not change later */void addsuffix(State *sp, char *suffix){ Suffix *suf; suf = (Suffix *) emalloc(sizeof(Suffix)); suf->word = suffix; suf->next = sp->suf; sp->suf = suf;}/* add: add word to suffix list, update prefix */void add(char *prefix[NPREF], char *suffix){ State *sp; sp = lookup(prefix, 1); /* create if not found */ addsuffix(sp, suffix); /* move the words down the prefix */ memmove(prefix, prefix+1, (NPREF-1)*sizeof(prefix[0])); prefix[NPREF-1] = suffix;}/* build: read input, build prefix table */void build(char *prefix[NPREF], FILE *f){ char buf[100], fmt[10]; /* create a format string; %s could overflow buf */ sprintf(fmt, "%%%ds", sizeof(buf)-1); while (fscanf(f, fmt, buf) != EOF) add(prefix, estrdup(buf));}/* generate: produce output, one word per line */void generate(int nwords){ State *sp; Suffix *suf; char *prefix[NPREF], *w; int i, nmatch; for (i = 0; i < NPREF; i++) /* reset initial prefix */ prefix[i] = NONWORD; for (i = 0; i < nwords; i++) { sp = lookup(prefix, 0); if (sp == NULL) eprintf("internal error: lookup failed"); nmatch = 0; for (suf = sp->suf; suf != NULL; suf = suf->next) if (rand() % ++nmatch == 0) /* prob = 1/nmatch */ w = suf->word; if (nmatch == 0) eprintf("internal error: no suffix %d %s", i, prefix[0]); if (strcmp(w, NONWORD) == 0) break; printf("%s\n", w); memmove(prefix, prefix+1, (NPREF-1)*sizeof(prefix[0])); prefix[NPREF-1] = w; }} |
