1. 問題描述
馬爾可夫鏈算法用于生成一段隨機的英文，其思想非常簡單。首先讀入數據，然后將讀入的數據分成前綴和后綴兩部分，通過前綴來隨機獲取后綴，籍此產生一段可讀的隨機英文。
為了說明方便，假設我們有如下一段話：
復制代碼 代碼如下:
Show your flowcharts and conceal your tables and I will be mystified. Show your tables and your flowcharts will be obvious.
假設前綴的長度為2,則我們處理輸入以后得到如下數據，我們首先獲取一個前綴，然后在前綴的后綴列表中隨機選擇一個單詞，然后改變前綴，重復上述過程，這樣，我們產生的句子將是可讀的。
下面是處理過的數據：
復制代碼 代碼如下:
前綴 后綴
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)
處理這個文本的馬爾可夫鏈算法將首先帶引show your,然后隨機取出flowcharts 或者table 兩個單詞，假設選擇的是flowcharts, 則新的前綴就是your flowcharts,同理，選擇table 時，新的前綴就是your table,有了新的前綴your flowcharts 以后，再次隨即選擇它的后綴，這次是在and 和 will 中隨機選擇，重復上述過程，就能夠產生一段可讀的文本。具體描述如下：
復制代碼 代碼如下:
設置 w1 和 w2 為文本的前兩個詞
輸出 w1 和 w2
循環：
隨機地選出 w3,它是文本中 w1 w2 的后綴中的一個
打印 w3
把 w1 和 w2 分別換成 w2 和 w3
重復循環
2.awk 程序
馬爾可夫鏈算法并不難，我們會在后面看到，用c語言來解決這個問題會相當麻煩，而用awk則只需要5分鐘就能搞定。這簡直就是一個演示awk優點的問題。
awk 中有關聯數組，正好可以用來表示前綴和后綴的關系。程序如下：
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# 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
該問題的主要難點就在于通過前綴隨機的獲取后綴，在C++ 中，我們可以借助map 來實現前綴和后綴的對應關系，以此得到較高的開發效率。
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/* 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
如果需要程序運行得足夠快，那就只能用較低級的語言來實現了。當我們用c 語言來實現時，就不得不考慮各種各樣的問題了。首先，面臨的第一個問題就是，如何表示前綴和后綴的關系?
這里采用前綴的key,后綴為value 的方式存儲前綴與后綴的關系，我們知道，hash表的查找速度最快，所以，這里采用hash表也是情理之中的事，只是看你能不能想到，用前綴作key,基于上面的思路，再仔細一點，就沒有什么大問題了。
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/* 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; }} |
