KMP文本匹配算法
KMP（Knuth–Morris–Pratt）算法的发明时间几乎跟BM（Boyer-Moore）算法在同一时期，即上世纪70年代末（巧合的是随着
互联网的发展对文本处理提出了更高的要求，从而最近几年字符处理又成了热门话题），二者在最坏情况下的时间复杂度都是O(n)。它与BM算法的主要区别
是：
1）在每次匹配中都是从左到右匹配，BM算法每一次匹配过程都是从模式串末尾开始匹配（指针从右到左移动），直到发现匹配失败字符(mismatch)才
根据两张表（好后缀位移表-good suffix shift table和坏字符位移表-bad character shift
table）决定向右移动一定的位置，因此在实践中KMP的比较次数一般要多于BM的比较次数，因为BM算法中最好情况下的比较次数为O(n/m)。(比
较一下下面的测试输出和我的另一篇BM-Horspool文中的输出，可以看出BM算法或其简化版一开始就从字符串尾部比较的优势了)
2）KMP算法不依赖于字符集的大小，只是根据模式串的信息做预处理，BM算法需要根据字符集给坏字符（因为坏字符的来源是文本，而不是模式串）建立一张位移表，因此KMP算法的存储空间可以少一些。
以下讨论设文本T长度为n，模式串P长度为m。T的当前位置指针为i(0<=i<n)，P的当前位置指针为j(0<=j<m)。
KMP算法跟BM算法一样，用空间换取时间，基本的要求是能够最大幅度地向右移动模式串，同时又要保证不会遗漏能够成功匹配的子串。分两大步骤：1) 对模式串预处理，建立失败函数; 2)匹配过程。
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首先需要根据模式串预先计算一张表叫做失败函数(failure function) -
f(j)。f(j)的变量j对应模式串中的下标，具体含义是，在模式串的前缀P[0...j]这个字符串中，存在一个它的最长的前缀和后缀二者完全相等，
该前缀的长度就是f(j)的值。定义f(0)=0。如果不存在这样的前缀和后缀完全相等，f(j)取值为0。
例如：模式串xyzabc，如果j=3, P[j]=a，则考虑前缀xyza中是否存在这样的最长前缀和后缀完全相等，这里不存在，所以f(3)=0;
又如：模式串ABABACA，如果j=4,
P[j]=A，则考虑前缀ABABA中是否存在这样的最长前缀和后缀完全相等，这里有一个最长的前缀ABA可以跟等值的后缀重叠，该前缀长度为3，所以
f(4)=3。注意f(j)是一个长度值，j是一个索引值，在高级语言中，长度值对应后一个字符的索引值，根据这个特点，可以在KMP算法中将f(j)作
为模式串中第j+1个字符出现匹配失败(mismatch)时下一次j指针位置值。
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KMP匹配过程也是通过不停地修改i和j的值直到找到匹配的文本子串，需要考虑这几种情况：
1) j指针等于0（即指向模式串的第一个字符位置），但是T[i] != P[j]，这时需要将模式串的第一个字符与文本的下一个字符比较，即i指针加1,但是j指针仍为0。
2）j指针不等于0，前面连续的j个字符P[0...j-1]与T[i-j...i-1]都匹配成功，这时候就要用到失败函数f了。具体做法是把f[j-1]的值作为下一次的j值，但是i指针的值不变,这样保证不会遗漏能够成功匹配的子串。例如：
有趣的是计算失败函数f可以使用KMP匹配算法本身的算法过程，这是因为计算f实质上就是模式串与自身匹配的过程，只是在匹配一开始，需要将模式串向右错开一个字符位置（即i=1，j=0）。
实现：
import java.util.Arrays;
/**
*
* @author ljs
* 2011-06-20
*
*/
public class KMP {
//caculate the failure function: f[0], f[1..m-1], m is the length of pattern
private int[] calFailureF(String pattern){
int m = pattern.length();
int[] f = new int[m];
//i is the right border position
int i = 1;
int j = 0;
f[0] = 0; //by definition
while(i<m){
if(pattern.charAt(i)==pattern.charAt(j)){
//j is index from 0, f[i] is the length of suffix/prefix
//so we need to add 1
f[i] = j + 1;
i++;
j++;
}else if(j==0){
//find no valid prefix
f[i] = 0;
//move i only, j is still 0
i++;
}else{
//move j only, i doesn't change position, thus f[i]'s value is not determined yet.
//reuse the KMP algorithm: we already know f[j-1]'s value
j = f[j-1];
}
}
return f;
}
//find the first match in textL: return the first char's index if found; return -1 otherwise
public int match(String text,String pattern){
int m = pattern.length();
int n = text.length();
if(m>n)
return -1;
int[] f = this.calFailureF(pattern);
//text's index
int i = 0;
//pattern's index
int j = 0;
/****BEGIN TEST: the following code snippet can be commented out****/
System.out.format("%s%n",text);
System.out.format("%s%n",pattern);
/****END TEST: the above code snippet can be commented out****/
while(i<n){
if(text.charAt(i)==pattern.charAt(j)){
//if we find the first match, return immediately
if(j==m-1) //the border
return i-(m-1);
i++;
j++;
}else if(j==0){
i++;
/****BEGIN TEST: the following code snippet can be commented out****/
int dotsCount = i;
byte dot[] = new byte[dotsCount];
Arrays.fill(dot, (byte)'.');
System.out.format("%s%s%n",new String(dot),pattern);
/****END TEST: the above code snippet can be commented out****/
}else {
//j-1>=0
j = f[j-1];
/****BEGIN TEST: the following code snippet can be commented out****/
int dotsCount = i-j;
byte dot[] = new byte[dotsCount];
Arrays.fill(dot, (byte)'.');
System.out.format("%s%s%n",new String(dot),pattern);
/****END TEST: the above code snippet can be commented out****/
}
}
return -1;
}
public static void printFailureFunction(String pattern,int[] failureFunc){
//pattern index positions
System.out.print("i:");
for(int i=0;i<pattern.length();i++){
System.out.format(" %2s", i);
}
System.out.println();
//pattern print
System.out.print("P:");
for(int i=0;i<pattern.length();i++){
System.out.format(" %2s", pattern.charAt(i));
}
System.out.println();
//failure function output
System.out.print("f:");
for(int i=0;i<failureFunc.length;i++){
System.out.format(" %2d", failureFunc[i]);
}
System.out.println();
System.out.println();
}
public static void findMatch(KMP solver,String text,String pattern){
int index = solver.match(text, pattern);
if(index>=0){
System.out.format("Found at position %d%n",index);
}else{
System.out.format("No match%n");
}
}
public static void main(String[] args) {
KMP kmp = new KMP();
String pattern = "cbcbcb";
int[] f = kmp.calFailureF(pattern);
KMP.printFailureFunction(pattern,f);
pattern = "ababaca";
f = kmp.calFailureF(pattern);
KMP.printFailureFunction(pattern,f);
pattern = "aaaaaabb";
f = kmp.calFailureF(pattern);
KMP.printFailureFunction(pattern,f);
String text = "BABCXXXX";
pattern = "BABD";
KMP.findMatch(kmp,text,pattern);
text = "After a long text, here's a needle ZZZZZ";
pattern = "ZZZZZ";
KMP.findMatch(kmp,text,pattern);
text = "The quick brown fox jumps over the lazy dog.";
pattern = "lazy";
KMP.findMatch(kmp,text,pattern);
System.out.format("**************%n");
text = "Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna...";
pattern = "tempor";
KMP.findMatch(kmp,text,pattern);
}
}
测试输出：
i: 0 1 2 3 4 5 P: c b c b c b f: 0 0 1 2 3 4 i: 0 1 2 3 4 5 6 P: a b a b a c a f: 0 0 1 2 3 0 1 i: 0 1 2 3 4 5 6 7 P: a a a a a a b b f: 0 1 2 3 4 5 0 0 BABCXXXX BABD ..BABD ...BABD ....BABD .....BABD ......BABD .......BABD ........BABD No match After a long text, here's a needle ZZZZZ ZZZZZ .ZZZZZ ..ZZZZZ ...ZZZZZ ....ZZZZZ .....ZZZZZ ......ZZZZZ .......ZZZZZ ........ZZZZZ .........ZZZZZ ..........ZZZZZ ...........ZZZZZ ............ZZZZZ .............ZZZZZ ..............ZZZZZ ...............ZZZZZ ................ZZZZZ .................ZZZZZ ..................ZZZZZ ...................ZZZZZ ....................ZZZZZ .....................ZZZZZ ......................ZZZZZ .......................ZZZZZ ........................ZZZZZ .........................ZZZZZ ..........................ZZZZZ ...........................ZZZZZ ............................ZZZZZ .............................ZZZZZ ..............................ZZZZZ ...............................ZZZZZ ................................ZZZZZ .................................ZZZZZ ..................................ZZZZZ ...................................ZZZZZ Found at position 35 The quick brown fox jumps over the lazy dog. lazy .lazy ..lazy ...lazy ....lazy .....lazy ......lazy .......lazy ........lazy .........lazy ..........lazy ...........lazy ............lazy .............lazy ..............lazy ...............lazy ................lazy .................lazy ..................lazy ...................lazy ....................lazy .....................lazy ......................lazy .......................lazy ........................lazy .........................lazy ..........................lazy ...........................lazy ............................lazy .............................lazy ..............................lazy ...............................lazy ................................lazy .................................lazy ..................................lazy ...................................lazy Found at position 35 ************** Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna... tempor .tempor ..tempor ...tempor ....tempor .....tempor ......tempor .......tempor ........tempor .........tempor ..........tempor ...........tempor ............tempor .............tempor ..............tempor ...............tempor ................tempor .................tempor ..................tempor ...................tempor ....................tempor .....................tempor ......................tempor .......................tempor ........................tempor .........................tempor ..........................tempor ...........................tempor ............................tempor .............................tempor ..............................tempor ...............................tempor ................................tempor .................................tempor ..................................tempor ....................................tempor .....................................tempor ......................................tempor .......................................tempor ........................................tempor .........................................tempor ..........................................tempor ...........................................tempor ............................................tempor .............................................tempor ..............................................tempor ...............................................tempor ................................................tempor .................................................tempor ..................................................tempor ...................................................tempor ....................................................tempor .....................................................tempor ......................................................tempor .......................................................tempor ........................................................tempor .........................................................tempor ..........................................................tempor ...........................................................tempor ............................................................tempor .............................................................tempor ..............................................................tempor ...............................................................tempor ................................................................tempor .................................................................tempor ..................................................................tempor ...................................................................tempor ....................................................................tempor .....................................................................tempor ......................................................................tempor .......................................................................tempor ........................................................................tempor .........................................................................tempor Found at position 73
KMP算法
作者：ljs
2011-06-20
(转载请注明出处，谢谢！)
