KMP Algorithm Summary

The KMP algorithm is a basic string matching algorithm, but some of the details of the code implementation are error-prone. This essay will be carefully summed up.

The core of the KMP algorithm is:

The KMP algorithm searches for occurrences of a "word" W within a main "text string" S By employing the observation if a mismatch occurs, the word itself embodies sufficient information to dete Rmine where the next match could begin, thus bypassing re-examination of previously matched characters. (Form Wikipedia)

First define a concept

Given the string s[0..l-1], if there is a regular prefix of s (proper prefix) s[0..i] (I<L-1) is also the suffix of s, then the prefix is called the key (critical prefix).

Obviously an empty string is a key prefix for any non-empty string.

For pattern string W, preprocess An array of length |w| next[0..| W|-1],nt[i] The length of the longest key prefix of w[0..i] that represents the prefix of W.

With next[] arrays, you can use the O (|s|) Complete the search within the time.

Specific implementation and complexity analysis skipped, leaving K. M. P. Links to three-person papers

Knuth, Donald; Morris, James H.; Pratt, Vaughan (1977). "Fast pattern matching in strings". SIAM Journal on Computing 6 (2): 323–350.doi:10.1137/0206024.

------------------------------------------------------------

Title Link: Hihocoder 1015

#include <bits/stdc++.h>using namespacestd;Const intN (1e4+5), M (1e6+5);CharS[n], t[m];intNt[n];intMain () {intN; scanf ("%d", &N);  for(intLS, K, ans;n--;) {scanf ("%s%s", S, t); K=nt[0]=0;  for(inti=ls=1; S[i]; i++, ls++){             for(; k&&s[k]!=s[i];) k=Nt[k]; Nt[i]=s[i]==s[k]?++k:k; } ans=k=0;  for(intI=0; S[n]; i++){            //K:t[0..i-1] The matching length             for(; K&&s[k]!=t[i];) k=nt[k-1];//Error-prone            if(t[i]==S[k]) {k++; if(K==ls) ans++; }} printf ("%d\n", ans); }}

Two of the comments in the code are easy to write wrong, and the typical error is

 for (; k&&s[k]!=s[i];) k=nt[k];

For

This error pit in: Often can be over the sample, after submission will not WA but will tle.

----------------------

Next[i] can also be defined as the length of the longest key prefix of the prefix w[0..i] minus one, at which point the meaning of next[i] can be changed to the end of the longest critical prefix of the prefix w[0..i].

The code has to be changed slightly.

#include <bits/stdc++.h>using namespacestd;Const intmax_n=1e6+Ten;CharS[max_n], t[max_n];intNt[max_n];voidGet_next (Char*s) {nt[0]=-1; intk=-1;  for(intI=1; S[i]; i++){         while(k!=-1&&s[k+1]!=s[i]) k=Nt[k]; if(s[k+1]==s[i]) k++; Nt[i]=K; }}intans;voidMatchChar*s,Char*t) {    intLs=strlen (s), k=-1;  for(intI=0; S[n]; i++){         while(k!=-1&&s[k+1]!=t[i]) k=Nt[k]; if(s[k+1]==t[i]) k++; if(k==ls-1) ans++; }}intMain () {intN; scanf ("%d", &N);  while(n--) {scanf ("%s%s", S, t);        Get_next (s); Ans=0;        Match (S, T); printf ("%d\n", ans); }    return 0;}

KMP Algorithm Summary