Z Algorithm Algorithm
In statistics, an expectation – maximization (EM) algorithm is an iterative method to find (local) maximal likelihood or maximum a posteriori (map) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (e) step, which makes a function for the expectation of the log-likelihood evaluated use the current estimate for the parameters, and a maximization (M) step, which calculates parameters maximizing the expected log-likelihood found on the e step. The Dempster – Laird – Rubin paper in 1977 generalized the method and sketched a convergence analysis for a wider class of problems. Wu's proof established the EM method's convergence outside of the exponential family, as claimed by Dempster – Laird – Rubin. The Dempster – Laird –
/*
Petar 'PetarV' Velickovic
Algorithm: Z Algorithm
*/
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <iostream>
#include <vector>
#include <list>
#include <string>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <complex>
#define MAX_N 1000001
using namespace std;
typedef long long lld;
int n, m;
string needle, haystack;
int Z[MAX_N];
vector<int> matches;
//Z Algoritam koji racuna Z-funkciju nad datim stringom; moze se koristiti za efikasan string matching
//Slozenost: O(N + M)
inline void Z_Algorithm(string s)
{
int len = s.length();
int L = 0, R = 0;
for (int i=1;i<len;i++)
{
if (i > R)
{
L = R = i;
while (R < len && s[R-L] == s[R]) R++;
Z[i] = R-L;
R--;
}
else
{
int k = i - L;
if (Z[k] < R-i+1) Z[i] = Z[k];
else
{
L = i;
while (R < len && s[R-L] == s[R]) R++;
Z[i] = R - L;
R--;
}
}
if (Z[i] == m) matches.push_back(i - m - 1);
}
}
int main()
{
n = 6, m = 2;
haystack = "abcabc";
needle = "bc";
Z_Algorithm(needle + "#" + haystack);
for (int i=0;i<matches.size();i++) printf("%d ",matches[i]);
printf("\n");
return 0;
}
