Merge pull request #42 from cp-sapienza/string_periods

String periods

Author: podd0

content/strings.tex

@@ -24,10 +24,17 @@ \subsection{Z Function}
 \begin{flushleft}
 $z[i] = $ length of the longest substring starting at i that is a prefix of s \\
 $z[i] = $ max len s.t. $s[0..len-1] == s[i..i+len-1]$, $z[0] = 0$
-
 \end{flushleft}
 \snippet{source/z_func.h}
 
+\subsection{Periods}
+\bigo{N}
+
+$k \leq N$ is a period of a string $s$ iff $\forall i, s[i] = s[i\%k]$. \\
+Note this means that 2 is a valid period of "aba" 
+(uncomment the line if this is not wanted)
+\snippet{source/periods.h}
+
 \subsection{KMP}
 \bigo{N} construction, \bigo{N+M} search with \bigo{|pat|} space.
 

source/periods.h

@@ -0,0 +1,15 @@
+#pragma once
+#include "common.h"
+#include "z_func.h"
+
+vi periods(string s) {
+	vi z = z_function(s), p;
+	int n = ssize(z);
+	for(int i = 1; i < n; i++) {
+		// if(n%i == 0) // uncomment for no trailing subperiods
+		if(z[i]+i == n)
+			p.push_back(i);
+	}
+	p.push_back(n);
+	return p;
+}