adding string chapter

4 files changed, 100 insertions, 0 deletions

diff --git a/string/LCSubstring.cpp b/string/LCSubstring.cpp
new file mode 100644
index 0000000..69d636f
--- /dev/null
+++ b/string/LCSubstring.cpp
@@ -0,0 +1,26 @@
+//longest common substring.
+struct lcse {
+	int i = 0, s = 0;
+};
+string lcp(string s[2]) {
+	if(s[0].length() == 0 || s[1].length() == 0) return "";
+	vector<lcse> a(s[0].length()+s[1].length());
+	for(int k = 0; k < a.size(); k++) a[k].i=(k < s[0].length() ? k : k - s[0].length()), a[k].s = (k < s[0].length() ? 0 : 1);
+	sort(a.begin(), a.end(), [&] (const lcse &u, const lcse &l) {
+		int ui = u.i, li = l.i;
+		while(ui < s[u.s].length() && li < s[l.s].length()) {
+			if(s[u.s][ui] < s[l.s][li]) return true;
+			else if(s[u.s][ui] > s[l.s][li]) return false;
+			ui++; li++;
+		}
+		return !(ui < s[u.s].length());
+	});
+	int r = 0, m=0, c=0;
+	for(int i = 0; i < a.size() - 1; i++) { 
+		if(a[i].s == a[i+1].s) continue;
+		c = 0;
+		while(a[i].i+c < s[a[i].s].length() && a[i+1].i+c < s[a[i+1].s].length() && s[a[i].s][a[i].i+c] == s[a[i+1].s][a[i+1].i+c]) c++;
+		if(c > m) r=i, m=c;
+	}
+	return m == 0 ? "" : s[a[r].s].substr(a[r].i, m);
+}
diff --git a/string/string.tex b/string/string.tex
new file mode 100644
index 0000000..1335c4a
--- /dev/null
+++ b/string/string.tex
@@ -0,0 +1,13 @@
+\section{Strings}
+
+\subsection{\textsc{Knuth-Morris-Pratt}-Algorithmus}
+\lstinputlisting{string/kmp.cpp}
+
+\subsection{Trie}
+\lstinputlisting{string/trie.cpp}
+
+\subsection{Suffix-Array}
+\lstinputlisting{string/suffixArray.cpp}
+
+\subsection{Longest Common Substring}
+\lstinputlisting{string/LCSubstring.cpp}
diff --git a/string/suffixArray.cpp b/string/suffixArray.cpp
new file mode 100644
index 0000000..2b2a87b
--- /dev/null
+++ b/string/suffixArray.cpp
@@ -0,0 +1,36 @@
+//longest common substring in one string (overlapping not excluded)
+//contains suffix array:--------------------------------------------------------------------
+int cmp(string &s,vector<vector<int>> &v, vector<int> &a, int i, int vi, int u, int l) {
+	int vi2 = (vi + 1) % 2, u2 = u + i / 2, l2 = l + i / 2; 
+	if(i == 1) return s[u] - s[l];
+	else if (v[vi2][u] != v[vi2][l]) return (v[vi2][u] - v[vi2][l]);
+	else { //beide groesser tifft nicht mehr ein, da ansonsten vorher schon unterschied in Laenge
+		if(u2 >= s.length()) return -1;
+		else if(l2 >= s.length()) return 1;
+		else return v[vi2][u2] - v[vi2][l2];
+	}
+}
+
+string lcsub(string s) {
+	if(s.length() == 0) return "";
+	vector<int> a(s.length());
+	vector<vector<int>> v(2, vector<int>(s.length(), 0));
+	int vi = 0;
+	for(int k = 0; k < a.size(); k++) a[k] = k;	
+	for(int i = 1; i < s.length(); i *= 2, vi = (vi + 1) % 2) {
+		sort(a.begin(), a.end(), [&] (const int &u, const int &l) {
+			return cmp(s, v, a, i, vi, u, l) < 0;
+		});
+		v[vi][a[0]] = 0;
+		for(int z = 1; z < a.size(); z++) v[vi][a[z]] = v[vi][a[z-1]] + (cmp(s, v, a, i, vi, a[z], a[z-1]) == 0 ? 0 : 1);
+	}
+//-------------------------------------------------------------------------------------------
+	int r = 0, m=0, c=0;
+	for(int i = 0; i < a.size() - 1; i++) {
+		c = 0;
+		while(a[i]+c < s.length() && a[i+1]+c < s.length() && s[a[i]+c] == s[a[i+1]+c]) c++;
+		if(c > m) r=i, m=c;
+	}
+	return m == 0 ? "" : s.substr(a[r], m);
+}
+
diff --git a/string/trie.cpp b/string/trie.cpp
new file mode 100644
index 0000000..f4b979c
--- /dev/null
+++ b/string/trie.cpp
@@ -0,0 +1,25 @@
+//nur fuer kleinbuchstaben!
+struct node {
+	node *(e)[26];
+	int c = 0;//anzahl der woerter die an dem node enden.
+	node() { for(int i = 0; i < 26; i++) e[i] = NULL; }	
+};
+
+void insert(node *root, string *txt, int s) {
+	if(s >= txt->length()) root->c++;
+	else {
+		int idx = (int)((*txt).at(s) - 'a');
+		if(root->e[idx] == NULL) {
+			root->e[idx] = new node();
+		}
+		insert(root->e[idx], txt, s+1);
+	}
+}
+
+int contains(node *root, string *txt, int s) {
+	if(s >= txt->length()) return root->c;
+	int idx = (int)((*txt).at(s) - 'a');
+	if(root->e[idx] != NULL) {
+			return contains(root->e[idx], txt, s+1);
+	} else return 0;
+}