Lyndon factorization

Resources:

CP_Algorithms 

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wikipedia 

Problem link: 719 - Glass Beads 

Solution:

	#include <bits/stdc++.h>
	using namespace std;
	#define INF 1<<30
	#define endl '\n'
	#define maxn 100005
	#define tc printf("Case %d: ", cs)
	#define tcn printf("Case %d:\n", cs);
	#define FASTIO ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	typedef long long ll;
	const double PI = acos(-1.0);
	#define dbg1(x) cerr << #x << " = " << x << endl;
	#define dbg2(x, y) cerr << #x << " = " << x << ", " << #y << " = " << y << endl;
	#define dbg3(x, y, z) cerr << #x << " = " << x << ", " << #y << " = " << y << ", " << #z << " = " << z << endl;
	#define dbg4(w,x, y, z) cerr << #w << " = " << w << ", " <<#x << " = " << x << ", " << #y << " = " << y << ", " << #z << " = " << z << endl;
	template < typename F, typename S >
	ostream& operator << ( ostream& os, const pair< F, S > & p ) {
	return os << "(" << p.first << ", " << p.second << ")";
	}
	template < typename T >
	ostream &operator << ( ostream & os, const vector< T > &v ) {
	os << "{";
	for (auto it = v.begin(); it != v.end(); ++it) {
	if ( it != v.begin() ) os << ", ";
	os << *it;
	}
	return os << "}";
	}
	template < typename T >
	ostream &operator << ( ostream & os, const set< T > &v ) {
	os << "[";
	for (auto it = v.begin(); it != v.end(); ++it) {
	if ( it != v.begin()) os << ", ";
	os << *it;
	}
	return os << "]";
	}
	template < typename F, typename S >
	ostream &operator << ( ostream & os, const map< F, S > &v ) {
	os << "[";
	for (auto it = v.begin(); it != v.end(); ++it) {
	if ( it != v.begin() ) os << ", ";
	os << it -> first << " = " << it -> second ;
	}
	return os << "]";
	}
	#define dbg(args...) do {cerr << #args << " : "; faltu(args); } while(0)
	clock_t tStart = clock();
	#define timeStamp dbg("Execution Time: ", (double)(clock() - tStart)/CLOCKS_PER_SEC)
	void faltu () { cerr << endl; }
	template <typename T>
	void faltu( T a[], int n ) {
	for (int i = 0; i < n; ++i) cerr << a[i] << ' ';
	cerr << endl;
	}
	template <typename T, typename ... hello>
	void faltu( T arg, const hello &... rest) { cerr << arg << ' '; faltu(rest...); }
	// Program showing a policy-based data structure.
	#include <ext/pb_ds/assoc_container.hpp> // Common file
	#include <ext/pb_ds/tree_policy.hpp>
	#include <functional> // for less
	#include <iostream>
	using namespace __gnu_pbds;
	using namespace std;
	// GNU link : https://goo.gl/WVDL6g
	typedef tree<int, null_type, less_equal<int>, rb_tree_tag,
	tree_order_statistics_node_update>
	new_data_set;
	/**___________________________________________________**/
	//Here we present the implementation of the Duval algorithm,
	//which will return the desired Lyndon factorization of a given string s.
	vector<string> duval(string const& s)
	{
	int n = s.size();
	int i = 0;
	vector<string> factorization;
	while (i < n) {
	int j = i + 1, k = i;
	while (j < n && s[k] <= s[j]) {
	if (s[k] < s[j]) k = i;
	else k++;
	j++;
	}
	while (i <= k) {
	factorization.push_back(s.substr(i, j - k));
	i += j - k;
	}
	}
	return factorization;
	}
	int min_cyclic_string(string s)
	{
	s += s;
	int n = s.size();
	int i = 0, ans = 0;
	while (i < n / 2) {
	ans = i;
	int j = i + 1, k = i;
	while (j < n && s[k] <= s[j]) {
	if (s[k] < s[j]) k = i;
	else k++;
	j++;
	}
	while (i <= k) {
	i += j - k;
	}
	}
	return ans + 1;
	//dbg(ans);
	//return s.substr(ans, n / 2);
	}
	int main()
	{
	FASTIO
	///*
	#ifndef ONLINE_JUDGE
	freopen("in.txt", "r", stdin);
	freopen("out.txt", "w", stdout);
	freopen("error.txt", "w", stderr);
	#endif
	//*/
	int t;
	cin >> t;
	while (t--) {
	string s;
	cin >> s;
	// auto ans = duval(s);
	//dbg(ans);
	auto res = min_cyclic_string(s);
	// dbg(res);
	cout << res << endl;
	}
	}

view raw lyndon.cpp hosted with ❤ by GitHub

 

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