using Implab;
using System;
using System.Collections.Generic;
using System.Linq;

namespace Implab.Automaton {
    public class DFADefinition<TInput, TState, TTag> : IDFADefinitionBuilder<TTag>, IDFADefinition<TInput, TState, TTag> {
        DFAStateDescriptior<TTag>[] m_dfaTable;
        readonly IAlphabet<TInput> m_inputAlphabet;
        readonly IAlphabet<TState> m_stateAlphabet;

        readonly Dictionary<int, TTag[]> m_finalStates = new Dictionary<int, TTag[]>();
        readonly HashSet<AutomatonTransition> m_transitions = new HashSet<AutomatonTransition>();

        public DFADefinition(IAlphabet<TInput> inputAlphabet, IAlphabet<TState> stateAlphabet) {
            Safe.ArgumentNotNull(inputAlphabet, "inputAlphabet");
            Safe.ArgumentNotNull(stateAlphabet, "stateAlphabet");

            m_inputAlphabet = inputAlphabet;
            m_stateAlphabet = stateAlphabet;
        }

        public void DefineTransition(int s1, int s2, int symbol) {
            Safe.ArgumentInRange(s1, 0, m_stateAlphabet.Count-1, "s1");
            Safe.ArgumentInRange(s2, 0, m_stateAlphabet.Count-1, "s2");
            Safe.ArgumentInRange(symbol, 0, m_inputAlphabet.Count-1, "symbol");

            m_transitions.Add(new AutomatonTransition(s1, s2, symbol));
        }


        #region IDFADefinition implementation

        public DFAStateDescriptior<TTag>[] GetTransitionTable() {
            if (m_dfaTable == null) {
                m_dfaTable = new DFAStateDescriptior<TTag>[m_stateAlphabet.Count];

                foreach (var pair in m_finalStates) {
                    var idx = pair.Key;

                    m_dfaTable[idx].final = true;
                    m_dfaTable[idx].tag = m_dfaTable[idx].tag != null ?
                        m_dfaTable[idx].tag.Concat(pair.Value).Distinct().ToArray() :
                        pair.Value;
                }

                foreach (var t in m_transitions) {
                    if (m_dfaTable[t.s1].transitions == null) {
                        m_dfaTable[t.s1].transitions = new int[m_inputAlphabet.Count];
                        for (int i = 0; i < m_dfaTable[t.s1].transitions.Length; i++)
                            m_dfaTable[t.s1].transitions[i] = DFAConst.UNREACHABLE_STATE;
                    }

                    m_dfaTable[t.s1].transitions[t.edge] = t.s2;
                }
            }
            return m_dfaTable;
        }

        public IAlphabet<TInput> InputAlphabet {
            get {
                return m_inputAlphabet;
            }
        }

        public IAlphabet<TState> StateAlphabet {
            get {
                return m_stateAlphabet;
            }
        }

        #endregion

        #region IDFADefinitionBuilder

        public void DefineTransition(int s1, int s2, int symbol) {
            Safe.ArgumentInRange(s1, 0, m_stateAlphabet.Count - 1, "s1");
            Safe.ArgumentInRange(s2, 0, m_stateAlphabet.Count - 1, "s2");
            Safe.ArgumentInRange(symbol, 0, m_inputAlphabet.Count - 1, "symbol");

            m_transitions.Add(new AutomatonTransition(s1, s2, symbol));
        }

        public void MarkFinalState(int state, params TTag[] tags) {
            m_finalStates[state] = tags;
        }


        #endregion

        protected void Optimize(IDFADefinitionBuilder<TTag> optimalDFA,IAlphabetBuilder<TInput> optimalInputAlphabet, IAlphabetBuilder<TState> optimalStateAlphabet) {
            Safe.ArgumentNotNull(optimalDFA, "dfa");
            Safe.ArgumentNotNull(optimalInputAlphabet, "optimalInputAlphabet");
            Safe.ArgumentNotNull(optimalStateAlphabet, "optimalStateAlphabet");

            var setComparer = new CustomEqualityComparer<HashSet<int>>(
                (x, y) => x.SetEquals(y),
                s => s.Sum(x => x.GetHashCode())
            );

            var arrayComparer = new CustomEqualityComparer<TTag[]>(
                (x,y) => (new HashSet<int>(x)).SetEquals(new HashSet<int>(y)),
                a => a.Sum(x => x.GetHashCode())
            );

            var optimalStates = new HashSet<HashSet<int>>(setComparer);
            var queue = new HashSet<HashSet<int>>(setComparer);

            // получаем конечные состояния, сгруппированные по маркерам
            optimalStates.UnionWith(
                m_finalStates
                .GroupBy(pair => pair.Value, arrayComparer)
                .Select(
                    g => new HashSet<int>(
                        g.Select( pair => pair.Key)
                    )
                )
            );

            var state = new HashSet<int>(
                Enumerable
                .Range(0, m_stateAlphabet.Count - 1)
                .Where(i => !m_finalStates.ContainsKey(i))
            );
            optimalStates.Add(state);
            queue.Add(state);

            var rmap = m_transitions
                .GroupBy(t => t.s2)
                .ToLookup(
                    g => g.Key, // s2
                    g => g.ToLookup(t => t.edge, t => t.s1)
                );

            while (queue.Count > 0) {
                var stateA = queue.First();
                queue.Remove(stateA);

                for (int c = 0; c < m_inputAlphabet.Count; c++) {
                    var stateX = new HashSet<int>();
                        foreach(var a in stateA)
                            stateX.UnionWith(rmap[a][c]); // all states from wich 'c' leads to 'a'

                    foreach (var stateY in optimalStates.ToArray()) {
                        if (stateX.Overlaps(stateY) && !stateY.IsSubsetOf(stateX)) {
                            var stateR1 = new HashSet<int>(stateY);
                            var stateR2 = new HashSet<int>(stateY);

                            stateR1.IntersectWith(stateX);
                            stateR2.ExceptWith(stateX);

                            optimalStates.Remove(stateY);
                            optimalStates.Add(stateR1);
                            optimalStates.Add(stateR2);

                            if (queue.Contains(stateY)) {
                                queue.Remove(stateY);
                                queue.Add(stateR1);
                                queue.Add(stateR2);
                            } else {
                                queue.Add(stateR1.Count <= stateR2.Count ? stateR1 : stateR2);
                            }
                        }
                    }
                }
            }

            // карта получения оптимального состояния по соотвествующему ему простому состоянию
            var statesMap = m_stateAlphabet.Reclassify(optimalStateAlphabet, optimalStates);

            // получаем минимальный алфавит
            // входные символы не различимы, если Move(s,a1) == Move(s,a2)
            var optimalAlphabet = m_transitions
                .GroupBy(t => Tuple.Create(statesMap[t.s1], statesMap[t.s2]), t => t.edge);
            
            var alphabetMap = m_inputAlphabet.Reclassify(optimalInputAlphabet, optimalAlphabet);

            var optimalTags = m_finalStates
                .GroupBy(pair => statesMap[pair.Key])
                .ToDictionary(
                    g => g.Key,
                    g => g.SelectMany(pair => pair.Value).ToArray()
                );

            // построение автомата
            foreach (var pair in optimalTags)
                optimalDFA.MarkFinalState(pair.Key, pair.Value);

            foreach (var t in m_transitions.Select(t => new AutomatonTransition(statesMap[t.s1],statesMap[t.s2],alphabetMap[t.edge])).Distinct())
                optimalDFA.DefineTransition(t.s1, t.s2, t.edge);
        }

        public void PrintDFA() {
            
            var inputMap = InputAlphabet.CreateReverseMap();
            var stateMap = StateAlphabet.CreateReverseMap();
            
            for (int i = 0; i < inputMap.Length; i++) {
                Console.WriteLine("C{0}: {1}", i, String.Join(",", inputMap[i]));
            }

            foreach(var t in m_transitions)
                Console.WriteLine(
                    "S{0} -{1}-> S{2}{3}",
                    stateMap[t.s1],
                    String.Join(",", inputMap[t.edge]),
                    stateMap[t.s2],
                    m_finalStates.ContainsKey(t.s2) ? "$" : ""
                );

        }
    }
}