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

namespace Implab.Automaton {
    public class DFATable : IDFATableBuilder {
        DFAStateDescriptior[] m_dfaTable;

        int m_stateCount;
        int m_symbolCount;
        int m_initialState;

        readonly HashSet<int> m_finalStates = new HashSet<int>();
        readonly HashSet<AutomatonTransition> m_transitions = new HashSet<AutomatonTransition>();

        void AssertNotReadOnly() {
            if (m_dfaTable != null)
                throw new InvalidOperationException("The object is readonly");
        }


        #region IDFADefinition implementation

        public DFAStateDescriptior[] GetTransitionTable() {
            if (m_dfaTable == null) {
                if (m_stateCount <= 0)
                    throw new InvalidOperationException("Invalid automaton definition: states count = {0}", m_stateCount);
                if (m_symbolCount <= 0)
                    throw new InvalidOperationException("Invalid automaton definition: symbols count = {0}", m_symbolCount);

                m_dfaTable = ConstructTransitionTable();
            }
            return m_dfaTable;
        }

        public bool IsFinalState(int s) {
            Safe.ArgumentInRange(s, 0, m_stateCount, "s");

            return m_dfaTable != null ? m_dfaTable[s].final :  m_finalStates.Contains(s);
        }

        public IEnumerable<int> FinalStates {
            get {
                return m_finalStates;
            }
        }

        public int StateCount {
            get { return m_stateCount; }
        }

        public int AlphabetSize {
            get { return m_symbolCount; }
        }

        public int InitialState {
            get { return m_initialState; }
        }

        #endregion

        protected virtual DFAStateDescriptior[] ConstructTransitionTable() {
            var dfaTable = new DFAStateDescriptior[m_stateCount];


            foreach (var t in m_transitions) {
                if (dfaTable[t.s1].transitions == null)
                    dfaTable[t.s1] = new DFAStateDescriptior(m_symbolCount, m_finalStates.Contains(t.s1));
                
                dfaTable[t.s1].transitions[t.edge] = t.s2;
            }

            foreach (var s in m_finalStates)
                if (!dfaTable[s].final) 
                    m_dfaTable[s] = new DFAStateDescriptior(m_symbolCount, true);
                
        }

        public void SetInitialState(int s) {
            Safe.ArgumentAssert(s >= 0, "s");
            m_initialState = s;
        }

        public void MarkFinalState(int state) {
            AssertNotReadOnly();
            m_finalStates.Add(state);
        }

        public void Add(AutomatonTransition item) {
            AssertNotReadOnly();
            Safe.ArgumentAssert(item.s1 >= 0, "item");
            Safe.ArgumentAssert(item.s2 >= 0, "item");
            Safe.ArgumentAssert(item.edge >= 0, "item");

            m_stateCount = Math.Max(m_stateCount, Math.Max(item.s1, item.s2) + 1);
            m_symbolCount = Math.Max(m_symbolCount, item.edge);

            m_transitions.Add(item);
        }

        public void Clear() {
            AssertNotReadOnly();

            m_stateCount = 0;
            m_symbolCount = 0;
            m_finalStates.Clear();
            m_transitions.Clear();
        }

        public bool Contains(AutomatonTransition item) {
            return m_transitions.Contains(item);
        }

        public void CopyTo(AutomatonTransition[] array, int arrayIndex) {
            m_transitions.CopyTo(array, arrayIndex);
        }

        public bool Remove(AutomatonTransition item) {
            AssertNotReadOnly();
            m_transitions.Remove(item);
        }

        public int Count {
            get {
                return m_transitions.Count;
            }
        }

        public bool IsReadOnly {
            get {
                return m_dfaTable != null;
            }
        }

        public IEnumerator<AutomatonTransition> GetEnumerator() {
            return m_transitions.GetEnumerator();
        }

        System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() {
            return GetEnumerator();
        }

        /// <summary>Формирует множества конечных состояний перед началом работы алгоритма минимизации.</summary>
        /// <remarks>
        /// В процессе построения минимального автомата требуется разделить множество состояний,
        /// на два подмножества - конечные состояния и все остальные, после чего эти подмножества
        /// будут резделены на более мелкие. Иногда требуется гарантировать различия конечных сосотяний,
        /// для этого необходимо переопределить даннцю фукнцию, для получения множеств конечных состояний.
        /// </remarks>
        /// <returns>The final states.</returns>
        protected virtual IEnumerable<HashSet<int>> GroupFinalStates() {
            return new HashSet<int>[] { m_finalStates };
        }

        protected void Optimize<TInput, TState>(
            IDFATableBuilder optimalDFA,
            IAlphabet<TInput> inputAlphabet,
            IAlphabetBuilder<TInput> optimalInputAlphabet,
            IAlphabet<TState> stateAlphabet,
            IAlphabetBuilder<TState> optimalStateAlphabet
        ) {
            Safe.ArgumentNotNull(optimalDFA, "dfa");
            Safe.ArgumentNotNull(optimalInputAlphabet, "optimalInputAlphabet");
            Safe.ArgumentNotNull(optimalStateAlphabet, "optimalStateAlphabet");
            Safe.ArgumentNotNull(inputAlphabet, "inputAlphabet");
            Safe.ArgumentNotNull(stateAlphabet, "stateAlphabet");

            if (inputAlphabet.Count != m_symbolCount)
                throw new InvalidOperationException("The input symbols aphabet mismatch");
            if (stateAlphabet.Count != m_stateCount)
                throw new InvalidOperationException("The states alphabet mismatch");

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

            var state = new HashSet<int>(
                Enumerable
                .Range(0, m_stateCount - 1)
                .Where(i => !m_finalStates.Contains(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_symbolCount; 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 = 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 = inputAlphabet.Reclassify(optimalInputAlphabet, optimalAlphabet);

            // построение автомата
            optimalDFA.SetInitialState(statesMap[m_initialState]);

            foreach (var sf in m_finalStates.GroupBy(s => statesMap[s]))
                optimalDFA.MarkFinalState(sf.Key);

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

        }

        protected void PrintDFA<TInput, TState>(IAlphabet<TInput> inputAlphabet, IAlphabet<TState> stateAlphabet) {
            Safe.ArgumentNotNull(inputAlphabet, "inputAlphabet");
            Safe.ArgumentNotNull(stateAlphabet, "stateAlphabet");

            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(
                    "[{0}] -{{{1}}}-> [{2}]{3}",
                    stateMap[t.s1],
                    String.Join(",", inputMap[t.edge]),
                    stateMap[t.s2],
                    m_finalStates.Contains(t.s2) ? "$" : ""
                );

        }

    }
}