/*
 * TdZdd: a Top-down/Breadth-first Decision Diagram Manipulation Framework
 * by Hiroaki Iwashita <iwashita@erato.ist.hokudai.ac.jp>
 * Copyright (c) 2014 ERATO MINATO Project
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 * DEALINGS IN THE SOFTWARE.
 */

#pragma once

#include <cassert>
#include <cstring>
#include <stdint.h>
#include <iostream>
#include <stdexcept>
#include <vector>

#include <tdzdd/DdSpec.hpp>

#include "Graph.hpp"

struct GraphPartitionSpecCount {
    int16_t comp; ///< uncolored edge component counter.

    GraphPartitionSpecCount()
            : comp(0) {
    }

    GraphPartitionSpecCount(int16_t uncoloredEdgeComponents)
            : comp(uncoloredEdgeComponents) {
    }

    size_t hash() const {
        return comp;
    }

    bool operator==(GraphPartitionSpecCount const& o) const {
        return comp == o.comp;
    }

    friend std::ostream& operator<<(std::ostream& os,
            GraphPartitionSpecCount const& o) {
        return os << o.comp;
    }
};

static int16_t const UNCOLORED = 32766;
static int16_t const UNCOLORED_EDGE_COMPONENT = 32767;

union GraphPartitionSpecMate {
public:
    typedef int16_t Offset;
    typedef uint16_t uOffset;

private:
    struct {
        Offset hoc; ///< offset to head or color.
        Offset nxt; ///< offset to next connected vertex.
    };
    uint32_t fps_bits;

public:
    GraphPartitionSpecMate(Offset hoc = 0)
            : hoc(hoc), nxt(0) {
    }

    bool operator==(GraphPartitionSpecMate const& o) const {
        return this == &o;
    }

    bool operator!=(GraphPartitionSpecMate const& o) const {
        return this != &o;
    }

    void clear() {
        hoc = 0;
        nxt = 0;
    }

    bool isHead() const {
        return hoc >= 0;
    }

    bool isTail() const {
        return nxt == 0;
    }

    bool isIsolated() const {
        return isHead() && isTail();
    }

    GraphPartitionSpecMate& head() {
        return isHead() ? *this : *(this + hoc);
    }

    GraphPartitionSpecMate const& head() const {
        return isHead() ? *this : *(this + hoc);
    }

    GraphPartitionSpecMate& next() {
        return *(this + nxt);
    }

    GraphPartitionSpecMate const& next() const {
        return *(this + nxt);
    }

    bool isColored() const {
        return head().hoc < UNCOLORED;
    }

    bool isUncoloredEdgeComponent() const {
        return head().hoc == UNCOLORED_EDGE_COMPONENT;
    }

    bool isColoredTail() const {
        return hoc == 0 || (hoc < 0 && hoc + (this + hoc)->hoc == 0);
    }

    bool hasSameColorAs(GraphPartitionSpecMate const& o) const {
        GraphPartitionSpecMate const* p = &head();
        GraphPartitionSpecMate const* q = &o.head();
        return p + p->hoc == q + q->hoc;
    }

    GraphPartitionSpecMate const* findColorPredecessor(
            GraphPartitionSpecMate const& o) const {
        assert(o.isColoredTail());
        GraphPartitionSpecMate const* p = &o;

        while (--p >= this) {
            GraphPartitionSpecMate const* p1 = &p->head();
            if (p1 + p1->hoc == &o) return p;
        }

        return 0;
    }

    void print() const {
        std::cerr << "(" << hoc << "," << nxt << ")";
    }

    void print(std::ostream& ost) const {
        ost << "(" << hoc << "," << nxt << ")";
    }

    void print(FILE* fp) const {
        fprintf(fp, "(%d,%d)", hoc, nxt);
    }

    void mergeLists(GraphPartitionSpecMate& o1, GraphPartitionSpecMate& o2, bool countUEC) {
        GraphPartitionSpecMate* p1 = &o1.head();
        GraphPartitionSpecMate* p2 = &o2.head();
        if (p1 == p2) return;
        if (p1 > p2) std::swap(p1, p2);

        bool painting; // merging colored and uncolored

        if (p2->hoc < UNCOLORED) {
            painting = (p1->hoc >= UNCOLORED);

            if (painting || p1 + p1->hoc < p2 + p2->hoc) {
                p1->hoc = p2->hoc + (p2 - p1); // updated if uncolored element becomes tail
            }
        }
        else {
            painting = (p1->hoc < UNCOLORED);

            if (countUEC && p1->hoc == UNCOLORED) {
                p1->hoc = UNCOLORED_EDGE_COMPONENT;
            }
        }

        for (GraphPartitionSpecMate* q = p2;; q += q->nxt) {
            q->hoc = p1 - q;
            if (q->nxt == 0) break;
        }

        GraphPartitionSpecMate* p = p1;
        GraphPartitionSpecMate* q = p2;

        while (true) {
            assert(p != q);
            GraphPartitionSpecMate* pp = p + p->nxt;
            assert(p <= pp && pp != q);

            while (p < pp && pp < q) {
                p = pp;
                pp += pp->nxt;
                assert(p <= pp && pp != q);
            }

            assert(p == pp || q < pp);
            p->nxt = q - p;
            if (p == pp) break;
            p = q, q = pp;
        }

        if (painting) {
            while (q->nxt) {
                q += q->nxt;
            }

            GraphPartitionSpecMate* pp = p1 + p1->hoc;

            if (pp < q) { // q must be an uncolored tail.
                for (p = this; p <= pp; ++p) {
                    if (p + p->hoc == pp) p->hoc = q - p;
                }
            }
        }
    }

    void replaceHeadWith(GraphPartitionSpecMate& newHead) const {
        GraphPartitionSpecMate const* p = &head();
        GraphPartitionSpecMate* q = &newHead;

        q->hoc = (p->hoc < UNCOLORED) ? p->hoc + (p - q) : p->hoc;

        while (q->nxt > 0) {
            q += q->nxt;
            q->hoc = &newHead - q;
        }
    }

    void removeFromList(GraphPartitionSpecMate const& o) {
        if (o.isColoredTail()) {
            assert(o.nxt == 0);
            GraphPartitionSpecMate const* pp = findColorPredecessor(o);
            if (pp == 0) return;

            for (GraphPartitionSpecMate* p = this; p <= pp; ++p) {
                if (p + p->hoc == &o) p->hoc = pp - p;
                if (p + p->nxt == &o) p->nxt = 0;
            }
        }
        else if (o.nxt == 0) {
            for (GraphPartitionSpecMate* p = this; p <= &o; ++p) {
                if (p + p->nxt == &o) p->nxt = 0;
            }
        }
        else {
            for (GraphPartitionSpecMate* p = this; p <= &o; ++p) {
                if (p + p->nxt == &o) p->nxt += o.nxt;
            }
        }
    }

    friend std::ostream& operator<<(std::ostream& os,
            GraphPartitionSpecMate const& o) {
        return os << "<" << o.hoc << "," << o.nxt << ">";
    }

    friend class GraphPartitionSpec;
};

class GraphPartitionSpec: public tdzdd::HybridDdSpec<GraphPartitionSpec,
        GraphPartitionSpecCount,GraphPartitionSpecMate,2> {
    typedef GraphPartitionSpecCount Count;
    typedef GraphPartitionSpecMate Mate;

    Graph const& graph;
    int const m;
    int const n;
    int const mateSize;
    int const fpsCellSize;
    int const fpsSize;
    std::vector<Mate> initialMate;
    int numCOMP;
    bool const noLoop;
    bool const lookahead;
    bool const countUEC;

    void setF(Mate::Offset v1, Mate::Offset v2, Mate* mate, int value) const {
        assert(value == 0 || value == 1);
        assert(v1 != v2);
        if (v1 > v2) {
            std::swap(v1, v2);
        }
        assert(0 <= v1 && v2 < mateSize);
        int p = - v1 * (v1 + 3) / 2 + v1 * mateSize - 1 + v2;
        if (value == 1) {
            mate[mateSize + p / fpsCellSize].fps_bits |=
                (1u << (p % fpsCellSize));
        } else {
            mate[mateSize + p / fpsCellSize].fps_bits &=
                ~(1u << (p % fpsCellSize));
        }
    }

    int getF(Mate::Offset v1, Mate::Offset v2, Mate const* mate) const {
        assert(v1 != v2);
        if (v1 > v2) {
            std::swap(v1, v2);
        }
        assert(0 <= v1 && v2 < mateSize);
        int p = - v1 * (v1 + 3) / 2 + v1 * mateSize - 1 + v2;
        return ((mate[mateSize + p / fpsCellSize].fps_bits >>
                 (p % fpsCellSize)) & 1u);
    }

    void addToFPS(Mate::Offset v1, Mate::Offset v2, Mate* mate) const {
        setF(v1, v2, mate, 1);
    }

    void changeRepFPS(Mate::Offset v1, Mate::Offset v2, Mate* mate) const {
        for (int i = 0; i < mateSize; ++i) {
            if (i == v1 || i == v2) {
                continue;
            }
            assert(getF(v2, i, mate) == 0);
            setF(v2, i, mate, getF(v1, i, mate));
        }
    }

    void mergeFPS(Mate::Offset v1, Mate::Offset v2, Mate* mate) const {
        if (v1 > v2) {
            std::swap(v1, v2);
        }
        for (int i = 0; i < mateSize; ++i) {
            if (i == v1 || i == v2) {
                continue;
            }
            if (getF(v2, i, mate) != 0) {
                setF(v1, i, mate, 1);
            }
            setF(v2, i, mate, 0);
        }
    }

    void shiftFPS(Mate::Offset d, Mate* mate) const {
        for (int i = 0; i < mateSize - 1; ++i) {
            int j;
            for (j = i + 1; j < mateSize - d; ++j) {
                setF(i, j, mate, getF(i + d, j + d, mate));
            }
            for ( ; j < mateSize; ++j) {
                setF(i, j, mate, 0);
            }
        }
    }

    bool isInFPS(Mate::Offset v1, Mate::Offset v2, Mate const* mate) const {
        return getF(v1, v2, mate) != 0;
    }

    int takable(Count& c, Mate const* mate, Graph::EdgeInfo const& e) const {
        Mate const& w1 = mate[e.v1 - e.v0];
        Mate const& w2 = mate[e.v2 - e.v0];

        // don't connect again
        if (noLoop && w1.head() == w2.head()) return false;

        // don't connect different colors
        if (w1.isColored() && w2.isColored() && !w1.hasSameColorAs(w2)) return false;

        //if (w1.head() == w2.head()) return false;

        if (w1.head() != w2.head()) { // v1 and v2 are in distinct components
            if (isInFPS(&w1.head() - mate, &w2.head() - mate, mate)) {
                return false;
            }
        }

        if (e.v1final && e.v2final) {
            if (w1.isIsolated() && w2.isIsolated()) { // new component leaves immediately
                if (w2.isColored()) {
                    // don't leave the color unconnected
                    if (!w2.isColoredTail()) return false;
                    if (mate[1].findColorPredecessor(w2)) return false;
                }
                else {
                    if (w1.isColored()) {
                        // don't leave the color unconnected
                        if (!w1.isColoredTail()) return false;
                    }
                    else {
                        if (c.comp == 0) return false;
                        if (c.comp > 0) --c.comp;
                    }
                }
            }
            else if (w1.isHead() && w2 == w1.next() && w2.isTail()) { // existing component leaves
                if (w1.isColored()) {
                    // don't leave the color unconnected
                    if (!w2.isColoredTail()) return false;
                    if (w2.findColorPredecessor(mate[1])) return false;
                }
                else {
                    assert(!countUEC || w1.isUncoloredEdgeComponent());
                    if (c.comp == 0) return false;
                    if (c.comp > 0) --c.comp;
                }
            }
        }

        if (e.finalEdge && c.comp > 0) return false;
        return true;
    }

    bool doTake(Count& count, Mate* mate, Graph::EdgeInfo const& e) const {
        Count c = count;

        if (!takable(c, mate, e)) return false;

        count = c;

        Mate const& w1 = mate[e.v1 - e.v0];
        Mate const& w2 = mate[e.v2 - e.v0];
        if (w1.head() != w2.head()) {
            mergeFPS(&w1.head() - mate, &w2.head() - mate, mate);
        }

        mate[0].mergeLists(mate[e.v1 - e.v0], mate[e.v2 - e.v0], countUEC);

        return true;
    }

    bool doNotTake(Count& count, Mate* mate, Graph::EdgeInfo const& e) const {
        Count c = count;
        Mate const& w1 = mate[e.v1 - e.v0];
        Mate const& w2 = mate[e.v2 - e.v0];

        if (w1.head() == w2.head()) {
            return false;
        }
        addToFPS(&w1.head() - mate, &w2.head() - mate, mate);

        if (e.v1final && w1.isIsolated()) {
            if (w1.isColored()) {
                // don't leave the color unconnected
                if (!w1.isColoredTail()) return false;
            }
            else if (c.comp >= 0) {
                if (!countUEC || w1.isUncoloredEdgeComponent()) {
                    if (c.comp == 0) return false;
                    --c.comp;
                }
            }
        }

        if (e.v2final && w2.isIsolated()) {
            if (w2.isColored()) {
                // don't leave the color unconnected
                if (!w2.isColoredTail()) return false;
                if (mate[1].findColorPredecessor(w2)) return false;
            }
            else if (c.comp >= 0) {
                if (!countUEC || w2.isUncoloredEdgeComponent()) {
                    if (c.comp == 0) return false;
                    --c.comp;
                }
            }
        }

        if (e.v1final && e.v2final && w1.isHead() && w2 == w1.next()
                && w2.isTail()) { // existing component leaves) {
            if (w1.isColored()) {
                // don't leave the color unconnected
                if (!w2.isColoredTail()) return false;
                if (w2.findColorPredecessor(mate[1])) return false;
            }
            else {
                assert(!countUEC || w1.isUncoloredEdgeComponent());
                if (c.comp == 0) return false;
                if (c.comp > 0) --c.comp;
            }
        }

        if (e.finalEdge && c.comp > 0) return false;
        count = c;
        return true;
    }

    void update(Mate* mate, Graph::EdgeInfo const& e,
            Graph::EdgeInfo const& ee) const {
        int const d = ee.v0 - e.v0;
        assert(d >= 0);
        Mate* p1 = &mate[e.v1 - e.v0];
        Mate* p2 = &mate[e.v2 - e.v0];
        Mate* pd = p1 + d;

        for (Mate* q = p1; q < pd; ++q) {
            Mate* qq = &q->next();
            if (qq >= pd) {
                changeRepFPS(&q->head() - mate, qq - mate, mate);
                q->replaceHeadWith(*qq);
            }
        }

        // update fps
        if (d > 0) {
            shiftFPS(d, mate);
        }

        if (e.v2final) {
            mate[0].removeFromList(*p2);
            p2->clear();
        }

        if (e.v1final) {
            mate[0].removeFromList(*p1);
            p1->clear();
        }

        if (d > 0) {
            std::memmove(p1, pd, (mateSize - d) * sizeof(*mate));
            for (int i = mateSize - d; i < mateSize; ++i) {
                p1[i] = initialMate[ee.v0 + i];
            }
        }
    }

public:
    GraphPartitionSpec(Graph const& graph, int numCOMP = -1,
                       bool noLoop = false, bool lookahead = true,
                       bool countUEC = true)
            : graph(graph), m(graph.vertexSize()), n(graph.edgeSize()),
              mateSize(graph.maxFrontierSize()),
              fpsCellSize(2 * sizeof(Mate::Offset) * 8),
              fpsSize(((mateSize - 1) * mateSize / 2 - 1)
                      / fpsCellSize + 1),
              initialMate(1 + m + mateSize),
              numCOMP(numCOMP), noLoop(noLoop), lookahead(lookahead), countUEC(countUEC) {
        this->setArraySize(mateSize + fpsSize);

        std::vector<int> rootOfColor(graph.numColor() + 1);
        for (int v = 1; v <= m; ++v) {
            rootOfColor[graph.colorNumber(v)] = v;
        }

        for (int v = 1; v <= m; ++v) {
            int k = graph.colorNumber(v);
            int hoc = (k > 0) ? rootOfColor[k] - v : UNCOLORED;
            initialMate[v] = Mate(hoc);
        }
    }

    int getRoot(Count& count, Mate* mate) const {
        int const v0 = graph.edgeInfo(0).v0;

        count = Count(numCOMP);

        for (int i = 0; i < mateSize; ++i) {
            mate[i] = initialMate[v0 + i];
        }

        // for FPS
        for (int i = 0; i < fpsSize; ++i) {
            mate[mateSize + i].fps_bits = 0;
        }

        return n;
    }

    int getChild(Count& count, Mate* mate, int level, int take) const {
        assert(1 <= level && level <= n);
        int i = n - level;
        Graph::EdgeInfo const* e = &graph.edgeInfo(i);

        if (take) {
            if (!doTake(count, mate, *e)) return 0;
        }
        else {
            if (!doNotTake(count, mate, *e)) return 0;
        }

        if (++i == n) return -1;

        Graph::EdgeInfo const* ee = &graph.edgeInfo(i);
        update(mate, *e, *ee);

        while (lookahead) {
            e = ee;

            Count c = count;
            if (takable(c, mate, *e)) break;
            if (!doNotTake(count, mate, *e)) return 0;

            if (++i == n) return -1;

            ee = &graph.edgeInfo(i);
            update(mate, *e, *ee);
        }

        assert(i < n);
        return n - i;
    }

    size_t hashCode(Count const& count) const {
        return count.hash();
    }
};
