Submission #1511580

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Source Code Expand

#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=a;i<b;i++)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#pragma GCC optimize ("-O3")
using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); }
//---------------------------------------------------------------------------------------------------

 
#ifdef _MSC_VER
#pragma push_macro("long")
#undef long
#ifdef _WIN32
inline unsigned int __builtin_ctz(unsigned int x) { unsigned long r; _BitScanForward(&r, x); return r; }
inline unsigned int __builtin_clz(unsigned int x) { unsigned long r; _BitScanReverse(&r, x); return 31 - r; }
inline unsigned int __builtin_ffs(unsigned int x) { unsigned long r; return _BitScanForward(&r, x) ? r + 1 : 0; }
inline unsigned int __builtin_popcount(unsigned int x) { return __popcnt(x); }
#ifdef _WIN64
inline unsigned long long __builtin_ctzll(unsigned long long x) { unsigned long r; _BitScanForward64(&r, x); return r; }
inline unsigned long long __builtin_clzll(unsigned long long x) { unsigned long r; _BitScanReverse64(&r, x); return 63 - r; }
inline unsigned long long __builtin_ffsll(unsigned long long x) { unsigned long r; return _BitScanForward64(&r, x) ? r + 1 : 0; }
inline unsigned long long __builtin_popcountll(unsigned long long x) { return __popcnt64(x); }
#else
inline unsigned int hidword(unsigned long long x) { return static_cast<unsigned int>(x >> 32); }
inline unsigned int lodword(unsigned long long x) { return static_cast<unsigned int>(x & 0xFFFFFFFF); }
inline unsigned long long __builtin_ctzll(unsigned long long x) { return lodword(x) ? __builtin_ctz(lodword(x)) : __builtin_ctz(hidword(x)) + 32; }
inline unsigned long long __builtin_clzll(unsigned long long x) { return hidword(x) ? __builtin_clz(hidword(x)) : __builtin_clz(lodword(x)) + 32; }
inline unsigned long long __builtin_ffsll(unsigned long long x) { return lodword(x) ? __builtin_ffs(lodword(x)) : hidword(x) ? __builtin_ffs(hidword(x)) + 32 : 0; }
inline unsigned long long __builtin_popcountll(unsigned long long x) { return __builtin_popcount(lodword(x)) + __builtin_popcount(hidword(x)); }
#endif // _WIN64
#endif // _WIN32
#pragma pop_macro("long")
#endif // _MSC_VER


struct BitSet {
    enum { K = 2, W = 64 };
    uint64_t data[K];

    BitSet() : data{ 0 } {}

    explicit operator bool() const {
        uint64_t r = 0;
        rep(i, 0, K)
            r |= data[i];
        return r != 0;
    }

    bool get(unsigned pos) const {
        return data[pos / W] >> (pos % W) & 1;
    }

    void set(unsigned pos) {
        data[pos / W] |= uint64_t(1) << (pos % W);
    }

    void unset(unsigned pos) {
        data[pos / W] &= ~(uint64_t(1) << (pos % W));
    }

    int count() const {
        int res = 0;
        rep(i, 0, K) res += popcount(data[i]);
        return res;
    }

    BitSet operator&(BitSet that) const {
        BitSet res;
        rep(i, 0, K)
            res.data[i] = data[i] & that.data[i];
        return res;
    }

    bool isIntersectTo(const BitSet &that) const {
        return bool(*this & that);
    }

    int getSingleton() const {
        rep(i, 0, K) if (data[i]) {
            if ((data[i] & (data[i] - 1)) != 0)
                return -1;
            for (int j = i + 1; j < K; ++j)
                if (data[j])
                    return -1;
            return i * W + bsf(data[i]);
        }
        return -1;
    }

    static int bsf(uint64_t x) {
        return __builtin_ctzll(x);
    }

    static int popcount(uint64_t x) {
        return __builtin_popcountll(x);
    }

    std::string toBitString() const {
        std::string res(128, '0');
        for (int i = 0; i < 128; ++i)
            res[i] = '0' + get(i);
        return res;
    }
};

class MaximumCliqueBranchAndBound {
public:
    typedef uint8_t Vertex;

    BitSet maximumClique(const vector<BitSet> &originalGraph) {
        graph = originalGraph;
        int N = (int)graph.size();
        levels.assign(N, BitSet());
        vertexLevel.assign(N, -1);
        vertexDegree.assign(N, -1);
        BitSet initSet;
        for (int i = 0; i < N; ++i)
            initSet.set(i);
        globalBuffer.resize(N * N * 2 + N + N * 3 * N);
        levelVertices.resize(N);
        rep(i, 0, N)
            levelVertices[i].first = globalBuffer.data() + i * N;
        degreeVertices.resize(N);
        rep(i, 0, N)
            degreeVertices[i].first = globalBuffer.data() + (N + i) * N;
        Vertex *initOrder = globalBuffer.data() + N * N * 2,
            *nextBuffer = initOrder + N;
        rep(i, 0, N)
            initOrder[i] = i;

        curClique = maxClique = BitSet();
        curSize = maxSize = 0;
        numRecs = 0;

        rec(initSet, initOrder, N, nextBuffer);

        //cerr << "numRecs = " << numRecs << endl;
        return maxClique;
    }

private:

    void rec(BitSet remSet, const Vertex *originalOrder, int originalOrderSize, Vertex *buffer) {
        ++numRecs;

        int numLevels = 0, numVertices = 0;
        for (int ix = 0; ix < originalOrderSize; ++ix) {
            int p = originalOrder[ix];
            if (!remSet.get(p)) continue;
            ++numVertices;
            int k = 0;
            while (k < numLevels && levels[k].isIntersectTo(graph[p]))
                ++k;
            if (k == numLevels) {
                levels[k] = BitSet();
                ++numLevels;
            }
            levels[k].set(p);
            vertexLevel[p] = k;
            vertexDegree[p] = (remSet & graph[p]).count();

            int threshold = maxSize - curSize;
            if (k > threshold && k == numLevels - 1) {
                reNumber(p, k, threshold);
                if (!levels[k])
                    --numLevels;
            }
        }

        Vertex *levelOrder = buffer,
            *levelOffsets = levelOrder + numVertices,
            *degreeOrder = levelOffsets + numLevels,
            *nextBuffer = degreeOrder + numVertices;
        for (int k = 0; k < numLevels; ++k)
            levelVertices[k].second = 0;
        for (int d = 0; d < numVertices; ++d)
            degreeVertices[d].second = 0;

        for (int ix = 0; ix < originalOrderSize; ++ix) {
            int v = originalOrder[ix];
            if (remSet.get(v)) {
                {
                    auto &p = levelVertices[vertexLevel[v]];
                    p.first[p.second++] = v;
                }
                {
                    auto &p = degreeVertices[vertexDegree[v]];
                    p.first[p.second++] = v;
                }
            }
        }
        for (int k = 0, num = 0; k < numLevels; ++k) {
            levelOffsets[k] = num;
            auto p = levelVertices[k];
            for (int i = 0; i < p.second; ++i)
                levelOrder[num++] = p.first[i];
        }
        for (int d = numVertices - 1, num = 0; d >= 0; --d) {
            auto p = degreeVertices[d];
            for (int i = 0; i < p.second; ++i)
                degreeOrder[num++] = p.first[i];
        }

        for (int i = numVertices; ; --i) {
            int threshold = max(maxSize - curSize, 0);
            if (threshold >= numLevels || i <= levelOffsets[threshold])
                break;

            int u = levelOrder[i - 1];

            curClique.set(u), ++curSize;

            BitSet newSet = remSet & graph[u];
            if (newSet) {
                rec(newSet, degreeOrder, numVertices, nextBuffer);
            }
            else if (curSize > maxSize) {
                maxClique = curClique, maxSize = curSize;
            }
            curClique.unset(u), --curSize;
            remSet.unset(u);
        }
    }

    void reNumber(int p, int k, int threshold) {
        for (int i = 0; i < threshold; ++i) {
            BitSet S = graph[p] & levels[i];
            int q = S.getSingleton();
            if (q == -1) continue;
            for (int j = i + 1; j <= threshold; ++j) {
                if (graph[q] & levels[j]) continue;
                levels[k].unset(p);
                levels[i].unset(q);
                levels[i].set(p);
                levels[j].set(q);
                vertexLevel[p] = i;
                vertexLevel[q] = j;
                return;
            }
        }
    }

    vector<BitSet> graph;
    BitSet curClique, maxClique;
    int curSize, maxSize;

    vector<BitSet> levels;
    vector<int> vertexLevel, vertexDegree;
    vector<pair<Vertex*, int>> levelVertices;
    vector<pair<Vertex*, int>> degreeVertices;
    vector<Vertex> globalBuffer;
    long long numRecs;
};
/*---------------------------------------------------------------------------------------------------
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---------------------------------------------------------------------------------------------------*/




int N, M;
//---------------------------------------------------------------------------------------------------
void _main() {
    cin >> N >> M;

    vector<BitSet> g(N);
    rep(i, 0, M) {
        int x, y; cin >> x >> y;
        x--; y--;
        g[x].set(y);
        g[y].set(x);
    }
    MaximumCliqueBranchAndBound mc;
    BitSet ans = mc.maximumClique(g);
    cout << ans.count() << endl;
}

Submission Info

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