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【C/C++】最大团(n小于64)(faster)

作者:Parker / 发布于2016/3/17/ 529

/**
 * WishingBone's ACM/ICPC Routine Library
 *
 * maximum clique solver
 */

#include <vector>

using std::vector;

// clique solver calculates both size and consitution of maximum clique
// uses bit operation to accelerate searching
// graph size limit is 63, the graph should be undirected
// can optimize to calculate on each component, and sort on vertex degrees
// can be used to solve maximum independent set
class clique {
public:
    static const long long ONE = 1;
    static const long long MASK = (1 << 21) - 1;
    char* bits;
    int n, size, cmax[63];
    long long mask[63], cons;
    // initiate lookup table
    clique() {
        bits = new char[1 << 21];
        bits[0] = 0;
        for (int i = 1; i < 1 << 21; ++i) bits[i] = bits[i >> 1] + (i & 1);
    }
    ~clique() {
        delete bits;
    }
    // search routine
    bool search(int step, int size, long long more, long long con);
    // solve maximum clique and return size
    int sizeClique(vector<vector<int> >& mat);
    // solve maximum clique and return constitution
    vector<int> consClique(vector<vector<int> >& mat);
};

// search routine
// step is node id, size is current solution, more is available mask, cons is
constitution mask
bool clique::search(int step, int size, long long more, long long cons) {
    if (step >= n) {
        // a new solution reached
        this->size = size;
        this->cons = cons;
        return true;
    }
    long long now = ONE << step;
    if ((now & more) > 0) {
        long long next = more & mask[step];
        if (size + bits[next & MASK] + bits[(next >> 21) & MASK] + bits[next >>
42] >= this->size
                && size + cmax[step] > this->size) {
            // the current node is in the clique
            if (search(step + 1, size + 1, next, cons | now)) return true;
        }
    }
    long long next = more & ~now;
    if (size + bits[next & MASK] + bits[(next >> 21) & MASK] + bits[next >> 42]
> this->size) {
        // the current node is not in the clique
        if (search(step + 1, size, next, cons)) return true;
    }
    return false;
}

// solve maximum clique and return size
int clique::sizeClique(vector<vector<int> >& mat) {
    n = mat.size();
    // generate mask vectors
    for (int i = 0; i < n; ++i) {
        mask[i] = 0;
        for (int j = 0; j < n; ++j) if (mat[i][j] > 0) mask[i] |= ONE << j;
    }
    size = 0;
    for (int i = n - 1; i >= 0; --i) {
        search(i + 1, 1, mask[i], ONE << i);
        cmax[i] = size;
    }
    return size;
}

// solve maximum clique and return constitution
// calls sizeClique and restore cons
vector<int> clique::consClique(vector<vector<int> >& mat) {
    sizeClique(mat);
    vector<int> ret;
    for (int i = 0; i < n; ++i) if ((cons & (ONE << i)) > 0) ret.push_back(i);
    return ret;
}

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