子图同构算法系列（1）

Naive alogrithm for Subgraph Isomorphism.

1. 如何判定子图同构。

　　有个G_α和G_β， G_α有pa个点，qa条边，G_β有pb个点，qb条边。A是G_α的邻接矩阵，相应的B是G_β的邻接矩阵。那么如何判断同构呢。设A是子图，B是原图。那么有一个A的点到B的点的映射。这个映射的模式叫做M。M是pa行，pb列的。M有一个性质就是每行只有一个1，每列至多一个1。这个就是一个A中的点到B中的点的一个映射。我们定义一个C = [c_ij] = M(MB)^T。如果在图A中i和j有边能推导出图C中i和j有边。那为什么是对的呢。因为M是映射，MB就是把B中被映射的点按照顺序抽出来在和B点对应。 M中第i行j列为1的意义是A的第i个点对应，B的第j个点。MB中第i行j列为1的意义是现在A的第i个点对应到的点到B的第j个点有一条边。把这个矩阵转置在乘以M。C就是B中和A对应的点和在B中的边全部抽出来组成的图。

　　那么如果aij = 1能推导出cij = 1。A就是B的一个子图的同构。

 

#include <iostream>
#include <stdio.h>

class Matrix{
private:int **cont;
        int a, b;
public:
    Matrix(){
        cont = 0;
        a = b = 0;
    }
    Matrix(int a, int b){
        this->a = a;
        this->b = b;
        cont = new int*[a];
        for (int i = 0; i < a; i++){
            cont[i] = new int[b];
            for (int j = 0; j < b; j++){
                cont[i][j] = 0;
            }
        }
    }
    Matrix(void *x, int a, int b){
        int *y = (int*) x;
        this->a = a;
        this->b = b;
        cont = new int*[a];
        for (int i = 0; i < a; i++){
            cont[i] = new int[b];
            for (int j = 0; j < b; j++){
                cont[i][j] = y[i*a + j];
            }
        }
    }
    Matrix(const Matrix& x){
        if (x.isNULL()){
            cont = 0;
            a = b = 0;
        }
        else{
            a = x.a; b = x.b;
            cont = new int*[a];
            for (int i = 0; i < a; i++){
                cont[i] = new int[b];
                for (int j = 0; j < b; j++){
                    cont[i][j] = x.cont[i][j];
                }
            }
        }
    }
    ~Matrix(){
        for (int i = 0; i < b; i++){
            delete[] cont[i];
        }
        delete cont;
    }
    Matrix Muiltply(Matrix y){
        if (isNULL() || y.isNULL() || b != y.a){
            return Matrix();
        }
        Matrix z(a, y.b);
        for (int i = 0; i < a; i++){
            for (int j = 0; j < y.b; j++){
                for (int k = 0; k < b; k++){
                    z.cont[i][j] += cont[i][k] * y.cont[k][j];
                }
            }
        }
        return z;
    }
    Matrix boolMuiltply(Matrix y){
        if (isNULL() || y.isNULL() || b != y.a){
            return Matrix();
        }
        Matrix z(a, y.b);
        for (int i = 0; i < a; i++){
            for (int j = 0; j < y.b; j++){
                for (int k = 0; k < b; k++){
                    z.cont[i][j] += cont[i][k] * y.cont[k][j];
                }
                if(z.cont[i][j] > 0){
                    z.cont[i][j] = 1;
                }
            }
        }
        return z;
    }
    bool isNULL() const{
        if (cont == 0){
            return true;
        }
        else{
            return false;
        }
    }
    bool isequal(Matrix& y){
        if(a == y.a && b == y.b){
            for (int i = 0; i < a; i++){
                for (int j = 0; j < a; j++){
                    if(cont[i][j] != y.cont[i][j]){
                        return false;
                    }
                }
            }
            return true;
        } else{
            return false;
        }
    }
    Matrix Trans(){
        Matrix x(b,a);
        for (int i = 0; i < a; i++){
            for (int j = 0; j < b; j++){
                x.cont[j][i] = cont[i][j];
            }
        }
        return x;
    }
    bool iscontent(const Matrix &A)const{
        if(a == A.a && b == A.b){
            for (int i = 1; i <= a; i++){
                for (int j = 1; j <= b; j++){
                    if(A.cont[i][j] == 1 && cont[i][j] == 0){
                        return 0;
                    }
                }
            }
            return 1;
        }
        return 0;
    }
    void print(){
        if (isNULL()){
            printf("NULL\n");
        }
        for (int i = 0; i < a; i++){
            for (int j = 0; j < b; j++){
                std::cout << cont[i][j] << " ";
            }
            std::cout << std::endl;
        }
    }
};

int main(){
    typedef Matrix Map;
    typedef Matrix Transfer;
    Map A,B;Transfer M;
    Map x = M.boolMuiltply(M.boolMuiltply(B).Trans());
    x.iscontent(A);
}