[FR] perm.h -- manipuler des permutations !

class Permutation {

    public:
    Permutation id(int m);
    void apres(Permutation s);
    void montrer ();
    Permutation array2perm(int arr[], int m);
    void inverse(Permutation & perm);
    Permutation tau (int arr[], int m);
    int signature();
    void mappedFrom(int arr[]);
    // oui je sais c'est écrit en anglais bla bla bla c'est pas grave on l'utilise quasi pas

    private:
    int de[50];
    int n;

};
Permutation Permutation::id(int m) {
    n = m;
    de[0] = 0;
    for (int i = 1; i <= n; i++)
        de[i] = i;
}
void Permutation::montrer() {
    printf("(%i",de[1]);
    for (int i = 2; i <= n; i++)
        printf(" %i",de[i]);
    printf(")");
}
void Permutation::apres(Permutation s) {
    n = s.n;
    int deRet[n];
    for (int i = 1; i <= n; i++)
        deRet[i] = de[s.de[i]];
    for (int i = 1; i <= n; i++)
        de[i] = deRet[i];
}
Permutation operator * (Permutation a, Permutation b) {
    a.apres(b);
    return a;
}
Permutation Permutation::array2perm(int arr[], int m) {
    n = m;
    for (int i = 1; i <= n; i++)
        de[i] = arr[i-1];
}
void Permutation::mappedFrom(int arr[]) {
    for (int i = 1; i <= n; i++) {
        arr[de[i]] = i;
    }
}
Permutation Permutation::tau (int arr[], int m) {
    Permutation ret;
    ret.id(m);
    for (int i = 1; i <= m; i++) {
        if (arr[0] == i) ret.de[i] = arr[1];
        else if (arr[1] == i) ret.de[i] = arr[0];
        else ret.de[i] = i;
    }
    return ret;
}
void Permutation::inverse(Permutation & perm) {

    perm.n = n;
    for (int i = 1; i <= n; i++)
        perm.de[i] = de[i];

    int taus[n+1][2];

    Permutation identity;
    int array[n+1];
    Permutation inverse;

    identity.id(n);
    inverse.id(n);

    Permutation tau;

    perm.mappedFrom(array);
    for (int i = 1; i <= n; i++) {
        taus[i][0] = i;
        taus[i][1] = identity.de[array[i]];
        tau = tau.tau(taus[i],n);
        identity = tau * identity;
        inverse = inverse * tau;
    }

    perm = inverse;

}
int Permutation::signature() {

    int epsilon = 1;

    Permutation perm;
    perm.n = n;
    for (int i = 1; i <= n; i++)
        perm.de[i] = de[i];

    int taus[n+1][2];

    Permutation identity;
    int array[n+1];
    Permutation inverse;

    identity.id(n);
    inverse.id(n);

    Permutation tau;

    perm.mappedFrom(array);
    for (int i = 1; i <= n; i++) {
        taus[i][0] = i;
        taus[i][1] = identity.de[array[i]];
        tau = tau.tau(taus[i],n);
        if (i != identity.de[array[i]])
            epsilon *= -1;
        identity = tau * identity;
    }

    return epsilon;

}