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#include "symmetric.h"
q_t *symmetric_compose(q_t q, const q_t *g1, const q_t *g2) {
q_t *g3 = (q_t *)malloc(q * sizeof(q_t));
for (q_t i = 0; i < q; i++) {
g3[i] = g1[g2[i]];
}
return g3;
}
q_t symmetric_act(const q_t *g, q_t s) {
return g[s];
}
q_t *symmetric_invert(q_t q, const q_t *g) {
q_t *g_inv = (q_t *)malloc(q * sizeof(q_t));
for (q_t i = 0; i < q; i++) {
g_inv[g[i]] = i;
}
return g_inv;
}
void swap(q_t *q1, q_t *q2) {
q_t temp = *q1;
*q1 = *q2;
*q2 = temp;
}
R_t factorial(q_t q) {
if (q == 0) {
return 1;
} else {
return q * factorial(q - 1);
}
}
void permute(q_t *a, q_t l, q_t r, R_t pos, q_t *transformations) {
if (l == r - 1) {
for (q_t i = 0; i < r; i++) {
transformations[r * pos + i] = a[i];
}
} else {
for (q_t i = l; i < r; i++) {
swap((a+l), (a+i));
permute(a, l+1, r, pos + (i - l) * factorial(r - l - 1), transformations);
swap((a+l), (a+i));
}
}
}
q_t *symmetric_gen_transformations(q_t q) {
q_t *transformations = (q_t *)malloc(q * factorial(q) * sizeof(q_t));
q_t *tmp = (q_t *)malloc(q * sizeof(q_t));
for (q_t i = 0; i < q; i++) {
tmp[i] = i;
}
permute(tmp, 0, q, 0, transformations);
free(tmp);
return transformations;
}
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