1 files changed, 249 insertions, 107 deletions

diff --git a/src/utils.c b/src/utils.c
index 5b7df06..f72a00e 100644
--- a/src/utils.c
+++ b/src/utils.c
@@ -1,132 +1,274 @@
 #include "utils.h"
 
-/* Hardcoded factorial of small numbers (n<=12). */
-int factorial[13] = {
-  1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600
-};
+void
+apply_permutation(int *perm, int *set, int n)
+{
+        int *aux = malloc(n * sizeof(int));
+        int i;
 
-/* swaps two integers */
-void swap(int *a, int *b) {
-  int aux = *a;
-  *a = *b;
-  *b = aux;
+        if (!is_perm(perm, n))
+                return;
+                
+        for (i = 0; i < n; i++)
+                aux[i] = set[perm[i]];
+
+        memcpy(set, aux, n * sizeof(int));
+        free(aux);
+}
+
+int
+binomial(int n, int k)
+{
+        if (n < 0 || k < 0 || k > n)
+                return 0;
+
+        return factorial(n) / (factorial(k) * factorial(n-k));
+}
+
+int
+digit_array_to_int(int *a, int n, int b)
+{
+        int i, ret = 0, p = 1;
+
+        for (i = 0; i < n; i++, p *= b)
+                ret += a[i] * p;
+
+        return ret;
+}
+
+int
+factorial(int n)
+{
+        int i, ret = 1;
+
+        if (n < 0)
+                return 0;
+
+        for (i = 1; i <= n; i++)
+                ret *= i;
+
+        return ret;
+}
+
+void
+index_to_perm(int p, int n, int *r)
+{
+        int *a = malloc(n * sizeof(int));
+        int i, j, c;
+
+        for (i = 0; i < n; i++)
+                a[i] = 0;
+
+        if (p < 0 || p >= factorial(n))
+                for (i = 0; i < n; i++)
+                        r[i] = -1;
+
+        for (i = 0; i < n; i++) {
+                c = 0;
+                j = 0;
+                while (c <= p / factorial(n-i-1))
+                        c += a[j++] ? 0 : 1;
+                r[i] = j-1;
+                a[j-1] = 1;
+                p %= factorial(n-i-1);
+        }
+
+        free(a);
+}
+
+void
+index_to_subset(int s, int n, int k, int *r)
+{
+        int i, j, v;
+
+        if (s < 0 || s >= binomial(n, k)) {
+                for (i = 0; i < n; i++)
+                        r[i] = -1;
+                return;
+        }
+
+        for (i = 0; i < n; i++) {
+                if (k == n-i) {
+                        for (j = i; j < n; j++)
+                                r[j] = 1;
+                        return;
+                }
+
+                if (k == 0) {
+                        for (j = i; j < n; j++)
+                                r[j] = 0;
+                        return;
+                }
+
+                v = binomial(n-i-1, k);
+                if (s >= v) {
+                        r[i] = 1;
+                        k--;
+                        s -= v;
+                } else {
+                        r[i] = 0;
+                }
+        }
+}
+
+void
+int_to_digit_array(int a, int b, int n, int *r)
+{
+        int i;
+
+        if (b <= 1)
+                for (i = 0; i < n; i++)
+                        r[i] = 0;
+        else
+                for (i = 0; i < n; i++, a /= b)
+                        r[i] = a % b;
+}
+
+void
+int_to_sum_zero_array(int x, int b, int n, int *a)
+{
+        int i, s = 0;
+
+        if (b <= 1) {
+                for (i = 0; i < n; i++)
+                    a[i] = 0;
+        } else {
+                int_to_digit_array(x, b, n-1, a);
+                for (i = 0; i < n - 1; i++)
+                    s = (s + a[i]) % b;
+                a[n-1] = (b - s) % b;
+        }
 }
 
-/* Converts the integer a to its representation in base b (first n digits
- * only) and saves the result in r. */
-void int_to_digit_array(int a, int b, int n, int *r) {
-  for (int i = 0; i < n; i++) {
-    r[i] = a % b;
-    a /= b;
-  }
+int
+invert_digits(int a, int b, int n)
+{
+        int i, ret, *r = malloc(n * sizeof(int));
+
+        int_to_digit_array(a, b, n, r);
+        for (i = 0; i < n; i++)
+                r[i] = (b-r[i]) % b;
+
+        ret = digit_array_to_int(r, n, b);
+        free(r);
+        return ret;
 }
 
-/* Converts the array of n digits a to a integer using base b. */
-int digit_array_to_int(int *a, int n, int b) {
-  int ret = 0, p = 1;
-  for (int i = 0; i < n; i++) {
-    ret += a[i] * p;
-    p *= b;
-  }
-  return ret;
+bool
+is_perm(int *a, int n)
+{
+        int *aux = malloc(n * sizeof(int));
+        int i;
+        
+        for (i = 0; i < n; i++)
+                if (a[i] < 0 || a[i] >= n)
+                        return false;
+                else
+                        aux[a[i]] = 1;
+
+        for (i = 0; i < n; i++)
+                if (!aux[i])
+                        return false;
+
+        free(aux);
+
+        return true;
 }
 
-/* Converts a permutation on [0..(n-1)] into the integer i which is the index
- * of the permutation in the sorted list of all n! such permutations.
- * Only works for n<=12. */
-int perm_to_index(int *a, int n) {
-  int ret = 0;
-  for (int i = 0; i < n; i++) {
-    int c = 0;
-    for (int j = i+1; j < n; j++)
-      if (a[i] > a[j])
-        c++;
-    ret += factorial[n-i-1] * c;
-  }
-  return ret;
+bool
+is_subset(int *a, int n, int k)
+{
+        int i, sum = 0;
+
+        for (i = 0; i < n; i++)
+                sum += a[i] ? 1 : 0;
+
+        return sum == k;
 }
 
-/* Converts a permutation index to the actual permutation as an array
- * (see perm_to_index) and saves the result to r. */
-void index_to_perm(int p, int n, int *r) {
-  int a[n];
-  for (int j = 0; j < n; j++)
-    a[j] = 0; /* picked elements */
-  for (int i = 0; i < n; i++) {
-    int c = 0, j = 0;
-    while (c <= p / factorial[n-i-1]) {
-      if (!a[j])
-        c++;
-      j++;
-    }
-    r[i] = j-1;
-    a[j-1] = 1;
-    p %= factorial[n-i-1];
-  }
+int
+perm_sign(int *a, int n)
+{
+        int i, j, ret = 0;
+
+        if (!is_perm(a,n))
+                return -1;
+
+        for (i = 0; i < n; i++)
+                for (j = i+1; j < n; j++)
+                        ret += (a[i] > a[j]) ? 1 : 0;
+
+        return ret % 2;
 }
 
+int
+perm_to_index(int *a, int n)
+{
+        int i, j, c, ret = 0;
+
+        if (!is_perm(a, n))
+                return -1;
 
-int perm_sign_array(int a[], int n) {
-  int ret = 0;
-  for (int i = 0; i < n; i++)
-    for (int j = i+1; j < n; j++)
-      if (a[i]>a[j])
-        ret++;
-  return ret % 2;
+        for (i = 0; i < n; i++) {
+                c = 0;
+                for (j = i+1; j < n; j++)
+                        c += (a[i] > a[j]) ? 1 : 0;
+                ret += factorial(n-i-1) * c;
+        }
+
+        return ret;
 }
 
-int perm_sign_int(int p, int n) {
-  int a[n];
-  index_to_perm(p, n, a);
-  return perm_sign_array(a, n);
+int
+powint(int a, int b)
+{
+        if (b < 0)
+                return 0;
+        if (b == 0)
+                return 1;
+
+        if (b % 2)
+                return a * powint(a, b-1);
+        else
+                return powint(a*a, b/2);
 }
 
+int 
+subset_to_index(int *a, int n, int k)
+{
+        int i, ret = 0;
+
+        if (!is_subset(a, n, k))
+                return binomial(n, k);
 
-/* Converts a k-element subset of a set with an element from an array of n
- * elements, of which k are 1 (or just non-zero) and n-k are 0, to its index
- * in the sorted list of all such subsets.
- * Works only for n <= 12. */
-int subset_to_index(int *a, int n, int k) {
-  int ret = 0;
-  for (int i = 0; i < n; i++) {
-    if (k == n-i)
-      return ret;
-    if (a[i]) {
-      ret += factorial[n-i-1] / (factorial[k] * factorial[n-i-1-k]);
-      k--;
-    }
-  }
-  return ret;
+        for (i = 0; i < n; i++) {
+                if (k == n-i)
+                        return ret;
+                if (a[i]) {
+                        ret += binomial(n-i-1, k);
+                        k--;
+                }
+        }
+
+        return ret;
 }
 
-/* Inverse of the above */
-void index_to_subset(int s, int n, int k, int *r) {
-  for (int i = 0; i < n; i++) {
-    if (k == n-i) {
-      for (int j = i; j < n; j++)
-        r[j] = 1;
-      return;
-    }
-    int v = factorial[n-i-1] / (factorial[k] * factorial[n-i-1-k]);
-    if (s >= v) {
-      r[i] = 1;
-      k--;
-      s -= v;
-    } else {
-      r[i] = 0;
-    }
-  }
+void
+sum_arrays_mod(int *src, int *dst, int n, int m)
+{
+        int i;
+
+        for (i = 0; i < n; i++)
+                dst[i] = (m <= 0) ? 0 : (src[i] + dst[i]) % m;
 }
 
-/* Converts the first n-1 digits of a number to an array a of digits in base b;
- * then adds one element to the array, so that the sum of the elements of a is
- * zero modulo b.
- * This is used for determing the edge orientation from an 11-bits integer or
- * the corner orientation from a 7-trits integer. */
-void int_to_sum_zero_array(int x, int b, int n, int *a) {
-  int_to_digit_array(x, b, n-1, a);
-  int s = 0;
-  for (int i = 0; i < n - 1; i++) s = (s + a[i]) % b;
-  a[n-1] = (b - s) % b;
+void
+swap(int *a, int *b)
+{
+        int aux;
+
+        aux = *a;
+        *a = *b;
+        *b = aux;
 }