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1 files changed, 115 insertions, 0 deletions

diff --git a/src/utils.c b/src/utils.c
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index 0000000..c672453
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+++ b/src/utils.c
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+#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
+};
+
+/* swaps two integers */
+void swap(int *a, int *b) {
+  int aux = *a;
+  *a = *b;
+  *b = aux;
+}
+
+/* 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;
+  }
+}
+
+/* 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;
+}
+
+/* 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;
+}
+
+/* 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];
+  }
+}
+
+/* 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;
+}
+
+/* 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;
+    }
+  }
+}
+
+/* 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;
+}
+