Data commit

Task/Evaluate-binomial-coefficients/C/evaluate-binomial-coefficients.c

@@ -0,0 +1,43 @@
+#include <stdio.h>
+#include <limits.h>
+
+/* We go to some effort to handle overflow situations */
+
+static unsigned long gcd_ui(unsigned long x, unsigned long y) {
+  unsigned long t;
+  if (y < x) { t = x; x = y; y = t; }
+  while (y > 0) {
+    t = y;  y = x % y;  x = t;  /* y1 <- x0 % y0 ; x1 <- y0 */
+  }
+  return x;
+}
+
+unsigned long binomial(unsigned long n, unsigned long k) {
+  unsigned long d, g, r = 1;
+  if (k == 0) return 1;
+  if (k == 1) return n;
+  if (k >= n) return (k == n);
+  if (k > n/2) k = n-k;
+  for (d = 1; d <= k; d++) {
+    if (r >= ULONG_MAX/n) {  /* Possible overflow */
+      unsigned long nr, dr;  /* reduced numerator / denominator */
+      g = gcd_ui(n, d);  nr = n/g;  dr = d/g;
+      g = gcd_ui(r, dr);  r = r/g;  dr = dr/g;
+      if (r >= ULONG_MAX/nr) return 0;  /* Unavoidable overflow */
+      r *= nr;
+      r /= dr;
+      n--;
+    } else {
+      r *= n--;
+      r /= d;
+    }
+  }
+  return r;
+}
+
+int main() {
+    printf("%lu\n", binomial(5, 3));
+    printf("%lu\n", binomial(40, 19));
+    printf("%lu\n", binomial(67, 31));
+    return 0;
+}