cc19.3: implemented.

CMakeLists.txt

@@ -58,6 +58,10 @@ add_executable(cc192 cc192.cc)
 target_link_libraries(cc192 ${CONAN_LIBS})
 add_test(cc192 bin/cc192)
 
+add_executable(cc193 cc193.cc)
+target_link_libraries(cc193 ${CONAN_LIBS})
+add_test(cc193 bin/cc193)
+
 add_executable(cx_shuffle cx_shuffle.cc)
 target_link_libraries(cx_shuffle ${CONAN_LIBS})
 add_test(cx_shuffle bin/cx_shuffle)

cc193.cc

@@ -0,0 +1,65 @@
+// Calculate the number of trailing zeros on n!
+
+#define CATCH_CONFIG_MAIN
+#include <catch.hpp>
+
+#include <cstdint>
+
+using Number = uint64_t;
+
+static Number factorial(int n) {
+  switch (n) {
+    case 1:
+      return 1;
+    case 2:
+      return 2;
+    default:
+      return n * factorial(n-1);
+  }
+}
+
+static int zeros(int n) {
+  if (n < 5) {
+    return 0;
+  }
+
+  // Count the factors that will add a zero.
+  if (n % 5 == 0) {
+    return 1 + zeros(n-1);
+  }
+  return 0 + zeros(n-1);
+}
+
+TEST_CASE("cc19.3", "zeros") {
+  static const struct {
+    int n;
+    Number fact;
+    int zeros;
+  } tests[] = {
+    { 1, 1, 0 },
+    { 2, 2, 0 },
+    { 3, 6, 0 },
+    { 4, 24, 0 },
+    { 5, 120, 1 },
+    { 6, 720, 1 },
+    { 7, 5040, 1 },
+    { 8, 40320, 1 },
+    { 9, 362880, 1 },
+    { 10, 3628800, 2 },
+    { 11, 39916800, 2 },
+    { 12, 479001600, 2 },
+    { 13, 6227020800, 2 },
+    { 14, 87178291200, 2 },
+    { 15, 1307674368000, 3 },
+    { 16, 20922789888000, 3 },
+    { 17, 355687428096000, 3 },
+    { 18, 6402373705728000, 3 },
+    { 19, 121645100408832000, 3 },
+    { 20, 2432902008176640000, 4 },
+  };
+
+  for (const auto& test : tests) {
+    CHECK(factorial(test.n) == test.fact);
+    CHECK(zeros(test.n) == test.zeros);
+  }
+}