chore: import upstream snapshot with attribution

dynamic_programming/catalan_numbers.cpp

@@ -0,0 +1,82 @@
+/**
+ * @file
+ * @brief Provides utilities to compute Catalan numbers using dynamic
+ programming.
+ * A Catalan numbers satisfy these recurrence relations:
+ * C(0) = C(1) = 1; C(n) = sum(C(i).C(n-i-1)), for i = 0 to n-1
+ * Read more about Catalan numbers here:
+    https://en.wikipedia.org/wiki/Catalan_number
+    https://oeis.org/A000108/
+ */
+
+#include <cassert>     /// for assert
+#include <cstdint>     /// for std::uint64_t
+#include <cstdlib>     /// for std::size_t
+#include <functional>  /// for std::plus & std::multiplies
+#include <numeric>     /// for std::transform_reduce
+#include <vector>      /// for std::vector
+
+/**
+ * @brief computes and caches Catalan numbers
+ */
+class catalan_numbers {
+    using value_type = std::uint64_t;
+    std::vector<value_type> known{1, 1};
+
+    value_type compute_next() {
+        return std::transform_reduce(known.begin(), known.end(), known.rbegin(),
+                                     static_cast<value_type>(0), std::plus<>(),
+                                     std::multiplies<>());
+    }
+
+    void add() { known.push_back(this->compute_next()); }
+
+ public:
+    /**
+     * @brief computes the n-th Catalan number and updates the cache.
+     * @return the n-th Catalan number
+     */
+    value_type get(std::size_t n) {
+        while (known.size() <= n) {
+            this->add();
+        }
+        return known[n];
+    }
+};
+
+void test_catalan_numbers_up_to_20() {
+    // data verified with https://oeis.org/A000108/
+    catalan_numbers cn;
+    assert(cn.get(0) == 1ULL);
+    assert(cn.get(1) == 1ULL);
+    assert(cn.get(2) == 2ULL);
+    assert(cn.get(3) == 5ULL);
+    assert(cn.get(4) == 14ULL);
+    assert(cn.get(5) == 42ULL);
+    assert(cn.get(6) == 132ULL);
+    assert(cn.get(7) == 429ULL);
+    assert(cn.get(8) == 1430ULL);
+    assert(cn.get(9) == 4862ULL);
+    assert(cn.get(10) == 16796ULL);
+    assert(cn.get(11) == 58786ULL);
+    assert(cn.get(12) == 208012ULL);
+    assert(cn.get(13) == 742900ULL);
+    assert(cn.get(14) == 2674440ULL);
+    assert(cn.get(15) == 9694845ULL);
+    assert(cn.get(16) == 35357670ULL);
+    assert(cn.get(17) == 129644790ULL);
+    assert(cn.get(18) == 477638700ULL);
+    assert(cn.get(19) == 1767263190ULL);
+    assert(cn.get(20) == 6564120420ULL);
+}
+
+void test_catalan_numbers_25() {
+    // data verified with https://oeis.org/A000108/
+    catalan_numbers cn;
+    assert(cn.get(25) == 4861946401452ULL);
+}
+
+int main() {
+    test_catalan_numbers_up_to_20();
+    test_catalan_numbers_25();
+}