[feat/fix/docs]: Improve the Easter Determination algorithm (#1675)

* Create easter.cpp

* Update easter.cpp

* Update easter.cpp

* Update easter.cpp

* Update others/easter.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update others/easter.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update others/easter.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for f8e4e3fb

* Update others/easter.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update others/easter.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update others/easter.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update others/easter.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update others/easter.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update others/easter.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* clang-format and clang-tidy fixes for aae0d475

* Update easter.cpp

* Update easter.cpp

* clang-format and clang-tidy fixes for e033f98f

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

DIRECTORY.md

@@ -248,6 +248,7 @@
   * [Decimal To Binary](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_binary.cpp)
   * [Decimal To Hexadecimal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_hexadecimal.cpp)
   * [Decimal To Roman Numeral](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_roman_numeral.cpp)
+  * [Easter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/easter.cpp)
   * [Fast Integer Input](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/fast_integer_input.cpp)
   * [Happy Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/happy_number.cpp)
   * [Iterative Tree Traversals](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/iterative_tree_traversals.cpp)

others/easter.cpp

@@ -0,0 +1,109 @@
+/*
+ * @file
+ * @brief Determines the [Date of
+ * Easter](https://en.wikipedia.org/wiki/Date_of_Easter) after 1582
+ *
+ * @details
+ * The date of Easter is determined in each year through a calculation known as
+ * "computus." Easter is celebrated on the first Sunday after the Paschal full
+ * moon, which is the first full moon on or after 21 March. Determining this
+ * date in advance requires a correlation between the lunar months and the solar
+ * year, while also accounting for the month, date, and weekday of the Julian or
+ * Gregorian calendar. The complexity of the algorithm arises because of the
+ * desire to associate the date of Easter with the date of the Jewish feast of
+ * Passover which, Christians believe, is when Jesus was crucified.
+ *
+ *
+ * @author [AlternateWalls](https://github.com/AlternateWalls)
+ */
+
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO operations
+
+/*
+ * @brief Contains information for Easter date
+ */
+class EasterYearMonthDay {
+ public:
+    uint64_t year;   ///< year Easter is on
+    uint64_t month;  ///< month Easter is on
+    uint64_t day;    ///< day Easter is on
+
+    EasterYearMonthDay(uint64_t newYear, uint64_t newMonth, uint64_t newDay) {
+        year = newYear;  // Assigns year to class
+        month = newMonth;
+        day = newDay;
+    }
+};
+
+/*
+ * @brief Function that finds the month and day of Easter
+ * @params param1 An int "y" of the year you want to find Easter on after
+ * 1582
+ * @returns An instance of the easterYearMonthDay calss that contains the
+ * information (Ex. 420 - 4/20 or April 20th)
+ */
+EasterYearMonthDay findEaster(uint64_t y) {
+    if (y > 1582) {
+        uint64_t a = y % 19;   // Year's location on Metonic Calendar
+        uint64_t b = y / 100;  // Century index
+        uint64_t c = y % 100;
+        uint64_t d = b / 4;
+        uint64_t e = b % 4;  // Takes into account leap years
+        uint64_t f = (b + 8) / 25;
+        uint64_t g = (b - f + 1) / 3;
+        uint64_t h = (19 * a + b - d - g + 15) %
+                     30;  // Days from Mar. 21st until the full moon
+        uint64_t i = c / 4;
+        uint64_t k = c % 4;
+        uint64_t r =
+            (32 + 2 * e + 2 * i - h - k) %
+            7;  // The number of days from Paschal full moon to next Sunday
+        uint64_t m = (a + 11 * h + 22 * r) / 451;
+        uint64_t n = (h + r - 7 * m + 114) / 31;  // Month of Easter
+        uint64_t p = (h + r - 7 * m + 114) % 31;  // p + 1 is the day of Easter
+
+        // Assign values
+        EasterYearMonthDay date(
+            y, n, p + 1);  // Assign values to new instance of class
+
+        // Return date
+        return date;
+    } else {
+        EasterYearMonthDay date(0, 0, 0);
+
+        // Return date
+        return date;
+    }
+}
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // 2003 | April 20th
+    assert(findEaster(2003).month == 4);  // Should return true
+    assert(findEaster(2003).day == 20);   // Should return true
+
+    // 1910 | March 27th
+    assert(findEaster(1910).month == 3);  // Should return true
+    assert(findEaster(1910).day == 27);   // Should return true
+
+    // 1877 | April 1st
+    assert(findEaster(1877).month != 3);  // Should return true
+    assert(findEaster(1877).day != 22);   // Should return true
+
+    // 1400 | Invalid date
+    assert(findEaster(1400).month == 0);  // Should return true
+    assert(findEaster(1400).day == 0);    // Should return true
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}