feat: Add Zeller's congruence algorithm (TheAlgorithms#105)

Author: sunilbpandey

maths/test/zellers_congruence.test.ts

@@ -0,0 +1,112 @@
+import { Calendar, GetWeekday } from "../zellers_congruence";
+
+describe("Zeller's congruence", () => {
+  test.each([
+    { year: 2000, month: 1, day: 1, expected: 6 },
+    { year: 2000, month: 2, day: 1, expected: 2 },
+    { year: 2000, month: 3, day: 1, expected: 3 },
+    { year: 2000, month: 4, day: 1, expected: 6 },
+    { year: 2000, month: 5, day: 1, expected: 1 },
+    { year: 2000, month: 6, day: 1, expected: 4 },
+    { year: 2000, month: 7, day: 1, expected: 6 },
+    { year: 2000, month: 8, day: 1, expected: 2 },
+    { year: 2000, month: 9, day: 1, expected: 5 },
+    { year: 2000, month: 10, day: 1, expected: 0 },
+    { year: 2000, month: 11, day: 1, expected: 3 },
+    { year: 2000, month: 12, day: 1, expected: 5 },
+    { year: 1, month: 1, day: 1, expected: 1 },
+    { year: 23, month: 2, day: 28, expected: 2 },
+    { year: 456, month: 3, day: 31, expected: 5 },
+    { year: 1850, month: 4, day: 1, expected: 1 },
+    { year: 2100, month: 12, day: 31, expected: 5 },
+    { year: 3000, month: 12, day: 31, expected: 3 },
+  ])(
+    `The weekday of $year-$month-$day in the default calendar is $expected`,
+    ({ year, month, day, expected }) => {
+      expect(GetWeekday(year, month, day)).toEqual(expected);
+    }
+  );
+
+  test.each([
+    { year: 1500, month: 1, day: 1, expected: 3 },
+    { year: 1500, month: 2, day: 1, expected: 6 },
+    { year: 1500, month: 3, day: 1, expected: 0 },
+    { year: 1500, month: 4, day: 1, expected: 3 },
+    { year: 1500, month: 5, day: 1, expected: 5 },
+    { year: 1500, month: 6, day: 1, expected: 1 },
+    { year: 1500, month: 7, day: 1, expected: 3 },
+    { year: 1500, month: 8, day: 1, expected: 6 },
+    { year: 1500, month: 9, day: 1, expected: 2 },
+    { year: 1500, month: 10, day: 1, expected: 4 },
+    { year: 1500, month: 11, day: 1, expected: 0 },
+    { year: 1500, month: 12, day: 1, expected: 2 },
+    { year: 1, month: 1, day: 1, expected: 6 },
+    { year: 23, month: 2, day: 28, expected: 0 },
+    { year: 456, month: 3, day: 31, expected: 6 },
+    { year: 1582, month: 2, day: 1, expected: 4 },
+  ])(
+    `The weekday of $year-$month-$day in the Julian calendar is $expected`,
+    ({ year, month, day, expected }) => {
+      expect(GetWeekday(year, month, day, Calendar.Julian)).toEqual(expected);
+    }
+  );
+
+  test(`The default calendar is Gregorian`, () => {
+    expect(GetWeekday(1, 1, 1)).toEqual(1);
+  });
+
+  test.each([
+    { year: 1, month: 1, day: 1, expected: 1 },
+    { year: 23, month: 2, day: 28, expected: 2 },
+    { year: 456, month: 3, day: 31, expected: 5 },
+    { year: 1850, month: 4, day: 1, expected: 1 },
+    { year: 2000, month: 1, day: 1, expected: 6 },
+    { year: 2100, month: 12, day: 31, expected: 5 },
+    { year: 3000, month: 12, day: 31, expected: 3 },
+  ])(
+    `The weekday for $year-$month-$day in the default calendar matches getUTCDay`,
+    ({ year, month, day }) => {
+      // Convert to a string to avoid Date constructor mapping 1 to year 1901
+      const dateString = `${year.toString().padStart(4, "0")}-${month
+        .toString()
+        .padStart(2, "0")}-${day.toString().padStart(2, "0")}`;
+      expect(GetWeekday(year, month, day)).toEqual(
+        new Date(dateString).getUTCDay()
+      );
+    }
+  );
+
+  test.each([
+    { year: 0, month: 1, day: 1 },
+    { year: -5, month: 1, day: 1 },
+    { year: 12.2, month: 1, day: 1 },
+  ])(`Should throw an error for invalid year $year`, ({ year, month, day }) => {
+    expect(() => GetWeekday(year, month, day)).toThrow(
+      "Year must be an integer greater than 0"
+    );
+  });
+
+  test.each([
+    { year: 2001, month: -5, day: 1 },
+    { year: 2001, month: 0, day: 1 },
+    { year: 2001, month: 13, day: 1 },
+    { year: 2001, month: 9.3, day: 1 },
+  ])(
+    `Should throw an error for invalid month $month`,
+    ({ year, month, day }) => {
+      expect(() => GetWeekday(year, month, day)).toThrow(
+        "Month must be an integer between 1 and 12"
+      );
+    }
+  );
+
+  test.each([
+    { year: 2001, month: 1, day: -5 },
+    { year: 2001, month: 1, day: 0 },
+    { year: 2001, month: 1, day: 32 },
+  ])(`Should throw an error for invalid day $day`, ({ year, month, day }) => {
+    expect(() => GetWeekday(year, month, day)).toThrow(
+      "Day must be an integer between 1 and 31"
+    );
+  });
+});

maths/zellers_congruence.ts

@@ -0,0 +1,68 @@
+export enum Calendar {
+  Gregorian,
+  Julian,
+}
+
+/**
+ * @function GetWeekday
+ * @description Calculate the day of the week for any Julian or Gregorian calendar date.
+ * @param {number} year - Year with century.
+ * @param {number} month - Month of the year (1-12).
+ * @param {number} day - Day of the month (1-31).
+ * @return {number} Day of the week, where 0 represents Sunday.
+ * @see https://en.wikipedia.org/wiki/Zeller's_congruence
+ * @example GetWeekday(2000, 1, 1) = 6
+ * @example GetWeekday(1500, 1, 1, Calendar.Julian) = 3
+ */
+export const GetWeekday = (
+  year: number,
+  month: number,
+  day: number,
+  calendar: Calendar = Calendar.Gregorian
+): number => {
+  // Input validation
+  if (!Number.isInteger(year) || year < 1) {
+    throw new Error("Year must be an integer greater than 0");
+  }
+
+  if (!Number.isInteger(month) || month < 1 || month > 12) {
+    throw new Error("Month must be an integer between 1 and 12");
+  }
+
+  if (!Number.isInteger(day) || day < 1 || day > 31) {
+    throw new Error("Day must be an integer between 1 and 31");
+  }
+
+  // Move January and February to the end of the previous year
+  if (month < 3) {
+    month += 12;
+    year--;
+  }
+
+  const century = Math.floor(year / 100);
+  year %= 100;
+
+  let weekday: number | undefined = undefined;
+  if (calendar === Calendar.Gregorian) {
+    weekday =
+      (day +
+        Math.floor(2.6 * (month + 1)) +
+        year +
+        Math.floor(year / 4) +
+        Math.floor(century / 4) +
+        5 * century) %
+      7;
+  } else {
+    weekday =
+      (day +
+        Math.floor(2.6 * (month + 1)) +
+        year +
+        Math.floor(year / 4) +
+        5 +
+        6 * century) %
+      7;
+  }
+
+  // Convert to Sunday being 0
+  return (weekday + 6) % 7;
+};