Problem Description

The problem requires us to create a range of dates that starts with a given "start" date and ends at an "end" date, including both start and end dates. The range should be generated using a given "step" value, which specifies the interval between consecutive dates in terms of days. We want to yield each date in this range as a string in the format "YYYY-MM-DD".

Intuition

To solve this problem, we use the JavaScript Date object, which enables us to work easily with dates. The procedure includes:

1. Parsing the provided "start" and "end" string dates into JavaScript Date objects, which allows us to manipulate dates with built-in methods.

2. Iterating from the start date to the end date, increasing the date by the step value every iteration. We achieve this by using the getDate and setDate methods that the Date object provides. The getDate method gets the day of the month from a Date object and setDate sets the day of the month to a specified number. By adding the step to the current day, we move our date forward by that many days.

3. During each iteration, we convert the current date to an ISO string using toISOString. ISO strings are in the format "YYYY-MM-DDTHH:MM:SS.ZZZZ". However, since we only need the date part without the time, we use slice to obtain the first 10 characters of the ISO string which represent the date in the required "YYYY-MM-DD" format.

4. Yielding the formatted date string using yield, which is part of creating a generator. Generators are special functions in JavaScript that can be exited and re-entered later with their context (variable bindings) being saved between re-entries.

5. Continuing this process until the current date exceeds the end date, at which point the generator finishes.

This solution effectively gives us a custom range of dates, and by using a generator, we can efficiently go through the range one date at a time without needing to precompute the entire range at once.

Solution Approach

The solution to this problem involves a step-by-step approach using a generator function to yield the desired range of dates one by one. Here's how the solution is implemented:

1. Initialize Dates: First, we need to convert the input start and end strings into Date objects using JavaScript's new Date() constructor. This allows us to perform date arithmetic and make use of Date object methods.

2. Create Generator Function: We then declare a generator function called dateRangeGenerator that takes start, end, and step as arguments. A generator function is defined with function* syntax and is capable of yielding values one at a time with the yield keyword.

3. Iterate Through Dates: Inside the generator function, we initiate a while loop that will continue as long as the currentDate is less than or equal to the endDate.

4. Yield Current Date: For each iteration within the loop, the current date (formatted as "YYYY-MM-DD" using toISOString().slice(0, 10)) is yielded. This means that every time the generator's next() method is called, it will return an object with a value of the current date string and a done status indicating whether the generator has finished iterating.

5. Increment Date: To move to the next date in the range, we use currentDate.getDate() to get the day of the month for currentDate, add the step value to it, and update currentDate with this new value using currentDate.setDate(). This effectively increments currentDate by the step number of days.

6. Finish Iteration: As soon as currentDate exceeds endDate, the condition in the while loop becomes false, and the generator finishes its execution. Any further calls to next() after this point will return an object with a done status of true, indicating there are no more values to yield.

By utilizing a generator function and the JavaScript Date object, the solution elegantly traverses a range of dates and provides them on-demand, handling date arithmetic internally without the caller needing to manage the date range state. This allows for an efficient, on-the-fly generation of date strings that can be iterated over using the generator's next() method.

Example Walkthrough

Let's consider a small example to illustrate the solution approach. Suppose we want to create a range of dates from "2021-11-01" to "2021-11-05" with a step of 2 days. We will use the outlined solution approach to generate the desired date strings.

1. Initialize Dates: We convert the input strings "2021-11-01" and "2021-11-05" to JavaScript Date objects:

   const startDate = new Date("2021-11-01");
   const endDate = new Date("2021-11-05");

2. Create Generator Function: We create a generator function dateRangeGenerator which takes startDate, endDate, and step as parameters:

   function* dateRangeGenerator(start, end, step) {
       // Generator function body will be implemented here
   }

3. Iterate Through Dates: We initiate a loop inside the generator function, where we will generate dates from startDate to endDate. We use a while loop for this purpose:

   let currentDate = new Date(start.getTime()); // avoid modifying the original start date
   
   while (currentDate <= end) {
       // The body of the loop will yield dates and increment `currentDate`
   }

4. Yield Current Date: During each iteration, we format the currentDate as a string and yield it:

   yield currentDate.toISOString().slice(0, 10);

5. Increment Date: After yielding the date, we increment currentDate by the step value. In this example, we add 2 days:

   const nextDay = currentDate.getDate() + step;
   currentDate.setDate(nextDay); // This will increment `currentDate` by 2 days.

6. Finish Iteration: The loop continues until currentDate is greater than endDate. When that condition is met, the loop terminates, and the generator finishes:

   // Loop has ended, so the generator is complete.

Putting it all together, our generator function will be used as follows:

const dateRange = dateRangeGenerator(startDate, endDate, 2);
console.log(dateRange.next().value); // "2021-11-01"
console.log(dateRange.next().value); // "2021-11-03"
console.log(dateRange.next().value); // "2021-11-05"
console.log(dateRange.next().done);  // true, as no more dates are left

The output of each console.log illustrates how the generator yields each date string when .next() is called. After the last date, calling .next() indicates that the generator is finished by returning {done: true}.

Solution Implementation

Time and Space Complexity

The time complexity of the dateRangeGenerator function is O(N) where N is the number of dates generated between the start and end dates with the specified step. This is because the function generates each date in the range one by one in a loop, and the number of iterations of the loop equals the number of dates.

The space complexity of the function is O(1) since it yields the dates one by one and does not store all the dates in memory. The storage used does not grow with the size of the date range; the function only keeps track of the current date and the parameters provided.