Problem Description

In this problem, we are working with asynchronous operations in JavaScript, specifically with promises. A promise is an object representing the eventual completion or failure of an asynchronous operation. We are given two such objects, promise1 and promise2, both of which are expected to resolve with a numerical value. The task is to create and return a new promise that will resolve with the sum of the two numbers provided by promise1 and promise2.

Intuition

The key to solving this problem is understanding how promises work and how to handle the values they resolve with. The async keyword allows us to write asynchronous code in a way that looks synchronous, and the await keyword pauses the execution of the function until a promise is resolved. By using await on both promise1 and promise2, we can get their resolved values. Once both promises have been resolved, we can then simply add these two numerical values together. The sum is then implicitly returned as a resolved promise due to the async function's behavior—any value returned by an async function is automatically wrapped in a Promise.resolve().

So, the "intuition" behind this solution is:

1. Wait for each promise to resolve using await.
2. Once both numbers are available, add them together.
3. The async function will return a promise that resolves with the sum of the two numbers.

Solution Approach

The implementation of the solution is straightforward given the understanding of how JavaScript promises and async/await work.

Here's a step-by-step breakdown of the algorithm:

1. An async function named addTwoPromises is defined, which accepts two parameters: promise1 and promise2. Both parameters are expected to be promises that resolve to numbers.

2. Inside the function, we use the await keyword before promise1 and promise2. This instructs JavaScript to pause the execution of the function until each promise resolves. The await keyword can only be used within an async function.

3. When await promise1 is executed, the function execution is paused until promise1 is either fulfilled or rejected. If it's fulfilled, the resolved value (a number) is returned. If promise1 is rejected, an error will be thrown, which can be caught using try...catch blocks.

4. Similarly, await promise2 pauses the function execution until promise2 resolves, after which it provides the resolved value (a number).

5. After obtaining both numbers, the function adds these two numbers together with the + operator. The expression (await promise1) + (await promise2) computes the sum.

6. The resulting sum is then returned from the async function. Because the function is async, this return value is automatically wrapped in a promise. Essentially, return (await promise1) + (await promise2); is equivalent to return Promise.resolve((await promise1) + (await promise2));.

The data structure used here is the built-in JavaScript Promise, which is a proxy for a value that is not necessarily known when the promise is created. This lets asynchronous methods return values like synchronous methods: instead of immediately returning the final value, the asynchronous method returns a promise to supply the value at some point in the future.

The pattern used is async/await, which is syntactic sugar over JavaScript Promises, providing a simpler and cleaner way to handle asynchronous operations. It allows for writing promise-based code as if it were synchronous, but without blocking the main thread.

This solution leverages the concurrency nature of promises to potentially execute both promise1 and promise2 at the same time, reducing the overall waiting time for both promises to resolve.

Therefore, the solution is concise, clear, and leverages modern JavaScript features to work with asynchronous operations effectively.

Example Walkthrough

To illustrate the solution approach, let's walk through a small example using two sample promises that resolve to numerical values.

Suppose we have two promises:

const promise1 = new Promise((resolve, reject) => {
    setTimeout(() => resolve(10), 1000); // promise1 resolves with 10 after 1 second
});

const promise2 = new Promise((resolve, reject) => {
    setTimeout(() => resolve(20), 500); // promise2 resolves with 20 after 0.5 seconds
});

These promises, when executed, will resolve with the numbers 10 and 20, respectively, after their set timeouts.

Let's go through the steps of the solution with these promises:

1. We define an async function addTwoPromises that takes promise1 and promise2 as parameters.

async function addTwoPromises(promise1, promise2) {
    // The function body will be implemented according to the steps.
}

2. We await both promise1 and promise2 using the await keyword inside the async function. This way we can get their resolved values:

async function addTwoPromises(promise1, promise2) {
    const value1 = await promise1; // Execution pauses here until promise1 resolves.
    const value2 = await promise2; // Execution pauses here until promise2 resolves.
    // The rest of the function...
}

3. After both promises resolve, value1 has the value 10, and value2 has the value 20.

4. We then add value1 and value2 and return the result:

async function addTwoPromises(promise1, promise2) {
    const value1 = await promise1;
    const value2 = await promise2;
    return value1 + value2; // The function will return a Promise that resolves to 30
}

5. Since addTwoPromises is an async function, the returned result will be wrapped in a promise. Therefore, calling addTwoPromises(promise1, promise2) will return a promise that resolves to the sum of the two values, which is 30 in this case.

6. If we want to use the result of the addTwoPromises function, we can do so by attaching a .then method or using an await within another async function:

addTwoPromises(promise1, promise2).then(sum => {
    console.log(sum); // This will log 30 to the console once the promise resolves
});

or,

async function displayResult() {
    const result = await addTwoPromises(promise1, promise2);
    console.log(result); // This will also log 30 to the console
}

And that concludes the example walkthrough of how to use the solution approach to add two numbers provided by promises asynchronously.

Solution Implementation

Time and Space Complexity

Time Complexity

The time complexity of the function addTwoPromises largely depends on how promise1 and promise2 resolve. However, since it is awaiting both promises one after the other, it will be at least as long as the longest time taken for either of the promises to resolve. If the promises do not depend on each other and could resolve in parallel, this sequential waiting increases the total time unnecessarily. Therefore, if T1 is the time taken for promise1 to resolve and T2 is the time taken for promise2 to resolve, the time complexity would be O(T1 + T2) where T1 and T2 are the respective completion times for each promise. If promise1 and promise2 were to be awaited in parallel, the time complexity could be improved to O(max(T1, T2)).

Space Complexity

The space complexity of the function addTwoPromises itself is O(1), as it only needs the space for two number variables when the promises resolve, and one number for the return value. There is no additional space being used that scales with the size of the input.