Two Sum II - Sorted Input

Background Knowledge

The problem "Two Sum II - Sorted Input" involves finding two numbers in a 1-indexed sorted array that add up to a given target. To tackle this problem, it's essential to understand the concept of arrays and how to manipulate them. In particular, we need to recognize that the array is sorted, which means the elements are arranged in ascending order. This property can be leveraged to develop an efficient solution.

The problem also requires an understanding of searching algorithms, which are used to find specific elements within a data structure. In this case, we need to find two elements that satisfy a particular condition (i.e., their sum equals the target). Familiarity with common searching techniques, such as linear search and binary search, can help inform our approach. Additionally, we should be aware of the trade-offs between different searching algorithms, including their time complexity and space complexity.

To solve this problem, we'll need to apply problem-solving strategies, such as breaking down the problem into smaller sub-problems and identifying patterns or relationships between the elements. We'll also need to consider the constraints of the problem, including the fact that the array is 1-indexed and that we cannot use the same element twice. By combining these concepts and strategies, we can develop an effective solution to the problem.

Algorithm/Approach

The general approach to solving this type of problem involves using a two-pointer technique, which is commonly employed in array and string problems. This technique involves maintaining two pointers, typically at different positions in the array, and moving them based on certain conditions. In this case, we can use two pointers to find the two numbers that add up to the target. The key is to leverage the fact that the array is sorted to guide the movement of the pointers.

Step-by-Step Strategy

To implement the solution, we can follow these steps:

• Initialize two pointers, one at the start of the array and one at the end.
• Calculate the sum of the elements at the current positions of the two pointers.
• Compare the sum to the target and adjust the pointers accordingly.
• Repeat the process until the two pointers meet or the target is found.
• Return the 1-indexed positions of the two numbers that add up to the target.

Common Pitfalls

When implementing the solution, we should watch out for the following pitfalls:

• Forgetting to account for the 1-indexed nature of the array, which can lead to incorrect indexing.
• Failing to handle edge cases, such as an empty array or a target that is not achievable with the given numbers.
• Using an inefficient searching algorithm, such as linear search, which can result in a high time complexity.

Time & Space Complexity

The expected time complexity of the solution is $O(n)$, where $n$ is the length of the array, since we only need to traverse the array once to find the two numbers. The space complexity is $O(1)$, since we only need to use a constant amount of space to store the two pointers and the target. However, the actual complexity may vary depending on the specific implementation and the programming language used.