Two Sum II  Input Array Is Sorted
You can find the two numbers that add up to the target in a sorted array by using a twopointer approach. Since the array is sorted in nondecreasing order, we can initialize pointers at the beginning and end of the array and then move them toward each other to find the solution. Here’s the stepbystep explanation:
Initialize Pointers: Start with pointers at the beginning and end of the array,
left = 0
andright = len(numbers)  1
.Loop Until Pointers Meet: Continue searching as long as
left < right
.a. Calculate Sum: Calculate the sum of the elements at the
left
andright
indices.b. Compare to Target:
 If the sum is equal to the target, return
[left + 1, right + 1]
since the question asks for 1indexed solution.  If the sum is less than the target, increment
left
to move toward larger values.  If the sum is greater than the target, decrement
right
to move toward smaller values.
 If the sum is equal to the target, return
Here’s the code implementing this approach:


The twopointer approach ensures that the time complexity of this solution is O(n), where n is the length of the array, and the space complexity is O(1).


Identifying Problem Isomorphism
An approximate isomorphism: “Valid Triangle Number”
“Two Sum II  Input Array Is Sorted” requires you to find two numbers in a sorted array such that they add up to a specific target number. It uses a twopointer approach.
A problem that shares a similar solution strategy and is as an approximate isomorphism is “Valid Triangle Number”. In this problem, you are given an array consists of nonnegative integers. You have to find the number of triplets chosen from the array that can make triangles if we take them as side lengths of a triangle.
Both leverage the sorted nature of the input array and use a twopointer approach. In “Two Sum II  Input Array Is Sorted”, you move two pointers from both ends towards each other to find the target sum. Similarly, in “Valid Triangle Number”, you set a target (the longest side of a potential triangle), and use two pointers to explore possible combinations.
“Two Sum II  Input Array Is Sorted” is simpler than “Valid Triangle Number”. “Two Sum II” requires finding just two elements that add up to the target, while “Valid Triangle Number” requires finding three elements that satisfy the triangle inequality theorem, making it a more complex task.


Problem Classification
Language Agnostic Coding Drills
Variable assignment: Understanding how to assign values to variables in a programming language.
Array/List: Understanding how arrays (or lists in Python) work, how to access elements of an array, how array indices work.
Arithmetic operations: Understanding how to use basic arithmetic operations like addition, subtraction in a programming language.
Conditional statements (if, else): Understanding how to write conditional statements, how the flow of the program changes based on conditions.
While loop: Understanding how to write a while loop, how to control the flow of the loop, when the loop terminates.
Tuple: Understanding how tuples work in a programming language, how to return a tuple from a function.
Function/Method definition and invocation: Understanding how to define a function, how to pass parameters to a function, and how to call a function.
Twopointer Technique: Understanding the twopointer technique in algorithms. This technique uses two pointers which move towards each other until they meet in the middle, commonly used in array traversal problems.
Problem Solving and Algorithm Design: Understanding how to apply all the above concepts to design an algorithm to solve a specific problem. For example, the Two Sum problem here is solved using the twopointer technique.
Each of the above concepts can be coded separately and then combined together to build the final solution. You can create small exercises or coding drills for each concept to practice them independently.
Targeted Drills in Python
Concept 1  Variable Assignment:


Concept 2  Arrays/Lists:


Concept 3  Arithmetic Operations:


Concept 4  Conditional Statements (if, else):


Concept 5  While loop:


Concept 6  Tuple:


Concept 7  Function/Method Definition and Invocation:


Concept 8  Twopointer Technique:


Concept 9  Problem Solving and Algorithm Design:
This will require you to come up with a problem and try to solve it by integrating all the concepts you have learned. For example, you could attempt to solve the Two Sum problem in the final code example given. Practice similar problems to enhance your problem solving and algorithm design skills.