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 two-pointer approach. Since the array is sorted in non-decreasing 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 step-by-step explanation:

Initialize Pointers: Start with pointers at the beginning and end of the array, left = 0 and right = 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 and right indices.
b. Compare to Target:
- If the sum is equal to the target, return [left + 1, right + 1] since the question asks for 1-indexed 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.

Here’s the code implementing this approach:

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class Solution:
    def twoSum(self, numbers: List[int], target: int) -> List[int]:
        left, right = 0, len(numbers) - 1

        while left < right:
            current_sum = numbers[left] + numbers[right]
            if current_sum == target:
                return [left + 1, right + 1]
            elif current_sum < target:
                left += 1
            else:
                right -= 1

        return [] # This return statement is not required since the problem states that there is exactly one solution

The two-pointer 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).

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# @param {Integer[]} numbers
# @param {Integer} target
# @return {Integer[]}    
def two_sum(nums, target)
  i = 0
  j = nums.size - 1
  
  while i < j
    sum = nums[i] + nums[j]

    if sum == target
      return [i+1, j+1]
    end
    if sum < target
      i += 1
    end
    if sum > target
      j -= 1
    end
  end    
end

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 two-pointer 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 non-negative 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 two-pointer 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.

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class Solution:
    def two_sum(self, nums, target):
        l, r = 0, len(nums) - 1
        while l < r:
            if nums[l] + nums[r] == target: return (l + 1,  r + 1)
            if nums[l] + nums[r] > target: r -= 1
            else: l += 1

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.
Two-pointer Technique: Understanding the two-pointer 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 two-pointer 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:

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# Create two variables a and b, assign values 10 and 20 to them, respectively.
a = 10
b = 20
print(a, b)  # Expected output: 10 20

Concept 2 - Arrays/Lists:

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# Create a list, access its elements, and print them.
nums = [1, 2, 3, 4, 5]
print(nums[0])  # Expected output: 1
print(nums[4])  # Expected output: 5

Concept 3 - Arithmetic Operations:

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# Add two numbers and print the result.
a = 10
b = 20
print(a + b)  # Expected output: 30

Concept 4 - Conditional Statements (if, else):

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# Check if a number is even or odd.
num = 4
if num % 2 == 0:
    print("Even")
else:
    print("Odd")  # Expected output: Even

Concept 5 - While loop:

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# Print all numbers from 1 to 5 using a while loop.
i = 1
while i <= 5:
    print(i)
    i += 1
# Expected output: 
# 1
# 2
# 3
# 4
# 5

Concept 6 - Tuple:

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# Create a tuple and print its elements.
tup = (1, 2, 3)
print(tup[0])  # Expected output: 1
print(tup[2])  # Expected output: 3

Concept 7 - Function/Method Definition and Invocation:

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# Define a function that adds two numbers and call this function.
def add(a, b):
    return a + b

print(add(10, 20))  # Expected output: 30

Concept 8 - Two-pointer Technique:

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# Implement a simple example of the two-pointer technique. 
# Find if there is a pair in the list whose sum equals to target.
def two_sum(nums, target):
    nums.sort()
    l, r = 0, len(nums) - 1
    while l < r:
        if nums[l] + nums[r] == target:
            return (l, r)
        elif nums[l] + nums[r] < target:
            l += 1
        else:
            r -= 1
    return -1

print(two_sum([2, 7, 11, 15], 9))  # Expected output: (0, 1)

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.