Two-Pointer Algorithm

from typing import List, Optional

def two_sum_sorted(arr: List[int], target: int) -> Optional[List[int]]:
    """
    Find two numbers in a sorted array that sum to target using two-pointer technique.
    
    Uses two pointers starting at opposite ends, moving them based on whether
    the current sum is too small or too large. Only works for sorted arrays.
    
    Args:
        arr: Sorted list of integers (ascending order).
        target: Target sum to find.
    
    Returns:
        List containing two indices [i, j] where arr[i] + arr[j] == target,
        or None if no such pair exists.
    
    Time Complexity: O(n) where n is array length.
    Space Complexity: O(1).
    """
    left, right = 0, len(arr) - 1
    
    while left < right:
        current_sum = arr[left] + arr[right]
        
        if current_sum == target:
            return [left, right]  # Found pair
        elif current_sum < target:
            left += 1  # Need larger sum, move left pointer right
        else:
            right -= 1  # Need smaller sum, move right pointer left
    
    return None  # No pair found

# Example
arr = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
target = 24
result = two_sum_sorted(arr, target)
if result:
    print(f"Found at indices: {result}")  # Found at indices: [1, 4]
    print(f"Values: {arr[result[0]]} + {arr[result[1]]} = {target}")
else:
    print("No pair found")