When it comes to optimizing algorithms for lists, arrays, and strings (which may be thought of as arrays of characters), one powerful technique stands out: Pointer-Based Mental Models. This approach offers an optimization strategy that can transform our naive algorithms from quadratic solutions O(N^2) to linear solutions O(N), all while preserving a constant space complexity O(1). The greatest advantage of using pointer-based approaches is that they improve time complexity without the need for additional data structures.
In our exploration of pointer-based mental models, we will cover various optimization strategies that are highly effective in improving algorithm efficiency. These strategies include:
The Start-End Pointers approach involves using two pointers, namely the start and end pointers. These pointers define a segment within the list, and by manipulating them, we can efficiently process the elements within that segment. This technique is particularly useful in solving subarray problems, such as finding the longest increasing subarray or determining if an array is a palindrome.
The Anchor/Runner Pointers approach, also known as slow/fast pointers, employs two pointers with different speeds. The anchor pointer advances at a slower pace compared to the runner pointer. This technique is commonly used to solve problems such as finding the midpoint of an array or determining if an array has any duplicates. By carefully manipulating these pointers, we can efficiently navigate and process the elements of the array.