Connecting Data Structures & Logic

• Core Problem: Running Sum (Array Processing) ├── Slow Path (Brute Force): Nested Loops ──► Redundant Re-calculations ──► $O(n^2)$ Time └── Fast Path (Optimal): In-Place Update ──► Prefix Sum Reusability ──► $O(n)$ Time
• Technical Connections:
  • Array Index Manipulation ──► Modifying existing memory blocks.
  • Multi-pointer concepts ──► Tracking current index i while looking back at index i-1.

Mind Map: Array Concatenation

• Problem: Duplicate an existing list (n ──► 2n) ├── Manual Path: Two loops ──► Sequential memory filling ──► $O(n)$ └── Native Path: + or * operators ──► Replicating the sequence ──► $O(n)$
• Technical Connections: * Linear Data Structures ──► Array indexing and bounds.
  • Time Complexity ──► Linear time $O(n)$ is mandatory to visit all original elements.

Connecting Data Structures & Logic

• Core Problem: In-Place String Reversal (Array Modification) ◦ ├── Slow Path (Brute Force): Extra Array Copy ──► Redundant Memory Allocation ──► $O(n)$ Space ◦ └── Fast Path (Optimal): Two-Pointer Swap ──► Half-Way Termination ──► $O(1)$ Space • Technical Connections: ◦ Array Index Manipulation ──► Modifying existing elements directly in memory. ◦ Multi-pointer concepts ──► Tracking left index moving forward while looking at right index moving backward.

Connecting Data Structures & Logic

• Core Problem: Sorting Squares of a Pre-Sorted Array containing Negative Numbers ├── Slow Path (Brute Force): Square All ──► Run .sort() ──► $O(N \log N)$ Time └── Fast Path (Optimal): Two-Pointer Comparison ──► Fill Backwards ──► $O(N)$ Time • Technical Connections: ◦ Array Index Manipulation ──► Tracking left moving right, right moving left, and a tracking pointer p moving backward in the result array. ◦ Absolute Magnitude Concept ──► Recognizing that the largest values are at the edges, eliminating the need to check the center first.