CONCEPT BLOGS
Multi-phase guides with mental models, worked examples, diagrams, and real edge cases — the public form of Learnisim AI's conceptual learning. Read here; train it interactively in the app.
Trace the intersection of lists A=4→1→8→4→5 and B=5→6→1→8→4→5 meeting at node 8. Master the two-pointer bridge mental model with step-by-step execution.
Learn how the two-pointer technique finds the middle of a linked list. Trace through even (1→2→3→4) and odd (1→2→3→4→5) length examples.
Learn the two-pointer gap pattern to remove the nth node from the end of a linked list in one pass. Traces removing node 4 and the head from 1→2→3→4→5.
![Water trapped by [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1] overview diagram](/blogs/trapping-rain-water-explained-tracing-0-1-0-2-1-0-1-3-2-1-2-1/diagrams/hero.svg)
Master the trapping rain water problem using a two-pointer elevation valley mental model, traced step by step on [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1].
![Triplets in [-1, 0, 1, 2, -1, -4] overview diagram](/blogs/3sum-with-duplicate-skipping-explained-tracing-1-0-1-2-1-4/diagrams/hero.svg)
Learn 3Sum with duplicate skipping by tracing [-1, 0, 1, 2, -1, -4] step-by-step. Build a rock-solid mental model of sorting and two-pointer traversal.
![Max water in height = [1, 8, 6, 2, 5, 4, 8, 3, 7] overview diagram](/blogs/container-with-most-water-explained-tracing-1-8-6-2-5-4-8-3-7/diagrams/hero.svg)
Master the container with most water problem by tracing height [1,8,6,2,5,4,8,3,7] to max area 49. Build your two-pointer mental model and analyze time complexity.
