One-dimensional dynamic programming
These visualizers focus on linear state progression: every new state leans on a compact slice of earlier answers, but each problem gets its own cinematic metaphor and timeline.
Climb a cinematic staircase where each landing resolves from the previous two answers, making the Fibonacci recurrence feel spatial and inevitable.
1D DP / Fibonacci recurrence / stair counting
Step inside the coin forge as denominations sweep across the amount table, competing to produce the cheapest assembly for every target.
1D DP / unbounded knapsack / minimum coins
Plan a silent heist one house at a time and watch the DP planner choose between taking the current house or preserving the previous best prefix.
1D DP / take-or-skip / prefix maximization
Build a skyline of subsequence lengths and watch each number search left for a lower tower that can launch a longer increasing chain.
1D DP / subsequence extension / quadratic scan
See segmentation as a timeline of reachable cut positions, where dictionary words bridge one valid cut to the next across the source string.
1D DP / prefix reachability / string segmentation