complexity-classes #

Visualizes the set relationships P ⊆ NP, plus the definitions of NP-hard and NP-complete using an animated reduction “funnel” (<=_p) that shows many NP problems reducing to a highlighted NP-complete target. Steps cycle through: P inside NP, certificate verification for NP, reductions defining NP-completeness, and NP-hardness extending beyond NP.

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Explaining why NP-complete problems are considered “representative hardest” problems in NP
02.Teaching polynomial-time reductions (<=_p) as a way to compare problem difficulty
03.Clarifying the difference between NP-hard and NP-complete (outside vs inside NP)

technical notes #

Uses a 4-step timed narrative (1.2s per step) with cubic easing for highlights. Particles animate along a central reduction arrow to reinforce the “every NP problem reduces to it” idea. All geometry is snapped to a grid for a blocky aesthetic and scales with scale = min(w,h)/baseSize.

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