minimum-spanning-trees #

Visualizes MST construction using the cut property (safe edge is the lightest crossing a cut) and the cycle property (the heaviest edge on a cycle cannot be in any MST). The animation alternates between a greedy “safe-edge” selection view and a cycle-based exclusion view, highlighting why Kruskal/Prim work.

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Designing low-cost network wiring (fiber/roads/power) while keeping everything connected
02.Clustering and image segmentation (graph-based clustering uses MST variants)
03.Reducing graph complexity for routing/visualization by keeping a minimum-cost backbone

technical notes #

Self-contained Canvas2D render. Uses a fixed small weighted graph for clarity, precomputes Kruskal MST offline, then animates step-by-step safe-edge selection by computing a cut from the current partial MST and highlighting the minimum crossing edge. Cycle property view traces a specific cycle and marks its heaviest edge as excluded. Blocky Manhattan-routed edges and snapped coordinates maintain a retro grid aesthetic; animation phases run on a 4.5s loop with easing.

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