Diagonal grids
8-connected. Diagonal = 1 (Chebyshev) or √2 (octile). Manhattan invalid heuristic — use octile for A*.
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Weighted terrain
Each cell has traversal cost. Dijkstra or A*, treat as directed graph with edge cost = destination cell's cost.
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Teleport portals
Add zero-weight edges between paired cells. Standard shortest path applies.
Jump point search
Grid-specific A* optimization. Skip 'symmetric' paths. 10x faster in practice for uniform-cost 8-connected grids.