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∑MathAdvanced

Lie Groups & Lie Algebras

Lie groups model continuous symmetries like rotations and rigid-body motions, combining algebra (group law) and calculus (smooth manifolds).

#lie group#lie algebra#so(3)+12
🗂️Data StructureAdvanced

HLD - Path Queries and Updates

Heavy-Light Decomposition (HLD) breaks a tree into a small number of vertical chains so any path (u,v) becomes O(log n) contiguous segments in an array.

#heavy light decomposition
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#non-commutative
#hld
#path query
+12
🗂️Data StructureAdvanced

Segment Tree - Handling Multiple Lazy Operations

When a segment tree supports multiple range updates, you must define how lazy tags compose, because the order of operations matters and composition is not commutative.

#segment tree#lazy propagation#range add+12