You now understand Fenwick Trees: Core Operations: - Build: or - Point update: - Prefix query: Key Techniques: - lowbit: i & (-i) extracts lowest set bit - Query: subtract lowbit repeatedly - Update: add lowbit repeatedly - Range query: Extensions: - Range update + point query: use difference array - Range update + range query: use two BITs - 2D BIT: nest the 1D operations - Order statistics: binary search on prefix sums When to Use: - Point updates + prefix/range queries - Invertible operations (sum, XOR) - Want simpler code than segment tree Fenwick Trees are a competitive programmer's best friend for range sum problems. The code is short, fast, and hard to mess up.
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$ curl repovive.com/roadmaps/data-structures/fenwick-trees/section-recap
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