Add documentation for bit

src/bit.hpp

@@ -3,6 +3,28 @@
 #include <vector>
 #include <cassert>
 
+/** Binary-indexed tree
+ *
+ *  A binary indexed tree with N nodes of type T implicitly provides the
+ *  following two functions for 0 <= i <= N:
+ *
+ *      prefix(int i) -> list<T&>
+ *      suffix(int i) -> list<T&>
+ *
+ *  such that size(suffix(i) intersect prefix(j)) = (1 if i < j else 0).
+ *  Furthermore, the resulting lists always have size at most log_2(N).
+ *
+ *  This can be used to implement either point-update/(prefix|suffix)-query or
+ *  (prefix|suffix)-update/point-query over a virtual array of size N of a
+ *  commutative monoid. This can be generalized to implement
+ *  point-update/range-query or range-update/point-query over a virtual array
+ *  of size N of a commutative group.
+ *
+ *  With 0-indexed data, prefixes are more natural:
+ *   * For range update/query, use for_prefix for the ranges and for_suffix for the points.
+ *   * For prefix update/query, no change.
+ *   * For suffix update/query, use for_prefix(point + 1); 1-index the data.
+ */
 template <typename T> struct bit {
 private:
 	std::vector<T> dat;