Skip to content

Commit 52f8db2

Browse files
authored
Unescape *'s
It seems that they render differently through github markdown vs the one used for the official site.
1 parent eba7fac commit 52f8db2

File tree

1 file changed

+3
-3
lines changed

1 file changed

+3
-3
lines changed

src/data_structures/fenwick.md

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -7,18 +7,18 @@ e_maxx_link: fenwick_tree
77
# Fenwick Tree
88

99
Let $f$ be some group operation (a binary associative function over a set with an identity element and inverse elements) and $A$ be an array of integers of length $N$.
10-
Denote $f$'s infix notation as $\*$; that is, $f(x,y) = x\*y$ for arbitrary integers $x,y$.
10+
Denote $f$'s infix notation as $*$; that is, $f(x,y) = x*y$ for arbitrary integers $x,y$.
1111
(Since this is associative, we will omit parentheses for order of application of $f$ when using infix notation.)
1212

1313
The Fenwick tree is a data structure which:
1414

15-
* calculates the value of function $f$ in the given range $[l, r]$ $\left(\text{i.e. }A_l \* A_{l+1} \* \dots \* A_r)\right)$ in $O(\log N)$ time
15+
* calculates the value of function $f$ in the given range $[l, r]$ $\left(\text{i.e. }A_l * A_{l+1} * \dots * A_r)\right)$ in $O(\log N)$ time
1616
* updates the value of an element of $A$ in $O(\log N)$ time
1717
* requires $O(N)$ memory (the same amount required for $A$)
1818
* is easy to use and code, especially in the case of multidimensional arrays
1919

2020
The most common application of a Fenwick tree is _calculating the sum of a range_.
21-
For example, using addition over the set of integers as the group operation, i.e. $f(x,y) = x + y$: the binary operation, $\*$, is $+$ in this case, so $A_l \* A_{l+1} \* \dots \* A_r = A_l + A_{l+1} + \dots + A_{r}$.
21+
For example, using addition over the set of integers as the group operation, i.e. $f(x,y) = x + y$: the binary operation, $*$, is $+$ in this case, so $A_l * A_{l+1} * \dots * A_r = A_l + A_{l+1} + \dots + A_{r}$.
2222
(In terms of $f$, this would be $f(A_l, f(A_{l+1}, f(f(\dots, \dots),A_r)))$, or any other equivalent way to write this using associativity.)
2323

2424
The Fenwick tree is also called a **Binary Indexed Tree** (BIT).

0 commit comments

Comments
 (0)
pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy