add linear build (#48)

* add linear build

* format

* add docs

---------

Co-authored-by: Luke Videckis <lukevideckis@gmail.com>

Author: lrvideckis

examples/data_structures/fenwick_yosupo.rs

@@ -7,15 +7,10 @@ fn main() {
     input! {
         n: usize,
         q: usize,
+        a: [u64; n],
     }
 
-    let mut fenwick = Fenwick::<u64>::new(n);
-    for i in 0..n {
-        input! {
-            x: u64,
-        }
-        fenwick.add(i, x);
-    }
+    let mut fenwick = Fenwick::<u64>::build_on_array(&a);
 
     for _ in 0..q {
         input! {

src/data_structures/fenwick.rs

@@ -26,6 +26,23 @@ impl<T: Clone + Default + std::ops::AddAssign<T>> Fenwick<T> {
         }
     }
 
+    /// Creates a Fenwick Tree on a given array
+    ///
+    /// # Complexity
+    /// - Time: O(n)
+    /// - Space: O(n)
+    pub fn build_on_array(a: &[T]) -> Self {
+        let mut ary = a.to_vec();
+        for i in 0..a.len() {
+            let j = i | (i + 1);
+            if j < a.len() {
+                let tmp = ary[i].clone();
+                ary[j] += tmp;
+            }
+        }
+        Fenwick { ary }
+    }
+
     fn accum(&self, mut idx: usize) -> T {
         let mut sum = T::default();
         while idx > 0 {