use std::ops::{AddAssign, Sub};
/// `FenwickTree` is a data structure that can efficiently update elements
/// and calculate prefix sums in a table of numbers.
/// [https://en.wikipedia.org/wiki/Fenwick_tree](https://en.wikipedia.org/wiki/Fenwick_tree)
pub struct FenwickTree<T> {
    n: usize,
    data: Vec<T>,
    init: T,
}

impl<T: Copy + AddAssign + Sub<Output = T>> FenwickTree<T> {
    /// Constructs a new `FenwickTree`. The size of `FenwickTree` should be specified by `size`.
    pub fn new(size: usize, init: T) -> FenwickTree<T> {
        FenwickTree {
            n: size + 1,
            data: vec![init; size + 1],
            init: init,
        }
    }

    pub fn add(&mut self, k: usize, value: T) {
        let mut x = k;
        while x < self.n {
            self.data[x] += value;
            x |= x + 1;
        }
    }

    /// Returns a sum of range `[l, r)`
    pub fn sum(&self, l: usize, r: usize) -> T {
        self.sum_one(r) - self.sum_one(l)
    }

    /// Returns a sum of range `[0, k)`
    pub fn sum_one(&self, k: usize) -> T {
        if k >= self.n {
            panic!("");
        }

        let mut result = self.init;
        let mut x = k as i32 - 1;
        while x >= 0 {
            result += self.data[x as usize];
            x = (x & (x + 1)) - 1;
        }

        result
    }
}

#[cfg(test)]
mod test {
    extern crate rand;
    use self::rand::{thread_rng, Rng};
    use super::*;

    #[test]
    fn random_array() {
        let n = 1000;
        let mut bit = FenwickTree::new(n, 0);
        let mut v = vec![0; n];

        for _ in 0..10000 {
            let value = thread_rng().gen_range(0, 1000);
            let k = thread_rng().gen_range(0, n);
            v[k] += value;
            bit.add(k, value);

            let mut sum = 0;
            for i in 0..n {
                sum += v[i];
                assert_eq!(sum, bit.sum(0, i + 1));
            }
        }
    }
}