Problem:
Score : 600 points

Problem Statement

Silver Fox is fighting with N monsters.

The monsters are standing in a row, and we can assume them to be standing on a number line. The i-th monster, standing at the coordinate X_i, has the health of H_i.

Silver Fox can use bombs to attack the monsters.
Using a bomb at the coordinate x decreases the healths of all monsters between the coordinates x-D and x+D (inclusive) by A.
There is no way other than bombs to decrease the monster's health.

Silver Fox wins when all the monsters' healths become 0 or below.

Find the minimum number of bombs needed to win.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq D \leq 10^9

1 \leq A \leq 10^9

0 \leq X_i \leq 10^9

1 \leq H_i \leq 10^9

X_i are distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N D A
X_1 H_1
:
X_N H_N

Output

Print the minimum number of bombs needed to win.

Sample Input 1

3 3 2
1 2
5 4
9 2

Sample Output 1

2

First, let us use a bomb at the coordinate 4 to decrease the first and second monsters' health by 2.

Then, use a bomb at the coordinate 6 to decrease the second and third monsters' health by 2.

Now, all the monsters' healths are 0.
We cannot make all the monsters' health drop to 0 or below with just one bomb.

Sample Input 2

9 4 1
1 5
2 4
3 3
4 2
5 1
6 2
7 3
8 4
9 5

Sample Output 2

5

We should use five bombs at the coordinate 5.

Sample Input 3

3 0 1
300000000 1000000000
100000000 1000000000
200000000 1000000000

Sample Output 3

3000000000

Watch out for overflow.

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::cmp;

const INF: i64 = 1 << 50;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());
    let n: usize = sc.read();
    let d: i64 = sc.read();
    let a: i64 = sc.read();
    let mut xh = (0..n)
        .map(|_| (sc.read::<i64>(), sc.read::<i64>()))
        .collect::<Vec<_>>();
    xh.sort();

    let mut seg = range_add_segment_tree::RangeAddSegmentTree::new(n, -INF, cmp::max, 0);
    for i in 0..n {
        let (_, h) = xh[i];
        seg.update(i, h);
    }

    let mut ans = 0;
    let mut tail = 0;
    for i in 0..n {
        let (x, _) = xh[i];
        while tail < n && xh[tail].0 <= x + 2 * d {
            tail += 1;
        }
        let cur = cmp::max(seg.get(i, i + 1), 0);
        let count = (cur + a - 1) / a;
        seg.add(i, tail, -count * a);
        ans += count;
    }
    println!("{}", ans);
}

pub mod range_add_segment_tree {

    pub struct RangeAddSegmentTree<T, F> {
        seg: Vec<T>,
        seg_add: Vec<T>,
        num: usize,
        f: F,
        init: T,
    }

    impl<T, F> RangeAddSegmentTree<T, F>
    where
        T: PartialOrd + ::std::ops::Add<Output = T> + ::std::ops::Sub<Output = T> + Copy,
        F: Fn(T, T) -> T + Copy,
    {
        pub fn new(n: usize, init: T, f: F, zero: T) -> Self {
            let num = n.next_power_of_two();
            RangeAddSegmentTree {
                seg: vec![init; num * 2],
                seg_add: vec![zero; num * 2],
                num: num,
                init: init,
                f: f,
            }
        }

        /// add to [a, b)
        pub fn add(&mut self, a: usize, b: usize, value: T) {
            let t = self.num;
            self.add_to_range(a, b, value, 0, 0, t);
        }

        fn add_to_range(
            &mut self,
            a: usize,
            b: usize,
            value: T,
            mut k: usize,
            left: usize,
            right: usize,
        ) {
            if b <= left || right <= a {
                return;
            }
            if a <= left && right <= b {
                self.seg_add[k] = self.seg_add[k] + value;
                while k > 0 {
                    k = (k - 1) / 2;
                    self.seg[k] = (self.f)(
                        self.seg[k * 2 + 1] + self.seg_add[k * 2 + 1],
                        self.seg[k * 2 + 2] + self.seg_add[k * 2 + 2],
                    );
                }
            } else {
                self.add_to_range(a, b, value, k * 2 + 1, left, (left + right) / 2);
                self.add_to_range(a, b, value, k * 2 + 2, (left + right) / 2, right);
            }
        }

        pub fn update(&mut self, pos: usize, value: T) {
            let cur = self.get(pos, pos + 1);
            let mut k = pos + self.num - 1;
            let raw = self.seg[k];
            self.seg[k] = raw + value - cur;
            while k > 0 {
                k = (k - 1) / 2;
                self.seg[k] = (self.f)(self.seg[k * 2 + 1], self.seg[k * 2 + 2]);
            }
        }

        pub fn get(&self, a: usize, b: usize) -> T {
            self.get_from_range(a, b, 0, 0, self.num)
        }

        fn get_from_range(&self, a: usize, b: usize, k: usize, left: usize, right: usize) -> T {
            if b <= left || right <= a {
                self.init
            } else if a <= left && right <= b {
                self.seg[k] + self.seg_add[k]
            } else {
                let mid = (left + right) / 2;
                let x = self.get_from_range(a, b, k * 2 + 1, left, mid);
                let y = self.get_from_range(a, b, k * 2 + 2, mid, right);
                (self.f)(x, y) + self.seg_add[k]
            }
        }
    }
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: std::ops::Deref<Target = str>>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}