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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

// Monster .
type Monster struct {
	x int
	h int
}

// Monsters .
type Monsters []Monster

func (m Monsters) Len() int {
	return len(m)
}

func (m Monsters) Less(i, j int) bool {
	return m[i].x < m[j].x
}

func (m Monsters) Swap(i, j int) {
	m[i], m[j] = m[j], m[i]
}

var sc = bufio.NewScanner(os.Stdin)

func nextInt() int {
	sc.Scan()
	a, _ := strconv.Atoi(sc.Text())
	return a
}

func main() {
	sc.Split(bufio.ScanWords)
	var n, d, a int
	fmt.Scan(&n, &d, &a)

	monsters := make([]Monster, n)
	for i := 0; i < n; i++ {
		x, h := nextInt(), nextInt()
		monsters[i] = Monster{x, h}
	}
	sort.Sort(Monsters(monsters))

	im := make([]int, n+1)
	ans := 0
	for i := 0; i < n; i++ {
		m := monsters[i]
		if im[i] < m.h {
			tmp := monsters[i:]
			id := sort.Search(len(tmp), func(i int) bool {
				return m.x+d*2 < tmp[i].x
			}) + i
			c := (m.h - im[i] + a - 1) / a
			im[i] += c * a
			im[id] -= c * a
			ans += c
		}
		im[i+1] += im[i]
	}

	fmt.Println(ans)
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}