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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)


import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long d = sc.nextLong();
        long a = sc.nextLong();
        List<Pair> pairs = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            pairs.add(new Pair(sc.nextLong(), sc.nextLong()));
        }
        Collections.sort(pairs);
        Queue<Pair> pq = new LinkedList<>();
        int times = 0;
        long ans = 0;
        double max = 0;
        long lastPos = pairs.get(0).pos;
        for (int i = 0; i < n; i++) {
            Pair curr = pairs.get(i);
            if (pq.isEmpty()) {
                long newVal = ((curr.pos - lastPos) <= d) ? curr.val - times * a : curr.val;
                if (newVal > 0) {
                    Pair added = new Pair(curr.pos, newVal);
                    max = Math.max(max, newVal);
                    pq.add(added);
                }
            } else {
                Pair peek = pq.peek();
                if (curr.pos - peek.pos <= d) {
                    long newVal = ((curr.pos - lastPos) <= d) ? curr.val - times * a : curr.val;
                    if (newVal > 0) {
                        Pair added = new Pair(curr.pos, newVal);
                        max = Math.max(max, newVal);
                        pq.add(added);
                    }
                } else {
                    times = (int) Math.ceil(max / a);
                    ans += times;
                    lastPos = pq.poll().pos + d;
                    while (!pq.isEmpty()) {
                        pq.poll();
                    }
                    max = 0;
                    long newVal = ((curr.pos - lastPos) <= d) ? curr.val - times * a : curr.val;
                    if (newVal > 0) {
                        Pair added = new Pair(curr.pos, newVal);
                        max = Math.max(max, newVal);
                        pq.add(added);
                    }
                }
            }
        }
        if (!pq.isEmpty()) {
            times = (int) Math.ceil(max / a);
            ans += times;
        }
        System.out.println(ans);
    }


    public static int log2(long x) {
        return (int) (Math.log(x) / Math.log(2));
    }

    static class Pair implements Comparable<Pair> {
        long pos;
        long val;

        public Pair(long pos, long val) {
            this.pos = pos;
            this.val = val;
        }

        @Override
        public int compareTo(Pair o) {
            return Long.compare(this.pos, o.pos);
        }
    }
}