# Rambo Numbers

Mathematics

Hard

#### Problem Statement (Simplified):

For given three numbers `r`,`p`,`q`. We have to find the total number of values divisible by `r` in a range [`p`,`q`]. (Both Inclusive).

For example, let’s assume we’re given with range(`[-10,30]`) and `r`=`3`, there are total `14` numbers divisible by `r` in range. i.e `[-9,-6,-3,0,3,6,9,12,15,18,21,24,27,30]`

#### Solving Approach : 1) We can find that by dividing `p` and `q` by `r`.
2) `q/r` gives total number of values divisible by `r` in range [`1,q`] ( or [ `q,-1` ] if `q` is negative).
3) `p/r` gives total number of values divisible by `r` in range [`1,p`] ( or [ `p,-1` ] if `p` is negative).
4) We can get our answer on subtracting number of values found in range [`1,p`] ( or [`p,-1`] ) from number of values found in range [`1,q`] ( or [`q,-1`] ).
5) An extra value should also be considered if following conditions are satisfied:

1) If range contains `0`, we would add an additional 1, as `0` is divisible by `r` but is not counted by above method.
2) If `p` and `q` both values are positive and `p` is divisible by `r`.
3) If `p` and `q` both values are negative and `q` is divisible by `r`.

## Example

We’ll take an example for different range cases :

Case 1: Negative to Negative

Assuming range as [-12,-2] and `r=3`, here `p/r` gives `-4` and `q/r` gives `0`, hence there are `4` numbers between range `[-12,-1]` i.e. `[-12,-9,-6,-3]`. Also there is no number in range `[-2, -1]`, hence there are total `4` numbers which are divisible by ‘r’ in range `[-12,-2]`.
NOTE: If range near to 0 is divisible by `r`, we add additional 1 to answer, that it is counted in both ranges i.e. [p,-1] and [q,-1] and on substraction, it is discarded, so we add an extra 1 in answer for it.

Case 2: Positive to Positive

Assuming range as [2,12] and `r=3`, here `p/r` gives `0` and `q/r` gives `4`, hence there are `4` numbers between range `[1,12]` i.e. `[3,6,9,12]`. Also there is no number in range `[1,2]`, hence there are total `4` numbers which are divisible by ‘r’ in range `[2, 12]`.
NOTE: If range near to 0 is divisible by `r`, we add additional 1 to answer, that it is counted in both ranges i.e. [1,p] and [1,q] and on substraction, it is discarded, so we add an extra 1 in answer for it.

Case 3: Negative to Positive

Assuming range as [-12,12] and `r=3`, here `p/r` gives `-4` and `q/r` gives `4`, hence there are `4` numbers between range `[-12, 1]` i.e. `[3,6,9,12]`. Also there are `4` numbers in range `[1,12]`. Also, `0` is also divisible by `3`, so it will be included as well as. Hence there are total `9` numbers which are divisible by ‘r’ in range `[-12, 12]`.

## Solutions

```import java.util.*;
import java.io.*;

public class Main {

static long count(long r, long p, long q ){

if((p>0 && p%r==0)|| (p==0 || q==0) || (q<0 && p<0 && q%r==0) ||( p<0 && q>0) )
return (q/r)-(p/r)+1;
else
return (q/r)-(p/r);

}

public static void main(String args[]) throws IOException {
Scanner sc = new Scanner(System.in);
int test = sc.nextInt();

while(test--!=0){

long r = sc.nextLong(), p = sc.nextLong(), q = sc.nextLong();

System.out.println(count(r,p,q));
}

}
}```

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