Circular Track Solution

Problem

There is a circular track of length $M$ consisting of $M$ checkpoints and $M$ bidirectional roads such that each road has a length of $1$ unit.

Chef is currently at checkpoint $A$ and wants to reach checkpoint $B$. Find the minimum length of the road he needs to travel.

Input Format

• First line will contain $T$, the number of test cases. Then the test cases follow.
• Each test case contains a single line of input, three integers $A, B,$ and $M$ - the initial checkpoint, the final checkpoint, and the total number of checkpoints respectively.

Output Format

For each test case, output the minimum length Chef needs to travel.

Constraints

• $1 \leq T \leq 1000$
• $2 \leq M \leq 10^9$
• $1 \leq A, B \leq M$
• $A \neq B$

Sample 1:

Input

Output

4
1 3 100
1 98 100
40 30 50
2 1 2

2
3
10
1

Explanation:

Test Case $1$: Chef can go from $1$ to $3$ as: $1 \rightarrow 2$ and then $2 \rightarrow 3$. Thus, total length travelled is $2$ units.

Test Case $2$: Chef can go from $1$ to $98$ as: $98 \leftarrow 99 \leftarrow 100 \leftarrow 1$. Thus, minimum distance travelled is $3$ units.

Test Case $3$: Chef can go from $40$ to $30$ as: $30 \leftarrow 31 \leftarrow 32 \leftarrow \dots \leftarrow 39 \leftarrow 40$. Thus, minimum distance travelled is $10$ units.

Test Case $4$: Chef can go from $2$ to $1$ as: $1 \leftarrow 2$. Thus, minimum distance travelled is $1$ unit.

Program :

import java.util.*;

import java.lang.Math.*;

class Codechef 

{

public static void main(String[] args)

{

Scanner in = new Scanner(System.in);

long t,a,b,M,i,M1,M2,M3;

t=in.nextLong();

for(i=1;i<=t;i++)

{

a=in.nextLong();

b=in.nextLong();

M=in.nextLong();

if(a!=b&&a>=1&&b<=M&&M>=2)

{

M1=Math.abs(b-a);

M2=Math.abs((M-b)+a);

M3=Math.abs(M-a+b);

if(M1<=M2)

System.out.println(Math.min(M1,M3));

else

System.out.println(M2);

}

}

in.close();

}

}