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Ceiling Sum | codechef solution

Rajnish Tripathi 21:10

You are given two integers �,�. You have to choose an integer � in the range [minimum(�,�), maximum(�,�)] such that:

⌈�−�2⌉+⌈�−�2⌉ is maximum.

What is the maximum sum you can obtain if you choose � optimally?

Note: ⌈�⌉ : Returns the smallest integer that is greater than or equal to � (i.e rounds up to the nearest integer). For example, ⌈1.4⌉=2, ⌈5⌉=5, ⌈−1.5⌉=−1, ⌈−3⌉=−3 , ⌈0⌉=0.

Input Format

  • First line will contain �, number of testcases. Then the testcases follow.
  • Each testcase contains of a single line of input, two integers �,�.

Output Format

For each testcase, output the maximum sum of ⌈�−�2⌉+⌈�−�2⌉.

Constraints

  • 1≤�≤105
  • 1≤�,�≤109

Sample 1:

Input
Output
3
2 2
1 11
13 6

0
6
-3

Explanation:

  • In the first test case, there is only one possible value of � which is equal to 2. So the sum is equal to ⌈2−22⌉+⌈2−22⌉ = ⌈ 0⌉+⌈ 0⌉ = 0+0=0.

  • In the second test case, we can choose � to be 2. So sum is equal to ⌈11−22⌉+⌈2−12⌉ = ⌈ 4.5⌉+⌈ 0.5⌉ = 5+1=6. There is no possible way to choose an integer � in the range [1,11] such that sum is greater than 6.

 Code(C++):-

#include <iostream>
using namespace std;

int main() {
    // your code goes here
    int t;
    cin>>t;
    while(t--){
     int a,b;
     cin>>a>>b;
     if(a==b)cout<<"0"<<endl;
     else if(b>a)cout<<((b-a)/2)+1<<endl;
     else if((a-b)%2==0){
     cout<<((b-a)/2)+1<<endl;
    
     }else cout<<(b-a)/2<<endl;
    }
    return 0;
}

Code(JAVA):-

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
class Codechef
{
    public static void main (String[] args) throws java.lang.Exception
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t=Integer.parseInt(br.readLine()),a,b;
        while(t-->0)
        {
         String s[]=br.readLine().split(" ");
         a=Integer.parseInt(s[0]);
         b=Integer.parseInt(s[1]);
         if(b!=a)
         System.out.println(1+(((b-1-a)%2==0)?(b-1-a)/2:(b-a)/2));
         else
         System.out.println(0);
        }
    }
}

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