Alexa and Triplets

editorial
1

Author: @somashekhar001
Tester: @somashekhar001
Editorialist: @somashekhar001

DIFFICULTY:

SIMPLE

PREREQUISITES:

Mathematics

PROBLEM:

(a,b,c) is a pythagorean triplet you are given b and b is even and you have to find a and c and output maximum sum of triplet (a+b+c),

EXPLANATION:

Let us consider n as a number.

   4 * n^2 = 4 * n^2       ( multiply 4 both side)

               =  ( n^2 + 1 )^2  - ( n^2 - 1 )^2  
              

  ( n^2 - 1 )^2 + ( 2 * n )^2 =   ( n^2 + 1 )^2

     a^2           +      b^2      =       c^2

   a = n^2 - 1
   b = 2 * n   
   c= n^2 + 1
  sum=a+b+c; 
         =n^2 - 1 + b + n^2 + 1
         =2*n^2+b       (n=b/2)
         =(b^2 / 2 )+b

SOLUTIONS:

#include<bits/stdc++.h>

using namespace std;

int main()
{
long long T;
cin>>T;//input T testcases
while(T–)
{
long long b;
cin>>b;//taking input b which is even
cout<<((b*b)/2)+b<<endl;
}
return 0;
}