Question

re doing. A Pythagorean triple is a set of integers (a, b, c) satisfying a2+bc2. Write pseudocode (or Matlab code) that will output the number of unique Pythagorean triples that satisfy c< 200. [Unique means that you should not count (a 3, b 4, c 5) and (a 4, b 3, c 5) as two different triples, for example]. Explain why your program will work. Imagine a square n x n matrix A with diagonal elements which we believe to be sorted in descending rder. Using pseudocode (or Matlab code):

Answer 1

Matlab code:

#include <iostream>
#include <iomanip>
using namespace std;
int main()
{   int i,j,k,count=0,count1=0;
    for(i=1;i<=200;i++)
       for(j=1;j<=200;j++)
           for(k=1;k<=200;k++)
                {count1++;
                 if((i*i+j*j==k*k))
                      count++;
                 }
    cout<<"Number of Pythagorean Triples withduplicates: "<<count<<endl;
    cout<<"The Innermost for loop is entered"<<count1<<" times."<<endl<<endl;
    count=0;
    count1=0;
    for(i=1;i<=200;i++)
       for(j=i;j<=200;j++)
           for(k=j;k<=200;k++)
                {count1++;
                 if((i*i+j*j==k*k))
                      count++;
                 }
    cout<<"Number of Pythagorean Triples withduplicates: "<<count<<endl;
    cout<<"The Innermost for loop is entered"<<count1<<" times."<<endl;
  
   system("pause");           
    return 0;
}

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