c++ (OPTIONAL. Lastname Lab4_p6.cpp.) (Pythagorean Triples) A right triangle can

ID: 3669719 • Letter: C

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c++

(OPTIONAL. Lastname Lab4_p6.cpp.) (Pythagorean Triples) A right triangle can have sides that are all integers. The set of three integer values for the sides of a right triangle is called a Pythagorean triple. These three sides must satisfy the relationship that the sum of the square of two of the sides is equal to the square of the hypotenuse. Find all Pythagorean triples for side1, side2 and the hypotenuse all no larger than 500. Use a triple-nested for-loop that tries all possibilities. (This is an example of "brute force" computing. You will learn in more advanced computer science courses that there are many interesting problems for which there is no known algorithmic approach other than using sheer brute force.)

Explanation / Answer

#include <iostream>
#include <time.h>
using namespace std;

int main() {
clock_t start, end;
start = clock(); //Start clock

   int count = 0; //Number of triples found
   long int hypotenuseSquared; //Hypotenuse squared
   long int sidesSquared; //Sum of squares of sides

//Column Titles
cout << "Side 1 Side 2 Side3" << endl;

   //side1 values range from 1 to 500
   for (long int side1 = 1; side1 <= 500; side1++) {
       //side2 values range from current side1 to 500
       for (long int side2 = side1; side2 <= 500; side2++) {
           //Hypotenuse values range from current side2 to 500
           for (long int hypotenuse = side2; hypotenuse <= 500; hypotenuse++) {
               //Calculate square of hypotenuse value
               hypotenuseSquared = hypotenuse * hypotenuse;

//Calculate sum of squares of sides
sidesSquared = (side1 * side1) + (side2 * side2);

               //If (hypotenuse)^2 = (side1)^2 + (side2)^2, Pythagorean triple
               if (hypotenuseSquared == sidesSquared) {
                   //Display triple
                   cout << side1 << ' ' << side2 << ' ' << hypotenuse << ' ';
                   count++; //Update count
               }
           }
       }
   }

//Display total number of triples found
cout << "A total of " << count << " triples were found." << endl;

end = clock(); //End clock

cout << "Time required for execution: " << (double)(end-start)/CLOCKS_PER_SEC << " seconds.";
}

output

Side 1 Side 2 Side3
3       4       5
5       12      13
6       8       10
7       24      25
8       15      17
9       12      15
9       40      41
10      24      26
11      60      61
12      16      20
12      35      37
13      84      85
14      48      50
15      20      25
15      36      39
15      36      39
15      112     113
16      30      34
16      63      65
17      144     145
18      24      30
18      80      82
19      180     181
20      21      29
20      48      52
20      99      101
21      28      35
21      72      75
21      220     221
22      120     122
23      264     265
282     376     470
285     380     475
288     330     438
288     384     480
291     388     485
294     392     490
297     304     425
297     396     495
300     315     435
300     400     500
319     360     481
320     336     464
325     360     485
340     357     493
A total of 386 triples were found.
Time required for execution: 0.067651 seconds.sh-4.3$

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