Finding all possible pythagorean triangles within a set of triangles

Question

I've looked at this thread: All possible Pythagorean Triples Looks similar to mine but I can't get mine to work for some reason..

REVISION 1

#include <iostream>
#include <cmath>
using namespace std;

class Labb2_uppg1 {
public:
    void run() {
        compute();
    }
private:
void compute() {                                                            // performs the computations
    int a, b, c, counter = 0, counter_pyth = 0;                             // a = cathetus of triangle
                                                                            // b = cathetus of triangle
                                                                            // c = hypotenuse of triangle
                                                                            // counter = used to determine the amount of iterated triangles
                                                                            // counter_pyth = used to determine the subset of pythagorean triangles in the total amount of iterated triangles
    for (a = 1; a <= 500; a++) {
        for (b = a; b <= 500; b++) {                                        // starts from the same index as 'a' to omit duplicate results
            counter++;
            c = int_sqrt((a*a)+(b*b));
            if (c == 100 || c == 200 || c == 300 || c == 400 || c == 500)   // prints the triangles whose hypotenuse matches the integers 100, 200, 300, 400 and 500
                cout << "Triangel med hypotenusan " << c << ": a = " << a << ", b = " << b << endl;
            if (((a*a)+(b*b))==(c*c)) {
                cout << "DEBUG_01: a = " << a << ", b = " << b
                        << ", c = " << c << endl;
                counter_pyth++;
            }
        }
    }
    cout << "\nAntal itererade trianglar: " << counter;                     // prints the number of triangles that the program has iterated through
    cout << "\nAntal pytagoreiska trianglar: " << counter_pyth << "\n\n";   // prints the number of Pythagorean triangles that the program has iterated through
}

int int_sqrt(int r) {                                                       // simplification of the Bakhsali Approximation method to calculate square roots
                                                                            // only integers may be used when invoking this function
                                                                            // returns the integer square root if it was successfully calculated using the radicand r
    int i = 0;                                                              // initiates 'i' to a value of 0
    while ((i*i) <= r)                                                      // approximates the square of 'i' to the radicand 'r'
        i++;
    i--;

    if ((i*i) == r)                                                         // if the square of 'i' is exactly 'r'
        return i;                                                           // then the integer root of 'r' has successfully been found
    else
        return -1;                                                          // else -1 is returned, no real number (radicand) can have -1 as its root
    }

};

Output:

DEBUG_01: a = 95, b = 228, c = 247
DEBUG_01: a = 96, b = 110, c = 146
DEBUG_01: a = 96, b = 128, c = 160
DEBUG_01: a = 96, b = 180, c = 204
DEBUG_01: a = 96, b = 247, c = 265
DEBUG_01: a = 96, b = 280, c = 296
DEBUG_01: a = 96, b = 378, c = 390
DEBUG_01: a = 98, b = 336, c = 350
DEBUG_01: a = 99, b = 132, c = 165
DEBUG_01: a = 99, b = 168, c = 195
DEBUG_01: a = 99, b = 440, c = 451
DEBUG_01: a = 100, b = 105, c = 145
DEBUG_01: a = 100, b = 240, c = 260
DEBUG_01: a = 100, b = 495, c = 505
DEBUG_01: a = 102, b = 136, c = 170
DEBUG_01: a = 102, b = 280, c = 298
DEBUG_01: a = 104, b = 153, c = 185
DEBUG_01: a = 104, b = 195, c = 221
DEBUG_01: a = 104, b = 330, c = 346
DEBUG_01: a = 105, b = 140, c = 175
DEBUG_01: a = 105, b = 208, c = 233
DEBUG_01: a = 105, b = 252, c = 273
DEBUG_01: a = 105, b = 360, c = 375
DEBUG_01: a = 108, b = 144, c = 180
DEBUG_01: a = 108, b = 231, c = 255
DEBUG_01: a = 108, b = 315, c = 333
DEBUG_01: a = 108, b = 480, c = 492
DEBUG_01: a = 110, b = 264, c = 286
DEBUG_01: a = 111, b = 148, c = 185
DEBUG_01: a = 112, b = 180, c = 212
DEBUG_01: a = 112, b = 210, c = 238
Triangel med hypotenusan 400: a = 112, b = 384
DEBUG_01: a = 112, b = 384, c = 400
DEBUG_01: a = 112, b = 441, c = 455
DEBUG_01: a = 114, b = 152, c = 190
DEBUG_01: a = 114, b = 352, c = 370
DEBUG_01: a = 115, b = 252, c = 277
DEBUG_01: a = 115, b = 276, c = 299
DEBUG_01: a = 117, b = 156, c = 195
DEBUG_01: a = 117, b = 240, c = 267
DEBUG_01: a = 119, b = 120, c = 169
DEBUG_01: a = 119, b = 408, c = 425
DEBUG_01: a = 120, b = 126, c = 174
Triangel med hypotenusan 200: a = 120, b = 160
DEBUG_01: a = 120, b = 160, c = 200
DEBUG_01: a = 120, b = 182, c = 218
DEBUG_01: a = 120, b = 209, c = 241
DEBUG_01: a = 120, b = 225, c = 255
DEBUG_01: a = 120, b = 288, c = 312
DEBUG_01: a = 120, b = 350, c = 370
DEBUG_01: a = 120, b = 391, c = 409
DEBUG_01: a = 120, b = 442, c = 458
DEBUG_01: a = 123, b = 164, c = 205
DEBUG_01: a = 125, b = 300, c = 325
DEBUG_01: a = 126, b = 168, c = 210
DEBUG_01: a = 126, b = 432, c = 450
DEBUG_01: a = 128, b = 240, c = 272
DEBUG_01: a = 129, b = 172, c = 215
DEBUG_01: a = 130, b = 144, c = 194
DEBUG_01: a = 130, b = 312, c = 338
DEBUG_01: a = 132, b = 176, c = 220
DEBUG_01: a = 132, b = 224, c = 260
DEBUG_01: a = 132, b = 351, c = 375
DEBUG_01: a = 132, b = 385, c = 407
DEBUG_01: a = 132, b = 475, c = 493
DEBUG_01: a = 133, b = 156, c = 205
DEBUG_01: a = 133, b = 456, c = 475
DEBUG_01: a = 135, b = 180, c = 225
DEBUG_01: a = 135, b = 324, c = 351
DEBUG_01: a = 135, b = 352, c = 377
DEBUG_01: a = 136, b = 255, c = 289
DEBUG_01: a = 136, b = 273, c = 305
DEBUG_01: a = 138, b = 184, c = 230
DEBUG_01: a = 140, b = 147, c = 203
DEBUG_01: a = 140, b = 171, c = 221
DEBUG_01: a = 140, b = 225, c = 265
DEBUG_01: a = 140, b = 336, c = 364
Triangel med hypotenusan 500: a = 140, b = 480
DEBUG_01: a = 140, b = 480, c = 500
DEBUG_01: a = 141, b = 188, c = 235
DEBUG_01: a = 144, b = 165, c = 219
DEBUG_01: a = 144, b = 192, c = 240
DEBUG_01: a = 144, b = 270, c = 306
DEBUG_01: a = 144, b = 308, c = 340
DEBUG_01: a = 144, b = 420, c = 444
DEBUG_01: a = 145, b = 348, c = 377
DEBUG_01: a = 145, b = 408, c = 433
DEBUG_01: a = 147, b = 196, c = 245
DEBUG_01: a = 150, b = 200, c = 250
DEBUG_01: a = 150, b = 360, c = 390
DEBUG_01: a = 152, b = 285, c = 323
DEBUG_01: a = 152, b = 345, c = 377
DEBUG_01: a = 153, b = 204, c = 255
DEBUG_01: a = 153, b = 420, c = 447
DEBUG_01: a = 155, b = 372, c = 403
DEBUG_01: a = 155, b = 468, c = 493
DEBUG_01: a = 156, b = 208, c = 260
DEBUG_01: a = 156, b = 320, c = 356
DEBUG_01: a = 156, b = 455, c = 481
DEBUG_01: a = 156, b = 495, c = 519
DEBUG_01: a = 159, b = 212, c = 265
DEBUG_01: a = 160, b = 168, c = 232
DEBUG_01: a = 160, b = 231, c = 281
DEBUG_01: a = 160, b = 300, c = 340
DEBUG_01: a = 160, b = 384, c = 416
DEBUG_01: a = 161, b = 240, c = 289
DEBUG_01: a = 162, b = 216, c = 270
DEBUG_01: a = 165, b = 220, c = 275
DEBUG_01: a = 165, b = 280, c = 325
DEBUG_01: a = 165, b = 396, c = 429
DEBUG_01: a = 168, b = 224, c = 280
DEBUG_01: a = 168, b = 270, c = 318
DEBUG_01: a = 168, b = 315, c = 357
DEBUG_01: a = 168, b = 374, c = 410
DEBUG_01: a = 168, b = 425, c = 457
DEBUG_01: a = 168, b = 490, c = 518
DEBUG_01: a = 170, b = 264, c = 314
DEBUG_01: a = 170, b = 408, c = 442
DEBUG_01: a = 171, b = 228, c = 285
DEBUG_01: a = 174, b = 232, c = 290
DEBUG_01: a = 175, b = 288, c = 337
DEBUG_01: a = 175, b = 420, c = 455
DEBUG_01: a = 176, b = 210, c = 274
DEBUG_01: a = 176, b = 330, c = 374
Triangel med hypotenusan 500: a = 176, b = 468
DEBUG_01: a = 176, b = 468, c = 500
DEBUG_01: a = 177, b = 236, c = 295
DEBUG_01: a = 180, b = 189, c = 261
Triangel med hypotenusan 300: a = 180, b = 240
DEBUG_01: a = 180, b = 240, c = 300
DEBUG_01: a = 180, b = 273, c = 327
DEBUG_01: a = 180, b = 299, c = 349
DEBUG_01: a = 180, b = 385, c = 425
DEBUG_01: a = 180, b = 432, c = 468
DEBUG_01: a = 183, b = 244, c = 305
DEBUG_01: a = 184, b = 345, c = 391
DEBUG_01: a = 185, b = 444, c = 481
DEBUG_01: a = 186, b = 248, c = 310
DEBUG_01: a = 189, b = 252, c = 315
DEBUG_01: a = 189, b = 340, c = 389
DEBUG_01: a = 190, b = 336, c = 386
DEBUG_01: a = 190, b = 456, c = 494
DEBUG_01: a = 192, b = 220, c = 292
DEBUG_01: a = 192, b = 256, c = 320
DEBUG_01: a = 192, b = 360, c = 408
DEBUG_01: a = 192, b = 494, c = 530
DEBUG_01: a = 195, b = 216, c = 291
DEBUG_01: a = 195, b = 260, c = 325
DEBUG_01: a = 195, b = 400, c = 445
DEBUG_01: a = 195, b = 468, c = 507
DEBUG_01: a = 196, b = 315, c = 371
DEBUG_01: a = 198, b = 264, c = 330
DEBUG_01: a = 198, b = 336, c = 390
DEBUG_01: a = 200, b = 210, c = 290
DEBUG_01: a = 200, b = 375, c = 425
DEBUG_01: a = 200, b = 480, c = 520
DEBUG_01: a = 201, b = 268, c = 335
DEBUG_01: a = 203, b = 396, c = 445
DEBUG_01: a = 204, b = 253, c = 325
DEBUG_01: a = 204, b = 272, c = 340
DEBUG_01: a = 205, b = 492, c = 533
DEBUG_01: a = 207, b = 224, c = 305
DEBUG_01: a = 207, b = 276, c = 345
DEBUG_01: a = 208, b = 306, c = 370
DEBUG_01: a = 208, b = 390, c = 442
DEBUG_01: a = 210, b = 280, c = 350
DEBUG_01: a = 210, b = 416, c = 466
DEBUG_01: a = 213, b = 284, c = 355
DEBUG_01: a = 216, b = 288, c = 360
DEBUG_01: a = 216, b = 405, c = 459
DEBUG_01: a = 216, b = 462, c = 510
DEBUG_01: a = 217, b = 456, c = 505
DEBUG_01: a = 219, b = 292, c = 365
DEBUG_01: a = 220, b = 231, c = 319
DEBUG_01: a = 220, b = 459, c = 509
DEBUG_01: a = 222, b = 296, c = 370
DEBUG_01: a = 224, b = 360, c = 424
DEBUG_01: a = 224, b = 420, c = 476
DEBUG_01: a = 225, b = 272, c = 353
DEBUG_01: a = 225, b = 300, c = 375
DEBUG_01: a = 228, b = 304, c = 380
DEBUG_01: a = 228, b = 325, c = 397
DEBUG_01: a = 231, b = 308, c = 385
DEBUG_01: a = 231, b = 392, c = 455
DEBUG_01: a = 232, b = 435, c = 493
DEBUG_01: a = 234, b = 312, c = 390
DEBUG_01: a = 234, b = 480, c = 534
DEBUG_01: a = 237, b = 316, c = 395
DEBUG_01: a = 238, b = 240, c = 338
DEBUG_01: a = 240, b = 252, c = 348
DEBUG_01: a = 240, b = 275, c = 365
Triangel med hypotenusan 400: a = 240, b = 320
DEBUG_01: a = 240, b = 320, c = 400
DEBUG_01: a = 240, b = 364, c = 436
DEBUG_01: a = 240, b = 418, c = 482
DEBUG_01: a = 240, b = 450, c = 510
DEBUG_01: a = 243, b = 324, c = 405
DEBUG_01: a = 246, b = 328, c = 410
DEBUG_01: a = 248, b = 465, c = 527
DEBUG_01: a = 249, b = 332, c = 415
DEBUG_01: a = 252, b = 275, c = 373
DEBUG_01: a = 252, b = 336, c = 420
DEBUG_01: a = 252, b = 405, c = 477
DEBUG_01: a = 255, b = 340, c = 425
DEBUG_01: a = 255, b = 396, c = 471
DEBUG_01: a = 256, b = 480, c = 544
DEBUG_01: a = 258, b = 344, c = 430
DEBUG_01: a = 260, b = 273, c = 377
DEBUG_01: a = 260, b = 288, c = 388
DEBUG_01: a = 261, b = 348, c = 435
DEBUG_01: a = 261, b = 380, c = 461
DEBUG_01: a = 264, b = 315, c = 411
DEBUG_01: a = 264, b = 352, c = 440
DEBUG_01: a = 264, b = 448, c = 520
DEBUG_01: a = 264, b = 495, c = 561
DEBUG_01: a = 266, b = 312, c = 410
DEBUG_01: a = 267, b = 356, c = 445
DEBUG_01: a = 270, b = 360, c = 450
DEBUG_01: a = 273, b = 364, c = 455
DEBUG_01: a = 276, b = 368, c = 460
DEBUG_01: a = 276, b = 493, c = 565
DEBUG_01: a = 279, b = 372, c = 465
DEBUG_01: a = 279, b = 440, c = 521
DEBUG_01: a = 280, b = 294, c = 406
DEBUG_01: a = 280, b = 342, c = 442
DEBUG_01: a = 280, b = 351, c = 449
DEBUG_01: a = 280, b = 450, c = 530
DEBUG_01: a = 282, b = 376, c = 470
DEBUG_01: a = 285, b = 380, c = 475
DEBUG_01: a = 288, b = 330, c = 438
DEBUG_01: a = 288, b = 384, c = 480
DEBUG_01: a = 291, b = 388, c = 485
DEBUG_01: a = 294, b = 392, c = 490
DEBUG_01: a = 297, b = 304, c = 425
DEBUG_01: a = 297, b = 396, c = 495
DEBUG_01: a = 300, b = 315, c = 435
Triangel med hypotenusan 500: a = 300, b = 400
DEBUG_01: a = 300, b = 400, c = 500
DEBUG_01: a = 300, b = 455, c = 545
DEBUG_01: a = 303, b = 404, c = 505
DEBUG_01: a = 306, b = 408, c = 510
DEBUG_01: a = 308, b = 435, c = 533
DEBUG_01: a = 308, b = 495, c = 583
DEBUG_01: a = 309, b = 412, c = 515
DEBUG_01: a = 312, b = 416, c = 520
DEBUG_01: a = 312, b = 459, c = 555
DEBUG_01: a = 315, b = 420, c = 525
DEBUG_01: a = 318, b = 424, c = 530
DEBUG_01: a = 319, b = 360, c = 481
DEBUG_01: a = 320, b = 336, c = 464
DEBUG_01: a = 320, b = 462, c = 562
DEBUG_01: a = 321, b = 428, c = 535
DEBUG_01: a = 322, b = 480, c = 578
DEBUG_01: a = 324, b = 432, c = 540
DEBUG_01: a = 325, b = 360, c = 485
DEBUG_01: a = 327, b = 436, c = 545
DEBUG_01: a = 330, b = 440, c = 550
DEBUG_01: a = 333, b = 444, c = 555
DEBUG_01: a = 336, b = 377, c = 505
DEBUG_01: a = 336, b = 385, c = 511
DEBUG_01: a = 336, b = 448, c = 560
DEBUG_01: a = 339, b = 452, c = 565
DEBUG_01: a = 340, b = 357, c = 493
DEBUG_01: a = 341, b = 420, c = 541
DEBUG_01: a = 342, b = 456, c = 570
DEBUG_01: a = 345, b = 460, c = 575
DEBUG_01: a = 348, b = 464, c = 580
DEBUG_01: a = 351, b = 468, c = 585
DEBUG_01: a = 352, b = 420, c = 548
DEBUG_01: a = 354, b = 472, c = 590
DEBUG_01: a = 357, b = 360, c = 507
DEBUG_01: a = 357, b = 476, c = 595
DEBUG_01: a = 360, b = 378, c = 522
DEBUG_01: a = 360, b = 480, c = 600
DEBUG_01: a = 363, b = 484, c = 605
DEBUG_01: a = 366, b = 488, c = 610
DEBUG_01: a = 368, b = 465, c = 593
DEBUG_01: a = 369, b = 492, c = 615
DEBUG_01: a = 372, b = 496, c = 620
DEBUG_01: a = 375, b = 500, c = 625
DEBUG_01: a = 380, b = 399, c = 551
DEBUG_01: a = 384, b = 440, c = 584
DEBUG_01: a = 390, b = 432, c = 582
DEBUG_01: a = 396, b = 403, c = 565
DEBUG_01: a = 399, b = 468, c = 615
DEBUG_01: a = 400, b = 420, c = 580
DEBUG_01: a = 414, b = 448, c = 610
DEBUG_01: a = 420, b = 441, c = 609
DEBUG_01: a = 429, b = 460, c = 629
DEBUG_01: a = 432, b = 495, c = 657
DEBUG_01: a = 440, b = 462, c = 638
DEBUG_01: a = 460, b = 483, c = 667
DEBUG_01: a = 476, b = 480, c = 676

Antal itererade trianglar: 125250
Antal pytagoreiska trianglar: 456

As you can see, whenever I run this I get the answer 456 from the counter_pyth, according to my teacher the correct answer is 386 but I don't know what I've done wrong..

REVISION 2

.
.
.

for (a = 1; a <= 500; a++) {
    for (b = a; b <= 500; b++) {                                        // starts from the same index as 'a' to omit duplicate results
        counter++;
        c = int_sqrt((a*a)+(b*b));
        if (c == 100 || c == 200 || c == 300 || c == 400 || c == 500)   // prints the triangles whose hypotenuse matches the integers 100, 200, 300, 400 and 500
            cout << "Triangel med hypotenusan " << c << ": a = " << a << ", b = " << b << endl;
        if (((a*a)+(b*b))==(c*c)) {
            if (!((a > 500 ) || (b > 500) || (c > 500))) {
                cout << "DEBUG_01: a = " << a << ", b = " << b
                << ", c = " << c << endl;
                counter_pyth++;
            }
        }
    }
}

Answer 1

(Going with the question you linked) Try counting with c instead, since c must be at most 500 and there is no limit on either a or b:

for(int c = 1; c <= 500; c++) {
    for(int a = 1; a < c; a++) {
        int b = int_sqrt(c * c - a * a);
        if(b > 0) {
            //you've found a right triangle with c at most 500
        }
    }
}

You're probably counting more than 386 triangles because you're counting ones with c > 500.