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Problem Statement for "AddMultiply"

Problem Statement

You are given an int y. We are looking for any int[] x that satisfies the following constraints:
  • x has exactly three elements
  • ( x[0] * x[1] ) + x[2] = y
  • Each x[i] must be between -1000 and 1000, inclusive.
  • No x[i] can be equal to 0 or 1.
Find and return one such x.

If there are multiple valid solutions, you may return any of them. You may assume that for our constraints on y (specified below) at least one valid x always exists.

Definition

Class:
AddMultiply
Method:
makeExpression
Parameters:
int
Returns:
int[]
Method signature:
int[] makeExpression(int y)
(be sure your method is public)

Constraints

  • y will be between 0 and 500, inclusive.

Examples

  1. 6

    Returns: {2, 2, 2 }

    2*2 + 2 = 6 Note that this is one of many possible solutions. Another solution is: 3*3 + (-3) = 6

  2. 11

    Returns: {2, 3, 5 }

  3. 0

    Returns: {7, 10, -70 }

    Note that 0 and 1 are not allowed, thus a result like 0 * 0 + 0 would be incorrect.

  4. 500

    Returns: {-400, -3, -700 }

    Some or all of the returned numbers may be negative.

  5. 1

    Returns: {2, 2, -3 }

  6. 2

    Returns: {2, 2, -2 }

  7. 3

    Returns: {-1, -1, 2 }

  8. 4

    Returns: {-1, -1, 3 }

  9. 5

    Returns: {5, 2, -5 }

  10. 7

    Returns: {-1, -1, 6 }

  11. 8

    Returns: {-1, -1, 7 }

  12. 9

    Returns: {-1, -1, 8 }

  13. 10

    Returns: {-1, -1, 9 }

  14. 12

    Returns: {-1, -1, 11 }

  15. 13

    Returns: {-1, -1, 12 }

  16. 14

    Returns: {-1, -1, 13 }

  17. 15

    Returns: {-1, -1, 14 }

  18. 16

    Returns: {-1, -1, 15 }

  19. 17

    Returns: {-1, -1, 16 }

  20. 18

    Returns: {-1, -1, 17 }

  21. 19

    Returns: {-1, -1, 18 }

  22. 20

    Returns: {-1, -1, 19 }

  23. 31

    Returns: {-1, -1, 30 }

  24. 32

    Returns: {-1, -1, 31 }

  25. 37

    Returns: {-1, -1, 36 }

  26. 45

    Returns: {-1, -1, 44 }

  27. 58

    Returns: {-1, -1, 57 }

  28. 86

    Returns: {-1, -1, 85 }

  29. 101

    Returns: {-1, -1, 100 }

  30. 140

    Returns: {-1, -1, 139 }

  31. 141

    Returns: {-1, -1, 140 }

  32. 166

    Returns: {-1, -1, 165 }

  33. 170

    Returns: {-1, -1, 169 }

  34. 171

    Returns: {-1, -1, 170 }

  35. 172

    Returns: {-1, -1, 171 }

  36. 174

    Returns: {-1, -1, 173 }

  37. 193

    Returns: {-1, -1, 192 }

  38. 209

    Returns: {-1, -1, 208 }

  39. 216

    Returns: {-1, -1, 215 }

  40. 220

    Returns: {-1, -1, 219 }

  41. 231

    Returns: {-1, -1, 230 }

  42. 234

    Returns: {-1, -1, 233 }

  43. 238

    Returns: {-1, -1, 237 }

  44. 252

    Returns: {-1, -1, 251 }

  45. 255

    Returns: {-1, -1, 254 }

  46. 259

    Returns: {-1, -1, 258 }

  47. 290

    Returns: {-1, -1, 289 }

  48. 295

    Returns: {-1, -1, 294 }

  49. 312

    Returns: {-1, -1, 311 }

  50. 320

    Returns: {-1, -1, 319 }

  51. 329

    Returns: {-1, -1, 328 }

  52. 335

    Returns: {-1, -1, 334 }

  53. 342

    Returns: {-1, -1, 341 }

  54. 348

    Returns: {-1, -1, 347 }

  55. 350

    Returns: {-1, -1, 349 }

  56. 362

    Returns: {-1, -1, 361 }

  57. 363

    Returns: {-1, -1, 362 }

  58. 378

    Returns: {-1, -1, 377 }

  59. 389

    Returns: {-1, -1, 388 }

  60. 396

    Returns: {-1, -1, 395 }

  61. 398

    Returns: {-1, -1, 397 }

  62. 403

    Returns: {-1, -1, 402 }

  63. 404

    Returns: {-1, -1, 403 }

  64. 405

    Returns: {-1, -1, 404 }

  65. 411

    Returns: {-1, -1, 410 }

  66. 420

    Returns: {-1, -1, 419 }

  67. 421

    Returns: {-1, -1, 420 }

  68. 422

    Returns: {-1, -1, 421 }

  69. 423

    Returns: {-1, -1, 422 }

  70. 424

    Returns: {-1, -1, 423 }

  71. 450

    Returns: {-1, -1, 449 }

  72. 451

    Returns: {-1, -1, 450 }

  73. 452

    Returns: {-1, -1, 451 }

  74. 453

    Returns: {-1, -1, 452 }

  75. 454

    Returns: {-1, -1, 453 }

  76. 455

    Returns: {-1, -1, 454 }

  77. 456

    Returns: {-1, -1, 455 }

  78. 457

    Returns: {-1, -1, 456 }

  79. 458

    Returns: {-1, -1, 457 }

  80. 460

    Returns: {-1, -1, 459 }

  81. 462

    Returns: {-1, -1, 461 }

  82. 464

    Returns: {-1, -1, 463 }

  83. 465

    Returns: {-1, -1, 464 }

  84. 466

    Returns: {-1, -1, 465 }

  85. 468

    Returns: {-1, -1, 467 }

  86. 469

    Returns: {-1, -1, 468 }

  87. 483

    Returns: {-1, -1, 482 }

  88. 485

    Returns: {-1, -1, 484 }

  89. 486

    Returns: {-1, -1, 485 }

  90. 488

    Returns: {-1, -1, 487 }

  91. 490

    Returns: {-1, -1, 489 }

  92. 492

    Returns: {-1, -1, 491 }

  93. 493

    Returns: {-1, -1, 492 }

  94. 494

    Returns: {-1, -1, 493 }

  95. 495

    Returns: {-1, -1, 494 }

  96. 496

    Returns: {-1, -1, 495 }

  97. 497

    Returns: {-1, -1, 496 }

  98. 498

    Returns: {-1, -1, 497 }

  99. 499

    Returns: {-1, -1, 498 }

  100. 500

    Returns: {-400, -3, -700 }

  101. 250

    Returns: {-1, -1, 249 }

  102. 21

    Returns: {-1, -1, 20 }

  103. 50

    Returns: {-1, -1, 49 }

  104. 300

    Returns: {-1, -1, 299 }

  105. 188

    Returns: {-1, -1, 187 }

  106. 70

    Returns: {-1, -1, 69 }

  107. 100

    Returns: {-1, -1, 99 }

  108. 251

    Returns: {-1, -1, 250 }

  109. 24

    Returns: {-1, -1, 23 }

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