Statistics

Problem Statement for "FourSquareSum"

Problem Statement

You are given four non-negative integers a, b, c, d, and are given that 2n = a2 + b2 + c2 + d2.

You have to find four non-negative integers s, x, y, z such that n = s2 + x2 + y2 + z2.

(It may be proven that such a quadruple always exists.)

Return a int[] containing the values {s, x, y, z}.

Definition

Class:
FourSquareSum
Method:
DivideByTwo
Parameters:
int, int, int, int
Returns:
int[]
Method signature:
int[] DivideByTwo(int a, int b, int c, int d)
(be sure your method is public)

Notes

  • The order of the four elements in your return does not matter.

Constraints

  • 0 ≤ a,b,c,d ≤ 106,
  • a2+b2+c2+d2 is even.

Examples

  1. 1

    2

    3

    4

    Returns: {1, 1, 2, 3 }

    12+22+32+42=30, so 12+12+22+32=15 will do.

  2. 5

    7

    1

    3

    Returns: {1, 1, 2, 6 }

    52+72+12+32=84, so 12+12+22+62=42 will do.

  3. 0

    0

    0

    0

    Returns: {0, 0, 0, 0 }

  4. 0

    1234

    0

    1000000

    Returns: {617, 617, 500000, 500000 }

  5. 1000000

    0

    0

    1000000

    Returns: {500000, 500000, 500000, 500000 }

  6. 1000000

    1000000

    1000000

    1000000

    Returns: {0, 0, 1000000, 1000000 }

  7. 32107

    526060

    321395

    212220

    Returns: {144644, 156920, 176751, 369140 }

  8. 102158

    895877

    740930

    518477

    Returns: {188700, 319386, 421544, 707177 }

  9. 352055

    534256

    217460

    380949

    Returns: {14447, 158398, 366502, 375858 }

  10. 110044

    425511

    412352

    728349

    Returns: {151154, 151419, 261198, 576930 }

  11. 287460

    591711

    91312

    690821

    Returns: {49555, 98074, 189386, 641266 }

  12. 999996

    999997

    999999

    999998

    Returns: {1, 1, 999997, 999998 }

  13. 1000000

    1000000

    999999

    999999

    Returns: {0, 0, 999999, 1000000 }

  14. 9

    8

    7

    6

    Returns: {1, 1, 7, 8 }

  15. 123162

    162361

    879818

    888919

    Returns: {363279, 378328, 501490, 525640 }

  16. 0

    2

    3

    3

    Returns: {0, 1, 1, 3 }

  17. 6

    3

    1

    0

    Returns: {1, 2, 3, 3 }

  18. 15

    2

    3

    0

    Returns: {1, 1, 6, 9 }

  19. 999999

    999757

    995323

    997455

    Returns: {121, 1066, 996389, 999878 }

  20. 8

    0

    0

    0

    Returns: {0, 0, 4, 4 }

  21. 55553

    55554

    55553

    55554

    Returns: {0, 0, 55553, 55554 }

  22. 556255

    690877

    896479

    694315

    Returns: {67311, 101082, 623566, 795397 }

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