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sequence

Language/Type: PHP recursion

Write a recursive function named sequence that accepts an integer $k as its parameter and prints out the numbers 1 through $k inclusive in a particular pattern separated by plus signs and wrapped in parentheses.

The order of the numbers should begin with all of the evens in downward order, followed by all of the odds upward from 1. Each time a number is added to the pattern, a new set of parentheses and a plus sign are added to the pattern.

If the value for $k is 0 or negative, your function should throw an Exception.

Call Output
sequence(1); 1
sequence(2); (2 + 1)
sequence(3); ((2 + 1) + 3)
sequence(4); (4 + ((2 + 1) + 3))
sequence(5); ((4 + ((2 + 1) + 3)) + 5)
sequence(6); (6 + ((4 + ((2 + 1) + 3)) + 5))
sequence(7); ((6 + ((4 + ((2 + 1) + 3)) + 5)) + 7)
sequence(8); (8 + ((6 + ((4 + ((2 + 1) + 3)) + 5)) + 7))
sequence(9); ((8 + ((6 + ((4 + ((2 + 1) + 3)) + 5)) + 7)) + 9)
sequence(10); (10 + ((8 + ((6 + ((4 + ((2 + 1) + 3)) + 5)) + 7)) + 9))

Constraints:

  • Your solution must not use any loops; it must be recursive.
  • Do not construct any data structures (no array, list, set, map, etc.), and do not declare any global variables.
  • You are allowed to define other "helper" functions if you like.
Function: Write a PHP function as described, not a complete program.

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