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Code Golf

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Required fields*

Required fields*

Decompose a number into triangles

Given an integer n, decompose it into a sum of maximal triangular numbers (where Tm represents the mth triangular number, or the sum of the integers from 1 to m) as follows:

  • while n> 0,

    • find the largest possible triangular number Tm such that Tm ≤ n.

    • append m to the triangular-decomposition representation of n.

    • subtract Tm from n.

For example, an input of 44 would yield an output of 8311, because:

  • 1+たす2+たす3+たす4+たす5+たす6+たす7+たす8 =わ 36 < 44, but 1+たす2+たす3+たす4+たす5+たす6+たす7+たす8+たす9 =わ 45> 44.

    • the first digit is 8; subtract 36 from 44 to get 8 left over.

  • 1+2+3 = 6 < 8, but 1+2+3+4 = 10> 8.

    • the second digit is 3; subtract 6 from 8 to get 2 left over.

  • 1 < 2, but 1+2 = 3> 2.

    • the third and fourth digits must be 1 and 1.

Use the digits 1 through 9 to represent the first 9 triangular numbers, then use the letters a through z (can be capitalized or lowercase) to represent the 10th through 35th triangular number. You will never be given an input that will necessitate the use of a larger "digit".

The bounds on the input are 1 ≤ n < 666, and it will always be an integer.

All possible inputs and outputs, and some selected test cases (listed as input, then output):

1 1
2 11
3 2
4 21
5 211
6 3
100 d32
230 k5211
435 t
665 z731

An output of ∞ for an input of -1/12 is not required. :)

Answer*

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  • 1
    \$\begingroup\$ I had f=(n,t=0)=>n?t+1>n?t.toString(36)+f(n):f(n-++t,t):1 \$\endgroup\$ Commented May 2, 2017 at 0:37
  • \$\begingroup\$ @Arnauld Oh wow, that's way better. You should post it yourself... \$\endgroup\$ Commented May 2, 2017 at 0:39
  • 1
    \$\begingroup\$ Alright. In your version, would it be safe to do f=(n,p=q=0) and f(n,++q+p)? \$\endgroup\$ Commented May 2, 2017 at 0:58

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