Question

I was trying to solve random coding kata’s and found this one, my question here is what is the optimal algorithm and best design approach for solving this kata?

Given a sequence of numbers, determine the type of sequence, calculate and return the next number in
the sequence.

Integer guessNextNumber(List<Integer> sequence);

The given sequence can be one of two types, arithmetic sequence and geometric sequence.

Arithmetic sequence is defined as:
Arith_seq(p,q) = p, p+q, (p+q) +q, …
Example: Arith_seq(7,3) = 7, 10, 13, 16, 19, …

Geometric sequence is defined as:
Geo_seq(p,q) = p, p*q, (p*q) * q, …
Example: Geo_seq(2,3) = 2, 6, 18, 54, …

Expected input and output:
The input sequence will have at least 3 numbers.
For the input sequence (7, 10, 13, 16, 19), the return value would be 22.
For the input sequence (2, 6, 18, 54), the return value would be 162.

Algorithm:

1. Check input sequence
   if we have sequence as (a, b, c) then,

2. if difference between elements of sequence (b-a) or (c-b) is
   equal then its Arithmatic Sequence.

3. if division between elements of sequence is equal, eg: b/a and
   c/b then its Geometric Sequence

My question what would be an optimal algo for solving it?

Update: Is it possible to solve this constant run time?

Answer 1

Lets say your collection is a,b,c,d

• b - a + b = c then it is arithmetic
• b / a * b = c it is geometric

To return the right sequence you could thus do

• d – c + d = e and if e – d = d – c return e
• else
• d / c * d = e and if e / d = d / c return e

Java would be (assuming it is either artihmetic or geometric, never anything else, and always atleast 3 entries)

public int nextInt(int[] s){
  if( s[1] - s[0] == s[2] - s[1] ) return ( s[1] - s[0] ) + s[s.length - 1];
  return ( s[1] / s[0] ) * s[s.length - 1];
}

Safe code would be

public int nextInt(int[] s){
  if(s!=null && s.length > 3){
    if( s[1] - s[0] == s[2] - s[1] ) return ( s[1] - s[0] ) + s[s.length - 1];
    if( s[1] / s[0] == s[2] / s[1] ) return ( s[1] / s[0] ) * s[s.length - 1];
  }
  return -1;
}

With List instead of Array

public Integer guessNextNumber(List<Integer> sequence){
  if( sequence.get(1) - sequence.get(0) == sequence.get(2) - sequence.get(1) ) return (    sequence.get(1) -  sequence.get(0) ) +  sequence.get(sequence.size() - 1);
  return ( sequence.get(1) / sequence.get(0) ) * sequence.get(sequence.size() - 1);
}