Your browser (Unknown 0) is no longer supported. Some parts of the website may not work correctly. Please update your browser.

UPCOMING CHALLENGES:

CURRENT CHALLENGES:

Neon 2014

PAST CHALLENGES

Fluorum 2014

Oxygenium 2014

Nitrogenium 2013

Carbo 2013

Boron 2013

Beryllium 2013

Lithium 2013

Helium 2013

Hydrogenium 2013

Omega 2013

Psi 2012

Chi 2012

Phi 2012

Upsilon 2012

Tau 2012

Sigma 2012

Rho 2012

Pi 2012

Omicron 2012

Xi 2012

Nu 2011

Mu 2011

Lambda 2011

Kappa 2011

Iota 2011

Theta 2011

Eta 2011

Zeta 2011

Epsilon 2011

Delta 2011

Gamma 2011

December 2010

PrefixSet edition (2010-10)

Find the shortest addition chain ending with a given integer.

Do you like puzzles? Here is one for you. You are given a positive integer A. The goal is to construct the shortest possible sequence of integers ending with A, using the following rules:

- the first element of the sequence is 1,
- each of the successive elements is the sum of any two preceding elements (adding a single element to itself is also permissible),
- each element is larger than all the preceding elements; that is, the sequence is increasing.

For example, for A = 42, a possible solution is `[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

class Solution { public int[] solution(int A); }

that, given an integer A, returns the shortest possible sequence of integers satisfying the above conditions and ending with A.

Result array should be returned as an array of integers.

For example, given A = 42, the function may return the sequence `[1, 2, 3, 6, 12, 24, 30, 42]`, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- A is an integer within the range [1..600].

Copyright 2009–2024 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.