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Find the shortest addition chain ending with a given integer.

Programming language:
Spoken language:

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]`.

Assume that the following declarations are given:

struct Results { int * R; int N; // Length of the array };

Write a function:

struct Results solution(int A);

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

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

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 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

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:

vector<int> solution(int A);

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

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

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 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

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.

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

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 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

func Solution(A int) []int

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[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); }

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

function solution(A);

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

function solution(A)

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

NSMutableArray * solution(int A);

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Assume that the following declarations are given:

Results = record R : array of longint; N : longint; {Length of the array} end;

Write a function:

function solution(A: longint): Results;

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

function solution($A);

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

sub solution { my ($A)=@_; ... }

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

def solution(A)

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

def solution(a)

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

object Solution { def solution(a: Int): Array[Int] }

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

public func solution(A : Int) -> [Int]

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

public func solution(_ A : Int) -> [Int]

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

- the first element of the sequence is 1,
- each element is larger than all the preceding elements; that is, the sequence is increasing.

`[1, 2, 3, 6, 12, 24, 30, 42]`. Another possible solution is `[1, 2, 4, 5, 8, 16, 21, 42]`.

Write a function:

Private Function solution(A As Integer) As Integer()

The sequence should be returned as:

- a structure
Results(in C), or- a vector of integers (in C++), or
- a record
Results(in Pascal), or- an array of integers (in any other programming language).

`[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].

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