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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.

Result array should be returned as a structure `Results`.

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.

Result array should be returned as a vector 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 2009–2018 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.

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 2009–2018 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

Result array should be returned as an array of integers.

`[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); }

Result array should be returned as an array of integers.

`[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);

Result array should be returned as an array of integers.

`[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)

Result array should be returned as an array of integers.

`[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);

Result array should be returned as an array of integers.

`[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;

Result array should be returned as a record `Results`.

`[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);

Result array should be returned as an array of integers.

`[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)=@_; ... }

Result array should be returned as an array of integers.

`[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)

Result array should be returned as an array of integers.

`[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)

Result array should be returned as an array of integers.

`[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] }

Result array should be returned as an array of integers.

`[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]

Result array should be returned as an array of integers.

`[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]

Result array should be returned as an array of integers.

`[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()

Result array should be returned as an array of integers.

`[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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