IncrementAndDoubling | Topcoder Archive

Problem Statement

You have an array with N elements. Initially, each element is 0. You can perform the following operations:

Increment operation: Choose one element of the array and increment the value by one.
Doubling operation: Double the value of each element.

You are given a int[] desiredArray containing N elements. Compute and return the smallest possible number of operations needed to change the array from all zeros to desiredArray.

Definition

Class:: IncrementAndDoubling
Method:: getMin
Parameters:: int[]
Returns:: int
Method signature:: int getMin(int[] desiredArray)
(be sure your method is public)

Constraints

desiredArray will contain between 1 and 50 elements, inclusive.
Each element of desiredArray will be between 0 and 1,000, inclusive.

Examples

```
{2, 1}
```
```
Returns: 3
```
One of the optimal solutions is to apply increment operations to element 0 twice and then to element 1 once. Total number of operations is 3.
```
{16, 16, 16}
```
```
Returns: 7
```
The optimum solution looks as follows. First, apply an increment operation to each element. Then apply the doubling operation four times. Total number of operations is 3+4=7.
```
{100}
```
```
Returns: 9
```
```
{0, 0, 1, 0, 1}
```
```
Returns: 2
```
Some elements in desiredArray may be zeros.

{123, 234, 345, 456, 567, 789}

Returns: 40

{7,5,8,1,8,6,6,5,3,5,5,2,8,9,9,4,6,9,4,4,1,9,9,2,8,4,7,4,8,8,6,3,9,4,3,4,5,1,9,8,3,8,3,7,9,3,8,4,4,7}

Returns: 84

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