Hi fellow developers I'm participating in a developer contest in my county and I have got practice tasks for the exam, I have been successful with most of them however I'm having issues with this one in particular could you please take a look any ideas or assistance is welcomed, the programming language doesn't matter it can be solved in any language, here is the task:
There is an arithmetic progression written on a black-board. Having nothing better to do, you invented a game involving it. Namely, you erase all the even numbers and replace them with the numbers two times smaller.
You repeat this procedure until there is no more even numbers on the board.
For example, you transform the progression {1, 2, 3, 4, 5, 6} into {1, 1, 3, 2, 5, 3} and then once again into {1, 1, 3, 1, 5, 3}.
When your friends come over, you ask them to guess the original progression.
e.g.
Let’s take progression 6, 5, 4, 3, 2, 1
In the first step, it becomes 3, 5, 2, 3, 1, 1
Then it becomes 3, 5, 1, 3, 1, 1
This means for the numbers 3, 5, 1, 3, 1, 1 the solution is 6, 5, 4, 3, 2, 1, resulting in a sum of 21.
Input parameters:
progression - an array of integers representing the original progression after
all the numbers have been brought to odd elements
Constraints:
The number of elements in progression is between 4 and 500 inclusive.
Each element of progression is between 1 and 1000000 inclusive.
All elements of progression are odd.
Return value:
The sum of the elements of the original arithmetic progression
When there is more than one solution, return the one that has smaller sum of all the elements.
Note that there will always be a solution where each number of the original progression is smaller than 1000000.
Class Name:
Progression
Method signature:
public int reverse(int[] progression)
TEST CASES
Test Case 1: reverse({1, 1, 3, 1, 5, 3}) = 21
Test Case 2: reverse({1, 1, 1, 1, 1, 1}) = 6
Test Case 3: reverse({3, 3, 3, 3}) = 12
Test Case 4: reverse({3, 5, 1, 3, 1, 1}) = 21
Test Case 5: reverse({21, 27, 33, 39, 45, 51}) = 216
Test Case 6: reverse({37, 15, 23, 1, 9, 1}) = 117
Test Case 7: reverse({1019, 1077, 1135, 1193, 1251, 1309, 1367, 1425, 1483, 1541}) = 12800
Test Case 8: reverse({1103, 2067, 241, 1789, 825, 1511, 343, 1233, 547, 955, 51, 677, 269, 399, 65, 121}) = 18616
Test Case 9: reverse({5, 5, 5, 5, 5}) = 25
Test Case 10: reverse({5, 1, 11, 7, 17}) = 55
What I have tried:
I first tried when all elements in the array are the same, just to return their sum and I make another array with the difference of all the elements from the fist one and if the second array has all the same elements, just return their sum. I have no idea for the other test cases, which number should be multiplied by two which not.
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