I am Not getting approach of solution there are couple of doubt in the i=even how we come to know that it is always the case that i+1(which is decreasing case according to bottom up dp) will be always cost me more than i th case why same case was not applicable for the odd condition also ?
Apporoach Of Getting Solution Is Not Clear
Honestly i would say you shall use memoization if you face problem in bottom-up DP.
Simply, make calls based on given conditions.
Get the best answer.
Memoize it!
I understand your doubt, the reason is intuitive. Its very difficult to explain in writing. I would recommend you to watch video twice thrice. I too did same 
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