Why not take i+1 path for even?

How do we get to know that it will always cost more?

if i is even,
i+1 is odd, then dp[i] from ‘i+1’ would be dp[i+1] + cost of incrementing = dp[i+2] + 2cost of incrementing = dp[(i+2)/2] + 2cost of incrementing + cost of doubling.
this would be more than dp[i] = dp[i/2] + cost of doubling,

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cell mitosis.
I have done this through memoisation and it passed 3 taste cases.
i also figured the error but I m not able to resolve it.
plz help as soon as possibel
code. https://ide.codingblocks.com/s/262439.