 # IOIPRAC INOI : What's the expected approach for Calvin's Game ?

Whats the expected approach for Calvin’s Game INOI 13

My approach of choosing max(forwardphase_at_i + Reverse_At_i) apparently fails…

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### DP Solution: Compute the following quantities#

Forward[i] = Max score if we move forward from K to i, for all K <= i <= N

Backward[i] = Max score if we move backward from i to 1, for all K <= i <= N

Ans = Max (Forward[i] + Backward[i]) for all K <= i <= N

Make sure to include the case in which you don’t move forward at all.

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(http://paste.ofcode.org/t3F82vBwPyPtkVybbpJWjD)``````
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I have a doubt. May be the doubt is silly

if the input is
5 2

5 3 -2 1 1 (sample input) then we can continuously increase our score by from 3 to 1 and then 1 to 3 repeatedly (here 3 refers to the number 3 and not the third position)… I probably didnt read the question properly but pls clarify this doubt.

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We can only one forward phase(not move) followed by one backward phase. If you go from 3 to 1 and come back to three you have completed the forward phase and cannot go forward any more.

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That’s very generous ,Thank You Very much, Now I know what I missed  There’s also a simple enough graph side of things.

thanks!!!

I used the same approach. But cannot figure out the corner case where my soln fails
A test case would be really helpful.
Solution

you need to calculate the maximum from the (k-1)th index to n , not from the starting index.