Question Not Clear

#1

Does Piyush’s opponent also chooses the coin having the maximum value or he chooses any coin?

#2

Hello @Doctor_Insult,

You have raised the most appropriate doubt regarding this question.
Answer:

  1. He might not choose the maximum coin always.
  2. He will surely not choose any choice.
    What would he choose than?
    He will choose a coin so that Piyush will get the minimum value.

Let’s understand this:
let the index at which the leftmost coin is available be l (initially 0)
and the index at which the rightmost coin is available be r (initially n-1)

  1. if piyush chooses l
    then in the next pick he will have two possible choices:
    (l-1,r-1): the opponent has selected the rightmost coin
    (l-2,r): the opponent has selected the leftmost coin.
    sum= arr[l]+min(fun(l-1,r-1),fun(l-2,r))
    opponent will choose something that will cause piyush to have minimum sum.

  2. if piyush chooses r
    then in the next pick he will have two possible choices:
    (l-1,r-1): the opponent has selected the leftmost coin
    (l,r-2): the opponent has selected the rightmost coin.
    sum= arr[r]+min(fun(l-1,r-1),fun(l,r-2))
    opponent will choose something that will cause piyush to have minimum sum.

Hope, this would help.
Give a like if you are satisfied.

#3

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