Doubt in optimal strategy

#1

sir/mam in the code sir write

f(i,j)=max{a[i]+min{ f(i+2,j-1),f(i+1,j)}}
why we write “min in front of f()”.
we write min to take value which is less so that we increase profit of player.
Is my explanation right?

#2

hi @Royal_Yashasvi, what we have to do is to is to find maximum points , player 1 can win with , but we have to note here that both player are playing optimally , Playing optimally means that both players will have insight into all possible next moves and will play in such a way to maximize their chance of winning without making a mistake.
Now comming to the expression a[i]+min{ f(i+2,j-1),f(i+1,j)} now a[i] means that player 1 has chosen the ith value from the array Now we have two cases

  1. player 2 will choose i+1
    then player 1 will reach the state : f(i+2,j-1)
  2. player 2 will coose j
    then player 1 will reach the state : f(i+1,j-1)

Now , here comes the important part, since player 2 is also playing optimally due to which he will make player 1 reach a state in which he gets minimum value i.e. min{ f(i+2,j-1),f(i+1,j)}
that’s why we used min()

so our overall ans is f(i,j)=max(a,b)
where a is a[i]+min{ f(i+2,j-1),f(i+1,j)} // when player 1 choose ith value
and b is a[j]+min{ f(i+1,j-1),f(i,j-2)}

In case of any doubt feel free to ask :slight_smile:
If you got the answer mark your doubt as resolved

#3

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