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Given a list of transfers between two banks, determine the minimum initial account balance of each bank required for the given transfers to be carried out.

Task description

You are given a list of N transfers $($numbered from $0$ to N$1)$ between two banks: bank A and bank B$.$ The K$-$th transfer is described by two values:

$$ R$[$K$]($either $"$A$"$ or $"$B$")$ representing the recipient $($the bank the transfer is sent to$)$;

$$ V$[$K$]$ denoting the value sent via the transfer.

All transfers are completed in the order they appear on the list. The banks do not want to go into debt $($in other words, their account balance may not drop below $0).$ What minimum initial account balance in each bank is necessary in order to complete the transfers?

Write a function:

function solution$($R$,$ V$)$;

that, given a string R and an array of integers V$,$ both of length N$,$ returns an array of two integers. The integers should represent the minimum initial account balances for banks A and B in the following order: $[$bank A$,$ bank B$].$

Result array should be returned as an array of integers.

Examples:

$1.$ Given R $=$ "BAABA" and V $=[2,4,1,1,2],$ the function should return $[2,4].$ The bank accounts$$ balances after each transfer are shown in the following table:

$|$ A $|$ B

$------------------------+---+---$

initial balance $|2|4$

transfer $2$ from A to B $|0|6$

transfer $4$ from B to A $|4|2$

transfer $1$ from B to A $|5|1$

transfer $1$ from A to B $|4|2$

transfer $2$ from B to A $|6|0$

$2.$ Given R $=$ "ABAB" and V $=[10,5,10,15],$ the function should return $[0,15].$

$3.$ Given R $="$B$"$ and V $=[100],$ the function should return $[100,0].$

Write an efficient algorithm for the following assumptions:

$$ string R and array V are both of length N;

$$ N is an integer within the range $[1.\mathrm{.}100,000]$;

$$ each element of array V is an integer within the range $[1.\mathrm{.}10,000]$;

$$ string R is made only of the characters $\text{'}$A$\text{'}$ and$/$or $\text{'}$B$\text{'}.$