Coin$-$row problem: There is a row of $n$ coins whose values are some positive integers $c1,c2,$dots,$cn,$ not necessarily distinct. The

goal is to pick up the maximum amount of money subject to the constraint that no two coins adjacent in the initial row can be

picked up$.$

Solution: ALGORITHM CoinRow$($C $[1..$n$])$

$//$Applies formula $(8\mathrm{.}3),$ p$285$ of the textbook, bottom up to find the maximum amount of money

$//$that can be picked up from a coin row without picking two adjacent coins

$//$Input: Array C$[1..$n$]$ of positive integers indicating the coin values

$//$Output: The maximum amount of money that can be picked up

$F[0]larr0$;$F[1]larrC[1]$

for ilarr$2$ to n do

$F[i]larrmax(C[i]+F[i-2],F[i-1])$ return $F[n]$

Apply the algorithm to the coin row of denominations $8,7,9,10,6,6$ by filling the following table: