solveKnapsack is a function that takes three parameters: an array weights

where weights$[$i$]$ represents the weight of item i$,$ an array values where

values $[$i$]$ represents the value of item i$,$ and an integer capacity representing

the maximum weight the knapsack can hold. The function finds the maximum

total value that can be achieved by selecting items whose total weight does not

exceed the capacity. Each item can be selected at most once $(0//1$ knapsack$).$

The function returns both the maximum value achievable and the indices of

the selected items. The input arrays weights and values must have the same

length n $,$ representing the number of available items. please code in python

$```$

def print$\_$dp$\_$table$($dp$,$ n$,$ capacity$)$:

$"""$

Print the DP table showing maximum value for each subproblem.

Args:

dp $($List$[$List$[$int$]])$: $2$D array containing maximum values

n $($int$)$: Number of items

capacity $($int$)$: Maximum weight capacity

Returns:

None: Prints the table to stdout

$"""$

# Print column numbers $($weights$)$

print$("$

DP Table $($rows$=$items, cols$=$weights$)$:$")$

print$("",$ end$="")$

for w in range$($capacity $+1)$:

print$($f$"$w$\{$w:$3\}",$ end$="")$

print$("$

$"+"-----"*($capacity $+1))$

# Print each row with item number

for i in range$($n $+1)$:

print$($f$"$i$\{$i:$1\}|",$ end$="")$

for w in range$($capacity $+1)$:

print$($f$"\{$dp$[$i$][$w$]$:$4\}",$ end$="")$

print$()$

print$()$

$\backslash$checkmark def solve$\_$knapsack$($weights$,$ values, capacity$)$:

$"""$

Solves the $0/1$ Knapsack problem using dynamic programming.

Args:

weights $($List$[$int$])$: List of item weights

values $($List$[$int$])$: List of item values

capacity $($int$)$: Maximum weight capacity of knapsack

Returns:

int: Maximum value that can be achieved within weight capacity

List$[$int$]$: Indices of selected items

Example:

$>>$ weights $=[2,3,4,5]$

$>>>$ values $=[3,4,5,6]$

$>>>$ capacity $=10$

$>>>$ max$\_$value, selected $=$ solve$\_$knapsack$($weights$,$ values, capacity$)$

$""."$

n $=$ len$($weights$)$

# Initialize DP table with dimensions $($n$+1)$ x $($capacity$+1)$

dp $=[[0$ for $\_$ in range$($capacity $+1)]$ for $\_$ in range$($n $+1)]$

selected$\_$items $=[]$

# TODO: Your code here

return dp$[$n$][$capacity$],$ selected$\_$items

if $\_\_$name$\_\_=="\_\_$main$\_\_"$:

# Example usage

weights $=[2,3,4,5]$ # Weight of each item

values $=[3,4,5,6]$ # Value of each item

capacity $=10$ # Maximum weight capacity

max$\_$value, selected $=$ solve$\_$knapsack$($weights$,$ values, capacity$)$

print$($f$"$Maximum value: $\{$max$\_$value$\}")$

print$($f$"$Selected items $($indices$)$: $\{$selected$\}")$

$```$