Complete the implementation of the function k

$\_$

tsp

$\_$

mtz

$\_$

encoding

$($

n

$,$

$$k

$,$

$$cost

$\_$

matrix

$)$

$$below using PULP. It follows the same input convention as the code supplied in the notes. The input n denotes the size of the graph with vertices labeled

$0$

$,$

$.$

$.$

$,$

$$n

$-$

$1$

$,$

$$k is the number of salespeople, and cost

$\_$

matrix is a list of lists wherein cost

$\_$

matrix

$[$

i

$]$

$[$

j

$]$

$$is the edge cost to go from i to j for i

$!$

$=$

$$j

$.$

$$Your code must avoid accessing cost

$\_$

matrix

$[$

i

$]$

$[$

i

$]$

$$to avoid bugs. These entries will be supplied as None in the test cases.

Your code must return a list lst that has exactly k

$$ lists in it

$,$

$$wherein lst

$[$

j

$]$

$$represents the locations visited by the jth

$$ salesperson.

For the example above, for k

$=$

$2$

$$

$,$

$$your code must return

$[$

$[$

$0$

$,$

$2$

$,$

$1$

$,$

$4$

$]$

$,$

$[$

$0$

$,$

$3$

$]$

$]$

For the example above, for k

$=$

$3$

$$

$,$

$$your code must return

$[$

$[$

$0$

$,$

$1$

$,$

$4$

$]$

$,$

$[$

$0$

$,$

$2$

$]$

$,$

$[$

$0$

$,$

$3$

$]$

$]$

from pulp import

$*$

def k

$\_$

tsp

$\_$

mtz

$\_$

encoding

$($

n

$,$

$$k

$,$

$$cost

$\_$

matrix

$)$

:

$$ # check inputs are OK

$$ assert

$1$

$<$

$=$

$$k

$<$

$$n

$$ assert len

$($

cost

$\_$

matrix

$)$

$=$

$=$

$$n

$,$

$$f$\text{'}$Cost matrix is not

$\{$

n

$\}$

x

$\{$

n

$\}$

$\text{'}$

$$ assert all

$($

len

$($

cj

$)$

$=$

$=$

$$n for cj in cost

$\_$

matrix

$)$

$,$

$$f$\text{'}$Cost matrix is not

$\{$

n

$\}$

x

$\{$

n

$\}$

$\text{'}$

$$ prob

$=$

$$LpProblem

$($

$\text{'}$

kTSP

$\text{'}$

$,$

$$LpMinimize

$)$

$$ # finish your implementation here

$$ # your code must return a list of k

$-$

lists

$[$

$[$

$0$

$,$

$$i

$1$

$,$

$.$

$.$

$.$

$,$

$$il

$]$

$,$

$[$

$0$

$,$

$$j

$1$

$,$

$.$

$.$

$.$

$,$

jl

$]$

$,$

$.$

$.$

$.$

$]$

$$wherein

$$ # the ith entry in our list of lists represents the

$$ # tour undertaken by the ith salesperson

$$ # your code here

$$ raise NotImplementedError