Prunieim J

In Lahore $($L$),$ there is a factory that distributes its products to five cities: Qasur $($Q$),$ Sheikhupura $($S$),$ Okara $($O$),$ Gujranwala $($G$),$ and Muridke $($M$).$ Each supply line has a different fuel cost associated with it$.$ Here are the fuel consumption details for the truck transporting the products:

From Lahore $($L$)$ to Muridke $($M$)$: $300$ liters

From Lahore $($L$)$ to Qasur $($Q$)$: $200$ liters

From Lahore $($L$)$ to Okara $($O$)$: $400$ liters

From Qasur $($Q$)$ to Okara $($O$)$: $200$ liters

From Qasur $($Q$)$ to Muridke $($M$)$: $200$ liters

From Qasur $($Q$)$ to Gujranwala $($G$)$: $600$ liters

From Muridke $($M$)$ to Gujranwala $($G$)$: $100$ liters

From Gujranwala $($G$)$ to Sheikhupura $($S$)$: $200$ liters

From Okara $($O$)$ to Sheikhupura $($S$)$: $300$ liters

A consignment of the factory's products needs to be sent to Sheikhupura $($S$),$ and the truck has a limited fuel capacity of $650$ liters. Determine the best route to deliver the consignment while minimizing fuel consumption using Dijkstra's algorithm.

Problem $4$

There is a simple programing language for a specific architecture which can perform four basic arithmetic operations i$.$e$.$ addition, subtraction, multiplication and division between only two variables $x$ and $y.$ The syntax for these operations are Add, Sub, Mul and Div. Compiler of this programing language converts the each command into bit string of machine language $($string of $1\text{'}$s and $0\text{'}$s$)$ which is designed with prefix coding tree. Here is the tree given in the figure. For instance here is an example the command Add $x,y$ is converted into $110010.$

i$-$ Show the bit string of the command $lx,y.$

ii$-$ If $x=25$ and $y=31$ show the output of the command $1110100.$

Problem $5$

Here are the nodes of a tree which are ordered into preorder traversal method.

$\{$Book$,$ Chapter $1,$Section $1\mathrm{.}1,$Section $1\mathrm{.}2,$Section $1\mathrm{.}2\mathrm{.}2,$Section $1\mathrm{.}2\mathrm{.}2,$ Chapter $2,$ Section $2\mathrm{.}1,$Section $2\mathrm{.}2,$Section $2.2.1,$ Section $2\mathrm{.}2\mathrm{.}2\}$

i$-$ Draw the tree. Solve it completely

ii$-$ Apply in$-$order tree traversal technique on the above drawn tree.

iii$-$ Apply post$-$order tree traversal technique on the above drawn tree.

ii$-$ If chapter $3$ with only one subtopic section $3\mathrm{.}1$ is included in the tree where will it be placed in given ordered nodes.