Assume that we have a wooden bridge for persons to cross between two mountains. The bridge can hold a max number of persons. Up to $\text{'}K\text{'}$ persons can be hanging on the bridge at any one time. The bridge serve crossing from two directions east to west $($westward$)$ and west to east $($eastward$).$ Use semaphore to solve the problem of synchronizing passengers crossing the bridge.

Each person operates in a separate thread, and functions as follow:

void person$($int id$,$ Destination dest$)\{$

Wait Until Safe To Cross the destination$//$ your code to synchronize

CrossBridge$($id$,$ dest$)$; $//$CS

Done With Crossing the destination; $//$ your code after cross is done$\}$

a$)$ For this part, you solution should ensure that:

a$)$ i$)$ At most $10$ persons simultaneously execute CrossBridge$().$

b$)$ All persons executing in CrossBridge$()$ are heading in the same direction.

c$)$ Avoid starvation

d$)$ The first person in the same direction acquire the bridge, last one release the bridge

b$)$ For this part assume that persons can go in the two directions at the same time, your solution must ensure the following:

i$)$ At most $M$ eastward$-$moving persons simultaneously execute CrossBridge$()$

ii$)$ At most $N$ westward$-$moving persons simultaneously execute CrossBridge$()$

iii$)$ At most K persons simultaneously execute CrossBridge$()$

iv$)$ you solution should maximize the throughput under above conditions.

For the two parts solutions

In your submission, make the following clear:

shared semaphores; declarations and value assignment, add comment to explain for what each semaphore is used for in the code of the Person, add comment to explain the code especially the use of wait and signal functions