Question

You are running an art museum. There is a long hallway with k paintings on the wall. The locations of the paintings are l1, ..., lk . These locations are real numbers, but not necessarily integers. You can place guards at locations in the hallway, and a guard can protect all paintings within 1 unit of distance from his location. The guards can be placed at any location, not just a location where there is a painting. Design a greedy algorithm to determine the minimum number of guards needed to protect all paintings.

Answer 1

The answer to the algorithm is given below:

Step-by-step explanation:

Algorithm:

#Define a set to keep track of the locations of the paintings.

location = {l1, l2, l3, l4, …, lk}

#Sort the set of locations.

Sort(location)

#Define a set to keep track of the positioned guards.

set P = {NULL}

#Define a variable to keep track of

#the location of the guard last positioned.

curr_guard = -infinity

#Define a variable to access the

#locations of the paintings.

i = 0

#Run the loop to access the

#location of the paintings.

#Since the location set has been sorted, the paintings

#are accessed in the order of their increasing locations.

while i < k:

#Check if the current painting is

#not protected by the current guard.

if location(i) > curr_guard + 1:

#Assign a guard to

#protect the painting.

curr_guard = location(i) + 1

#Add the guard to the set

#of the positioned guards.

P = P + {curr_guard}

#Increase the value of

#the variable i by 1.

i = i + 1

#Define a variable to count

#the number of guards placed

count = 0

#Run the loop to count

#the number of guards.

for guard in P:

count = count + 1

#Display the number of guards

#required to protect all the paintings.

print ("The minimum number of guards required are: ", count)