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.

The answer to the algorithm is given below:

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)