How would you look at developing an algorithm for this hotel problem?

Question

There is a problem I am working on for a programming course and I am having trouble developing an algorithm to suit the problem. Here it is:

You are

Answer 1

Following is the MATLAB code for hotel problem.

clc
clear all

% Data     
% a = [0;50;180;150;50;40];    
% a = [0, 200, 400, 600, 601];    
  a = [0,10,180,350,450,600];    
% a = [0,1,2,3,201,202,203,403];

n = length(a);    
opt(1) = 0;    
prev(1)= 1;

for i=2:n
    opt(i) =Inf;
    for j = 1:i-1
        if(opt(i)>(opt(j)+ (200-a(i)+a(j))^2))
            opt(i)= opt(j)+ (200-a(i)+a(j))^2;
            prev(i) = j; 
        end
    end
    S(i) = opt(i);
end

k = 1;
i = n;
sol(1) = n;

while(i>1)
   k = k+1;
   sol(k)=prev(i);
   i = prev(i);   
end

for i =k:-1:1
    stops(i) = sol(i);
end
stops