C++ Chocolate Puzzle [closed] - c++

Question

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.
Closed 9 years ago.
Let's say I have N chocolates that have to be packed into exactly P boxes in the order they arrive. Each chocolate also has a number of calories X and each box has a capacity K which has to be less than or equal to 3*sum(x1, x2, ..., xn) + max(x1, x2, ..., xn)^2 - min(x1, x2, ..., xn)^2.
In the task I'm given N, P and X for each chocolate and I have to figure out the lowest possible K. Could anyone help me on this (not looking for a solution just for some hints regarding the problem)?
Example:
N = 8,
P = 3,
X = {1, 4, 5, 6, 3, 2, 5, 3}
K for first three chocolates = 3*(1+4+5) + 5^2 - 1^2 = 54
K for next two chocolates = 3*(6+3) + 6^2 - 3^2 = 54
K for last three chocolates = 3*(2+5+3) + 5^2 - 2^2 = 51
Lowest possible K = 54
So the goal is to find the best combination using exactly P boxes that has the lowest K.
Thanks!

Answer 1

Here is how I would solve this in Java:
import java.util.HashMap;
import java.util.Map;
import java.util.Random;
public class ChocolatePuzzle {
private static final Map <String, Integer> solutions =
new HashMap <String, Integer> ();
private static final Map <String, Integer> bestMoves =
new HashMap <String, Integer> ();
private static int [] x;
private static int k (int from, int to)
{
int sum = x [from];
int max = x [from];
int min = x [from];
for (int i = from + 1; i < to; i++)
{
sum += x [i];
max = Math.max (max, x [i]);
min = Math.min (min, x [i]);
}
return sum * 3 + max * max - min * min;
}
public static int solve (int n, int p)
{
String signature = n + "," + p;
Integer solution = solutions.get (signature);
if (solution == null)
{
solution = Integer.valueOf (doSolve (n, p, signature));
solutions.put (signature, solution);
}
return solution.intValue ();
}
public static int doSolve (int n, int p, String signature)
{
if (p == 1)
{
bestMoves.put (signature, Integer.valueOf (x.length - n));
return k (n, x.length);
}
else
{
int result = Integer.MAX_VALUE;
int bestMove = 0;
int maxI = x.length - n - p + 1;
for (int i = 1; i <= maxI; i++)
{
int k = Math.max (k (n, n + i), solve (n + i, p - 1));
if (k < result)
{
result = k;
bestMove = i;
}
}
bestMoves.put (signature, Integer.valueOf (bestMove));
return result;
}
}
public static void main(String[] args) {
int n = 20;
int p = 5;
x = new int [n];
Random r = new Random ();
for (int i = 0; i < n; i++)
x [i] = r.nextInt (9) + 1;
System.out.println("N: " + n);
System.out.println("P: " + p);
System.out.print("X: {");
for (int i = 0; i < n; i++)
{
if (i > 0) System.out.print (", ");
System.out.print (x [i]);
}
System.out.println("}");
System.out.println();
int k = solve (0, p);
int o = 0;
for (int i = p; i > 0; i--)
{
int m = bestMoves.get (o + "," + i);
System.out.print ("{");
for (int j = 0; j < m; j++)
{
if (j > 0)
System.out.print (", ");
System.out.print (x [o + j]);
}
System.out.print ("} (k: ");
System.out.print(k (o, o + m));
System.out.println (")");
o += m;
}
System.out.println("min(k): " + k);
}
}
Probably you could find some useful tips in this code.
Sample input:
N: 20
P: 5
X: {1, 7, 6, 6, 5, 5, 7, 9, 1, 3, 9, 5, 3, 7, 9, 1, 4, 2, 4, 8}
Sample output:
{1, 7, 6, 6} (k: 108)
{5, 5, 7, 9} (k: 134)
{1, 3, 9, 5} (k: 134)
{3, 7, 9} (k: 129)
{1, 4, 2, 4, 8} (k: 120)
min(k): 134