Knapsack problem/Bounded
See also: Knapsack problem/unbounded, Knapsack problem/0-1
You are encouraged to solve this task according to the task description, using any language you may know.
A tourist wants to make a good trip at the weekend with his friends. They will go to the mountains to see the wonders of nature. So he needs some items during the trip. Food, clothing, etc. He has a good knapsack for carrying the things, but he knows that he can carry only 4 kg weight in his knapsack, because they will make the trip from morning to evening. He creates a list of what he wants to bring for the trip, but the total weight of all items is too much. He adds a value to each item. The value represents how important the thing for the tourist. The list contains which items are the wanted things for the trip, what is the weight and value of an item, and how many units does he have from each items.
This is the list:
| Item | Weight (dag) | Value | Piece(s) |
|---|---|---|---|
| map | 9 | 150 | 1 |
| compass | 13 | 35 | 1 |
| water | 153 | 200 | 2 |
| sandwich | 50 | 60 | 2 |
| glucose | 15 | 60 | 2 |
| tin | 68 | 45 | 3 |
| banana | 27 | 60 | 3 |
| apple | 39 | 40 | 3 |
| cheese | 23 | 30 | 1 |
| beer | 52 | 10 | 3 |
| suntan cream | 11 | 70 | 1 |
| camera | 32 | 30 | 1 |
| t-shirt | 24 | 15 | 2 |
| trousers | 48 | 10 | 2 |
| umbrella | 73 | 40 | 1 |
| waterproof trousers | 42 | 70 | 1 |
| waterproof overclothes | 43 | 75 | 1 |
| note-case | 22 | 80 | 1 |
| sunglasses | 7 | 20 | 1 |
| towel | 18 | 12 | 2 |
| socks | 4 | 50 | 1 |
| book | 30 | 10 | 2 |
| Knapsack | <=400 dag | ? | ? |
The tourist can choose to take any combination of items from the list, and some pieces of each item is available (see the column "Piece(s)" of the list!). He do not may cut the items, so he can only take whole units of any item.
Which items does the tourist carry in his knapsack so that their total weight does not exceed 4 kg, and their total value is maximised?
Java
General dynamic solution after wikipedia. The solution uses the method of Knapsack problem/0-1 by Java language solution.
<lang java> package hu.pj.alg.test;
import hu.pj.alg.BoundedKnapsack; import hu.pj.obj.Item; import java.util.*; import java.text.*;
public class BoundedKnapsackForTourists {
public BoundedKnapsackForTourists() {
BoundedKnapsack bok = new BoundedKnapsack(400); // 400 dkg = 400 dag = 4 kg
// making the list of items that you want to bring
bok.add("map", 9, 150, 1);
bok.add("compass", 13, 35, 1);
bok.add("water", 153, 200, 3);
bok.add("sandwich", 50, 60, 2);
bok.add("glucose", 15, 60, 2);
bok.add("tin", 68, 45, 3);
bok.add("banana", 27, 60, 3);
bok.add("apple", 39, 40, 3);
bok.add("cheese", 23, 30, 1);
bok.add("beer", 52, 10, 3);
bok.add("suntan cream", 11, 70, 1);
bok.add("camera", 32, 30, 1);
bok.add("t-shirt", 24, 15, 2);
bok.add("trousers", 48, 10, 2);
bok.add("umbrella", 73, 40, 1);
bok.add("waterproof trousers", 42, 70, 1);
bok.add("waterproof overclothes", 43, 75, 1);
bok.add("note-case", 22, 80, 1);
bok.add("sunglasses", 7, 20, 1);
bok.add("towel", 18, 12, 2);
bok.add("socks", 4, 50, 1);
bok.add("book", 30, 10, 2);
// calculate the solution:
List<Item> itemList = bok.calcSolution();
// write out the solution in the standard output
if (bok.isCalculated()) {
NumberFormat nf = NumberFormat.getInstance();
System.out.println(
"Maximal weight = " +
nf.format(bok.getMaxWeight() / 100.0) + " kg"
);
System.out.println(
"Total weight of solution = " +
nf.format(bok.getSolutionWeight() / 100.0) + " kg"
);
System.out.println(
"Total value = " +
bok.getProfit()
);
System.out.println();
System.out.println(
"You can carry te following materials " +
"in the knapsack:"
);
for (Item item : itemList) {
if (item.getInKnapsack() > 0) {
System.out.format(
"%1$-10s %2$-23s %3$-3s %4$-5s %5$-15s \n",
item.getInKnapsack() + " unit(s) ",
item.getName(),
item.getInKnapsack() * item.getWeight(), "dag ",
"(value = " + item.getInKnapsack() * item.getValue() + ")"
);
}
}
} else {
System.out.println(
"The problem is not solved. " +
"Maybe you gave wrong data."
);
}
}
public static void main(String[] args) {
new BoundedKnapsackForTourists();
}
} // class </lang>
<lang java> package hu.pj.alg;
import hu.pj.obj.Item; import java.util.*;
public class BoundedKnapsack extends ZeroOneKnapsack {
public BoundedKnapsack() {}
public BoundedKnapsack(int _maxWeight) {
setMaxWeight(_maxWeight);
}
public BoundedKnapsack(List<Item> _itemList) {
setItemList(_itemList);
}
public BoundedKnapsack(List<Item> _itemList, int _maxWeight) {
setItemList(_itemList);
setMaxWeight(_maxWeight);
}
@Override
public List<Item> calcSolution() {
int n = itemList.size();
// add items to the list, if bounding > 1
for (int i = 0; i < n; i++) {
Item item = itemList.get(i);
if (item.getBounding() > 1) {
for (int j = 1; j < item.getBounding(); j++) {
add(item.getName(), item.getWeight(), item.getValue());
}
}
}
super.calcSolution();
// delete the added items, and increase the original items
while (itemList.size() > n) {
Item lastItem = itemList.get(itemList.size() - 1);
if (lastItem.getInKnapsack() == 1) {
for (int i = 0; i < n; i++) {
Item iH = itemList.get(i);
if (lastItem.getName().equals(iH.getName())) {
iH.setInKnapsack(1 + iH.getInKnapsack());
break;
}
}
}
itemList.remove(itemList.size() - 1);
}
return itemList; }
// add an item to the item list
public void add(String name, int weight, int value, int bounding) {
if (name.equals(""))
name = "" + (itemList.size() + 1);
itemList.add(new Item(name, weight, value, bounding));
setInitialStateForCalculation();
}
} // class </lang>
<lang java> package hu.pj.alg;
import hu.pj.obj.Item; import java.util.*;
public class ZeroOneKnapsack {
protected List<Item> itemList = new ArrayList<Item>(); protected int maxWeight = 0; protected int solutionWeight = 0; protected int profit = 0; protected boolean calculated = false;
public ZeroOneKnapsack() {}
public ZeroOneKnapsack(int _maxWeight) {
setMaxWeight(_maxWeight);
}
public ZeroOneKnapsack(List<Item> _itemList) {
setItemList(_itemList);
}
public ZeroOneKnapsack(List<Item> _itemList, int _maxWeight) {
setItemList(_itemList);
setMaxWeight(_maxWeight);
}
// calculte the solution of 0-1 knapsack problem with dynamic method:
public List<Item> calcSolution() {
int n = itemList.size();
setInitialStateForCalculation();
if (n > 0 && maxWeight > 0) {
List< List<Integer> > c = new ArrayList< List<Integer> >();
List<Integer> curr = new ArrayList<Integer>();
c.add(curr);
for (int j = 0; j <= maxWeight; j++)
curr.add(0);
for (int i = 1; i <= n; i++) {
List<Integer> prev = curr;
c.add(curr = new ArrayList<Integer>());
for (int j = 0; j <= maxWeight; j++) {
if (j > 0) {
int wH = itemList.get(i-1).getWeight();
curr.add(
(wH > j)
?
prev.get(j)
:
Math.max(
prev.get(j),
itemList.get(i-1).getValue() + prev.get(j-wH)
)
);
} else {
curr.add(0);
}
} // for (j...)
} // for (i...)
profit = curr.get(maxWeight);
for (int i = n, j = maxWeight; i > 0 && j >= 0; i--) {
int tempI = c.get(i).get(j);
int tempI_1 = c.get(i-1).get(j);
if (
(i == 0 && tempI > 0)
||
(i > 0 && tempI != tempI_1)
)
{
Item iH = itemList.get(i-1);
int wH = iH.getWeight();
iH.setInKnapsack(1);
j -= wH;
solutionWeight += wH;
}
} // for()
calculated = true;
} // if()
return itemList;
}
// add an item to the item list
public void add(String name, int weight, int value) {
if (name.equals(""))
name = "" + (itemList.size() + 1);
itemList.add(new Item(name, weight, value));
setInitialStateForCalculation();
}
// add an item to the item list
public void add(int weight, int value) {
add("", weight, value); // the name will be "itemList.size() + 1"!
}
// remove an item from the item list
public void remove(String name) {
for (Iterator<Item> it = itemList.iterator(); it.hasNext(); ) {
if (name.equals(it.next().getName())) {
it.remove();
}
}
setInitialStateForCalculation();
}
// remove all items from the item list
public void removeAllItems() {
itemList.clear();
setInitialStateForCalculation();
}
public int getProfit() {
if (!calculated)
calcSolution();
return profit;
}
public int getSolutionWeight() {return solutionWeight;}
public boolean isCalculated() {return calculated;}
public int getMaxWeight() {return maxWeight;}
public void setMaxWeight(int _maxWeight) {
maxWeight = Math.max(_maxWeight, 0);
}
public void setItemList(List<Item> _itemList) {
if (_itemList != null) {
itemList = _itemList;
for (Item item : _itemList) {
item.checkMembers();
}
}
}
// set the member with name "inKnapsack" by all items:
private void setInKnapsackByAll(int inKnapsack) {
for (Item item : itemList)
if (inKnapsack > 0)
item.setInKnapsack(1);
else
item.setInKnapsack(0);
}
// set the data members of class in the state of starting the calculation:
protected void setInitialStateForCalculation() {
setInKnapsackByAll(0);
calculated = false;
profit = 0;
solutionWeight = 0;
}
} // class </lang>
<lang java> package hu.pj.obj;
public class Item {
protected String name = ""; protected int weight = 0; protected int value = 0; protected int bounding = 1; // the maximal limit of item's pieces protected int inKnapsack = 0; // the pieces of item in solution
public Item() {}
public Item(Item item) {
setName(item.name);
setWeight(item.weight);
setValue(item.value);
setBounding(item.bounding);
}
public Item(int _weight, int _value) {
setWeight(_weight);
setValue(_value);
}
public Item(int _weight, int _value, int _bounding) {
setWeight(_weight);
setValue(_value);
setBounding(_bounding);
}
public Item(String _name, int _weight, int _value) {
setName(_name);
setWeight(_weight);
setValue(_value);
}
public Item(String _name, int _weight, int _value, int _bounding) {
setName(_name);
setWeight(_weight);
setValue(_value);
setBounding(_bounding);
}
public void setName(String _name) {name = _name;}
public void setWeight(int _weight) {weight = Math.max(_weight, 0);}
public void setValue(int _value) {value = Math.max(_value, 0);}
public void setInKnapsack(int _inKnapsack) {
inKnapsack = Math.min(getBounding(), Math.max(_inKnapsack, 0));
}
public void setBounding(int _bounding) {
bounding = Math.max(_bounding, 0);
if (bounding == 0)
inKnapsack = 0;
}
public void checkMembers() {
setWeight(weight);
setValue(value);
setBounding(bounding);
setInKnapsack(inKnapsack);
}
public String getName() {return name;}
public int getWeight() {return weight;}
public int getValue() {return value;}
public int getInKnapsack() {return inKnapsack;}
public int getBounding() {return bounding;}
} // class </lang>
output:
Maximal weight = 4 kg Total weight of solution = 3,96 kg Total value = 1010 You can carry te following materials in the knapsack: 1 unit(s) map 9 dag (value = 150) 1 unit(s) compass 13 dag (value = 35) 1 unit(s) water 153 dag (value = 200) 2 unit(s) glucose 30 dag (value = 120) 3 unit(s) banana 81 dag (value = 180) 1 unit(s) cheese 23 dag (value = 30) 1 unit(s) suntan cream 11 dag (value = 70) 1 unit(s) waterproof overclothes 43 dag (value = 75) 1 unit(s) note-case 22 dag (value = 80) 1 unit(s) sunglasses 7 dag (value = 20) 1 unit(s) socks 4 dag (value = 50)