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要解决这个问题,可以改用动态规划(Dynamic Programming, DP)的方法,而不是简单的贪心算法。这是因为贪心算法的局限在于它做的决策是局部最优的,而没有考虑到全局最优。通过动态规划,可以找到使箱子重量利用最优的方案。
然而,如果希望继续使用贪心算法,可以采用一些优化策略来提高放置物品的效率。例如,可以在尝试放置物品时,考虑多种组合情况,或者使用更复杂的贪心策略。
方案1:使用动态规划(DP)解决背包问题
下面是一个使用动态规划解决背包问题的简化版本:
import java.util.*;
public class BoxFilling {
static class Item {
private String name;
private double weight;
public Item(String name, double weight) {
this.name = name;
this.weight = weight;
}
public double getItemWeight() {
return weight;
}
@Override
public String toString() {
return name + " (" + weight + ")";
}
}
static class Box {
private double capacity;
private List<Item> items;
public Box(double capacity) {
this.capacity = capacity;
this.items = new ArrayList<>();
}
public boolean canAddItem(Item item) {
return getCurrentWeight() + item.getItemWeight() <= capacity;
}
public void addItem(Item item) {
items.add(item);
}
public double getCurrentWeight() {
return items.stream().mapToDouble(Item::getItemWeight).sum();
}
@Override
public String toString() {
return "Box{" +
"capacity=" + capacity +
", items=" + items +
'}';
}
}
public static void main(String[] args) {
Item[] items = {
new Item("Apple", 4.1),
new Item("Grapes", 1.9),
new Item("Orange", 2.5),
new Item("Banana", 3.0)
};
Box[] boxes = {
new Box(6.0),
new Box(6.0)
};
fillBoxes(items, boxes);
for (Box box : boxes) {
System.out.println(box);
}
}
private static void fillBoxes(Item[] items, Box[] boxes) {
Arrays.sort(items, Comparator.comparingDouble(Item::getItemWeight).reversed());
for (Box box : boxes) {
List<Item> remainingItems = new ArrayList<>(Arrays.asList(items));
List<Item> boxItems = findBestFit(remainingItems, box.capacity);
for (Item item : boxItems) {
box.addItem(item);
remainingItems.remove(item);
}
}
}
private static List<Item> findBestFit(List<Item> items, double capacity) {
int n = items.size();
double[][] dp = new double[n + 1][(int) (capacity * 100) + 1];
boolean[][] keep = new boolean[n + 1][(int) (capacity * 100) + 1];
for (int i = 1; i <= n; i++) {
Item item = items.get(i - 1);
int itemWeight = (int) (item.getItemWeight() * 100);
for (int w = 0; w <= (int) (capacity * 100); w++) {
if (itemWeight <= w && dp[i - 1][w - itemWeight] + item.getItemWeight() > dp[i - 1][w]) {
dp[i][w] = dp[i - 1][w - itemWeight] + item.getItemWeight();
keep[i][w] = true;
} else {
dp[i][w] = dp[i - 1][w];
}
}
}
List<Item> result = new ArrayList<>();
for (int i = n, w = (int) (capacity * 100); i > 0; i--) {
if (keep[i][w]) {
Item item = items.get(i - 1);
result.add(item);
w -= (int) (item.getItemWeight() * 100);
}
}
return result;
}
}
方案2:优化贪心算法
优化贪心算法,可以尝试以下方法:
尝试多个箱子的组合:在放置每个物品时,尝试将物品放置到不同的箱子,计算各个组合的利用率。
提前规划:在放置每个物品时,考虑未来可能要放置的物品,并且根据当前物品和未来物品的组合情况进行决策。
这是一个优化贪心算法的示例:
private static void fillBoxesOptimized(Item[] items, Box[] boxes) {
// Sort the items by their weight in descending order
Arrays.sort(items, Comparator.comparingDouble(Item::getItemWeight).reversed());
// Create a priority queue to keep track of the boxes by their remaining capacity
PriorityQueue<Box> pq = new PriorityQueue<>(Comparator.comparingDouble(Box::getCurrentWeight).reversed());
for (Box box : boxes) {
pq.offer(box);
}
// Fill each box with items
for (Item item : items) {
Box bestBox = null;
double minWaste = Double.MAX_VALUE;
// Find the best box to place the item
for (Box box : pq) {
if (box.canAddItem(item)) {
double waste = box.capacity - (box.getCurrentWeight() + item.getItemWeight());
if (waste < minWaste) {
minWaste = waste;
bestBox = box;
}
}
}
// Add item to the best box found
if (bestBox != null) {
bestBox.addItem(item);
pq.remove(bestBox);
pq.offer(bestBox);
}
}
}
在上述示例中,我们通过优化贪心策略来尽可能减少每次放置物品后的空闲空间,最大化利用箱子容量。
通过这些方法,可以在一定程度上解决单纯贪心算法在复杂情况下的局限性。