1.有一个背包，容量是c,有若干物品，价值各不相同，重量也各不相同。选择一部分物品装入背包，要保证不超过背包容量的前提下，背包的物品总价值最大。补充一点：允许选择一份物品的一部分，比如 0.2份 A物品，0.5份 C物品。

public class TanXin {
    public static void main(String[] args) {
        int capacity = 10;
        int[] weights = {4,6,3,2,5};
        int[] values = {9,3,1,6,5};
        System.out.println("背包最大价值：" + getHighestValue(capacity, weights, values));
    }

    public static double getHighestValue(int capacity, int[] weights,int[] values){

        //创建物品列表并按照性价比倒序
        List<Item> itemList = new ArrayList<>();
        for(int i=0;i<weights.length;i++){
            itemList.add(new Item(weights[i], values[i]));
        }
        itemList = itemList.stream().sorted(Comparator.comparing(Item::getRatio).reversed()).collect(Collectors.toList());

        //背包剩余容量
        int restCapacity = capacity;
        //当前背包物品的最大价值
        double highestValue = 0;

        //按照性价比从高到低选择物品
        for(Item item : itemList){
            if(item.weight <= restCapacity){
                highestValue += item.value;
                restCapacity -= item.weight;
            }else{
                //背包装不下完整物品时，选择该件物品的一部分
                highestValue += (double)restCapacity/(double)item.weight * item.value;
                break;
            }
        }

        return highestValue;
    }

    static class Item {
        private int weight;
        private int value;
        //物品的性价比
        private double ratio;

        public Item (int weight, int value){
            this.weight = weight;
            this.value = value;
            this.ratio = (double)value / (double)weight;
        }

        public double getRatio() {
            return ratio;
        }
    }
}