“马戏团塔”的算法

Question

(ht, wt): (65, 100) (70, 150) (56, 90) (75, 190) (60, 95) (68, 110) 

最长塔的长度为6，从上到下包括：

(56, 90) (60,95) (65,100) (68,110) (70,150) (75,190)

下面是书中的解决方案：

“当我们把这个问题的绒毛都剪掉的时候，我们就能明白问题其实是下面的了。

      {1,1} 
   {3,3} {7,2}
{6,4} {9,9} {8,5}

Answer 1

不，您的值不是按非递减顺序排列的。正如@mooseboys评论所说，在你的例子中，第三个值的权重大于第二个值。（{3,3}->{7,2},2<3)

该问题是最长递增子序列(LIS)(DP)的一个微小变化。

您可以根据高度对元素进行排序，然后对Weight应用find the longly Increasing subsequence。

请找到下面的java实现：

class Person implements Comparable<Person> {
    int height;
    int weight;

    public Person(int height, int weight) {
        this.height = height;
        this.weight = weight;
    }

    @Override
    public String toString() {
        return "Person{" +
                "height=" + height +
                ", weight=" + weight +
                '}';
    }

    @Override
    public int compareTo(Person p) {
        if(this.height>p.height) {
            return 1;
        } else if(this.height < p.height) {
            return -1;
        } else {
            return 0;
        }
    }
}

public class CircusTower {

    public void calculatePeople(Person[] input) {

        int weightArray[] = new int[input.length];
        String[] output = new String[input.length];
        for (int i=0;i<input.length;i++) {
            weightArray[i] = 1;
            output[i] = input[i].toString() + "";
        }
        int maxLength = 0;

        for (int i=1;i<input.length;i++) {
            for (int j=0;j<i;j++) {
                if( weightArray[j]+1>weightArray[i] && input[i].weight>input[j].weight) {
                    weightArray[i] = weightArray[j] + 1;
                    output[i] = output[j] + " " + input[i].toString();
                    if(maxLength<weightArray[i]) {
                        maxLength = weightArray[i];
                    }
                }
            }
        }

        System.out.println();


        for (int i = 0; i < input.length; i++) {
            if (weightArray[i] == maxLength) {
                System.out.println("Longest Increasing subsequence - " + output[i] + " of length = " + maxLength);
            }
        }

    }

    public static void main(String[] args) {
        CircusTower ct = new CircusTower();
        Person p1 = new Person(65,100);
        Person p2 = new Person(70,150);
        Person p3 = new Person(56, 90);
        Person p4 = new Person(75, 190);
        Person p5 = new Person(60, 95);
        Person p6 = new Person(68, 110);

        Person[] array = new Person[]{p1,p2,p3,p4,p5,p6};

        Arrays.sort(array);

        ct.calculatePeople(array);

    }

}

我在用LIS问题的n平方实现，U也可以用NlogN中更好的一个。

希望它能澄清。