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Java:Farey序列

2007-12-13 10:54:35

The Farey sequences of orders 1 to 8 are :
F1 = {0⁄1, 1⁄1}
F2 = {0⁄1, 1⁄2, 1⁄1}
F3 = {0⁄1, 1⁄3, 1⁄2, 2⁄3, 1⁄1}
F4 = {0⁄1, 1⁄4, 1⁄3, 1⁄2, 2⁄3, 3⁄4, 1⁄1}
F5 = {0⁄1, 1⁄5, 1⁄4, 1⁄3, 2⁄5, 1⁄2, 3⁄5, 2⁄3, 3⁄4, 4⁄5, 1⁄1}
F6 = {0⁄1, 1⁄6, 1⁄5, 1⁄4, 1⁄3, 2⁄5, 1⁄2, 3⁄5, 2⁄3, 3⁄4, 4⁄5, 5⁄6, 1⁄1}
F7 = {0⁄1, 1⁄7, 1⁄6, 1⁄5, 1⁄4, 2⁄7, 1⁄3, 2⁄5, 3⁄7, 1⁄2, 4⁄7, 3⁄5, 2⁄3, 5⁄7, 3⁄4, 4⁄5, 5⁄6, 6⁄7, 1⁄1}
F8 = {0⁄1, 1⁄8, 1⁄7, 1⁄6, 1⁄5, 1⁄4, 2⁄7, 1⁄3, 3⁄8, 2⁄5, 3⁄7, 1⁄2, 4⁄7, 3⁄5, 5⁄8, 2⁄3, 5⁄7, 3⁄4, 4⁄5, 5⁄6, 6⁄7, 7⁄8, 1⁄1}

在第n级上,仅当c+d<=n时,才将一个新的分数a+b/c+d插到两个相邻的分数a/c和b/d之间.下面的程序,对给定的自然数n,通过不断扩展以创建第n级的分数链表.

所使用的数据结构为一个链表节点

public class Node {
    private int upval;//分子
    private int dnval;//分母
    private Node next;

    public Node(int up, int down) {
        upval = up;
        dnval = down;
        next = null;
    }

    public Node(int up, int down, Node next) {
        upval = up;
        dnval = down;
        this.next = next;
    }

    public int getUpval() {
        return upval;
    }

    public void setUpval(int upval) {
        this.upval = upval;
    }

    public int getDnval() {
        return dnval;
    }

    public void setDnval(int dnval) {
        this.dnval = dnval;
    }

    public Node getNext() {
        return next;
    }

    public void setNext(Node next) {
        this.next = next;
    }
}

下面是Farey序列的具体实现
1.构造子先设定了两个节点,即n=1的情况;
2.generate(int n)用于生成序列,每次会遍历当前序列,如果具备插入的点,则插入之,且将added设置为真;
3.如果遍历完后布尔值added为假,则说明序列已构造完成;
4.整型数turn表示每次需要判断插入的次数,它和前一轮得到的链表长度有关;

public class FareyList {
    private Node head;
    private int size;

    public FareyList() {
        head = new Node(0, 1);
        Node next = new Node(1, 1);
        head.setNext(next);
        size = 2;
    }

    public void insertAfter(Node newNode, Node prev) {
        newNode.setNext(prev.getNext());
        prev.setNext(newNode);
        size++;
    }

    public void generate(int n) {
        if (n <= 0)
            throw new UnsupportedOperationException();
        if (n == 1) {
            printList();
            return;
        }

        boolean added = true;
        while (added == true) {
            int turn = size - 1;
            added = false;
            Node node1 = head;
            Node node2 = head.getNext();
            for (int i = 1; i <= turn; i++) {
                if ((node1.getDnval() + node2.getDnval()) <= n) {
                    Node newNode = new Node(
                            node1.getUpval() + node2.getUpval(), node1
                                    .getDnval()
                                    + node2.getDnval());
                    insertAfter(newNode, node1);
                    added = true;
                }
                node1 = node2;
                node2 = node2.getNext();
            }
        }
        printList();
    }

    private void printList() {
        Node node = head;
        while (node != null) {
            System.out.print(node.getUpval() + "  ");
            node = node.getNext();
        }
        System.out.println();
        node = head;
        while (node != null) {
            System.out.print(node.getDnval() + "  ");
            node = node.getNext();
        }
        System.out.println();
    }

    public static void main(String[] args) {
        new FareyList().generate(8);
    }
}

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文章评论

[匿名]jones

2007-12-13 11:49:13

不错哦我要C++ java同时学习

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