吸血鬼数字算法

Posted 2020-10-10 王明辉的部落

这个算法很巧妙，一定要留下：

class Eg0410_Vampire {
    public static void main(String[] args) {
        String[] ar_str1, ar_str2;
        int sum = 0;
        for (int i = 10; i < 100; i++) {
            for (int j = i + 1; j < 100; j++) {
                int i_val = i * j;
                if (i_val < 1000 || i_val > 9999)
                    continue; // 积小于1000或大于9999排除,继续下一轮环
                ar_str1 = String.valueOf(i_val).split("");
                ar_str2 = (String.valueOf(i) + String.valueOf(j)).split("");
                java.util.Arrays.sort(ar_str1);
                java.util.Arrays.sort(ar_str2);
                if (java.util.Arrays.equals(ar_str1, ar_str2)) {
                    // 排序后比较,为真则找到一组
                    sum++;
                    System.out.println("第" + sum + "组: " + i + "*" + j + "=" + i_val);
                }
            }
        }
        System.out.println("共找到" + sum + "组吸血鬼数");
    }
}

以下是官方答案，比较麻烦，完全没有涉及本节中所讲的中止循环语句：

// : c03:E11_Vampire.java
// Solution by Dan Forhan
import java.applet.*;
import java.awt.*;

public class Vampire extends Applet {
    private int num1, num2, product;
    private int[] startDigit = new int[4];
    private int[] productDigit = new int[4];
    private int count = 0;
    private int vampCount = 0;
    private int x, y;

    public void paint(Graphics g) {
        g.drawString("Vampire Numbers", 10, 20);
        g.drawLine(10, 22, 150, 22);
        // Positioning for output to applet:
        int column = 10, row = 35;
        for (num1 = 10; num1 <= 99; num1++)
            for (num2 = 10; num2 <= 99; num2++) {
                product = num1 * num2;
                startDigit[0] = num1 / 10;
                startDigit[1] = num1 % 10;
                startDigit[2] = num2 / 10;
                startDigit[3] = num2 % 10;
                productDigit[0] = product / 1000;
                productDigit[1] = (product % 1000) / 100;
                productDigit[2] = product % 1000 % 100 / 10;
                productDigit[3] = product % 1000 % 100 % 10;
                count = 0;
                for (x = 0; x < 4; x++)
                    for (y = 0; y < 4; y++) {
                        if (productDigit[x] == startDigit[y]) {
                            count++;
                            productDigit[x] = -1;
                            startDigit[y] = -2;
                            if (count == 4) {
                                vampCount++;
                                int a = (int) Math.random() * 100;
                                int b = (int) Math.random() * 100;
                                int c = (int) Math.random() * 100;
                                if (vampCount < 10) {
                                    g.drawString("Vampire number " + vampCount + " is " + num1 + " * " + num2 + " = "
                                            + product, column, row);
                                    row += 20;
                                } else {
                                    g.drawString("Vampire number " + vampCount + " is " + num1 + " * " + num2 + " = "
                                            + product, column, row);
                                    row += 20;
                                }
                            }
                        }
                    }
            }
    }
} /// :~

 下面是我写的，比较随意，没有整理，排除法，这个不行，那个不行，剩下的就是行的了。全面地用到了本节的各种中止循环及标签。直接输出是18个数字，去掉乘数互换的一半，4位的应当是9个数字。

其实没太明白“吸血鬼数字”是什么意思，为什么叫这个名字，为什么只能是4位数，6位行不行？8位行不行？16位呢？如果这是个隐喻，那么这个隐喻不是很通用，吸血鬼在西方可能很通用，他们有很多特点，作者也许取其一，西方人一看就知道，但是对于我们不是很了解的人，吸血鬼有什么特点？吸血？面色仓白？尖牙？黑暗？这些都跟这些4位数似乎没什么联系。也没有查到合理的解释。

static void vampire() {

        int result = -1;
        String strResult = "";
        String strj = "", strj2 = "";
        String[] arrayj, arrayj2;
        String strTotal = "";
        String[] arrResult;
        
        int n = 0;
        int limit1 = 1000, limit2 = 1000;
        ArrayList<String> arrTotal = new ArrayList<String>();
        ArrayList<Integer> arrTotalCheck = new ArrayList<Integer>();

        System.out.println("吸血鬼数字：");

        for (int num1 = 1; num1 < limit1; num1++) {
            strj = Integer.toString(num1);
            if (Integer.toString(num1).length() < 2)
                continue;

            l2: for (int num2 = 1; num2 < limit2; num2++) {
                strj2 = Integer.toString(num2);

                if (Integer.toString(num2).length() < 2)
                    continue;

                result = num1 * num2;

                strTotal = strj + strj2;

                strResult = Integer.toString(result);

                arrResult = strResult.split("");

                arrayj = String.valueOf(num1).split("");
                arrayj2 = String.valueOf(num2).split("");
                for (String t1 : arrayj) {
                    if (!strResult.contains(t1))
                        continue l2;
                }

                for (String t2 : arrayj2) {
                    if (!strResult.contains(t2))
                        continue l2;
                }

                for (String tTotal : arrResult) {
                    if (!strTotal.contains(tTotal))
                        continue l2;
                }

                arrayj2 = String.valueOf(num2).split("");

                if (result >= limit1 * limit2)
                    continue;
                else if (Integer.toString(result).length() < 4)
                    continue;
                else if (strResult.length() % 2 != 0)
                    continue;
                else if (result % 100 == 0)
                    continue;
                else if (strj.length() != strj2.length())
                    continue;
                else {
                    n++;
                    // System.out.println(n + "." + num1 + "*" + num2 + "=" + result + ",");

                    if (result == 102510 || result == 105264 || result == 105750 || result==108135
                            || result==110758
                            ) {
                        
                        
                        if(arrTotalCheck.contains(result)) continue;
                        arrTotalCheck.add(result);
                        
                        arrTotal.add(n + "." + num1 + "*" + num2 + "=" + result + ",");                        
                    };
                }

            }
        }
        
        for (String i : arrTotal) {
            System.out.println(i);
        }

        return;
    }

根据某百科上的资料可知，有6位的吸血鬼数字，那么有8位的吗？10位的？12位的？理论上应该有，偶数位即可。

那么5775是不是？

4位数的吸血鬼数有7个：

1260, 1395, 1435, 1530, 1827, 2187, 6880

6位数的吸血鬼数字有141个：

102510, 104260, 105210, 105264, 105750, 108135, 110758, 115672, 116725, 117067, 118440, 123354, 124483, 125248, 125433, 125460, 126027, 126846, 129640, 129775, 131242, 132430, 133245, 134725, 135828, 135837, 136525, 136948, 140350, 145314, 146137, 146952, 152608, 152685, 153436, 156240, 156289, 156915, 162976, 163944, 172822, 173250, 174370, 175329, 180225, 180297, 182250, 182650, 186624, 190260, 192150, 193257, 193945, 197725, 201852, 205785, 211896, 213466, 215860, 216733, 217638, 218488, 226498, 226872, 229648, 233896, 241564, 245182, 251896, 253750, 254740, 260338, 262984, 263074, 284598, 284760, 286416, 296320, 304717, 312475, 312975, 315594, 319059, 319536, 326452, 329346, 329656, 336550, 336960, 338296, 341653, 346968, 361989, 362992, 365638, 368550, 369189, 371893, 378418, 378450, 384912, 386415, 392566, 404968, 414895, 416650, 416988, 428980, 429664, 447916, 456840, 458640, 475380, 486720, 489159, 489955, 498550, 516879, 529672, 536539, 538650, 559188, 567648, 568750, 629680, 638950, 673920, 729688, 736695, 738468, 769792, 789250, 789525, 792585, 794088, 809919, 809964, 815958, 829696, 841995, 939658

其中125460比较特殊，因为125640=204*615且125640=246*510.

伪吸血鬼数和一般吸血鬼数不同之处在于其尖牙不强制是n/2个位的数，故伪吸血鬼数的位数可以是奇数。

2002年Carlos Rivera定义了质吸血鬼数：尖牙是质因子的吸血鬼数，例如117067, 124483, 146137, 371893, 536539。

 

根据“尖牙不强制是n/2个位的数”来推断，尖牙指的是两个乘数，但是，为什么？哪里尖了？莫非是说对称？那也太牵强了。