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考拉兹猜想的概率解释

2021-09-12 07:31:45 作者：互联网

考拉兹猜想：一个正整数x，如果是奇数就乘以3再加1，如果是偶数就析出偶数因数2ⁿ，这样经过若干个次数，最终回到1。

package com.yqq.algorithm;

import java.io.IOException;
import java.util.ArrayList;
import java.util.List;

/**

考拉兹猜想的概率解释：
```
 create by yqq
```
```
 date on 2021-9-4
```
```
 code for 考拉兹猜想
```
```
 ch2函数密度为2/3
```
```
 ch3函数密度为1/3
```

 if limit -> infinite : count(ch2)/count(ch3) -> 2

 对正整数k,作用偶变换f(n) = 2^n 以及 作用奇变换 g(m) = 3^m 有：

```
 k 除以 (2^n) 乘以 (3^m) -> 1
```
```
 需要 2^n > 3^m
```
```
 令：
```
```
 2^n = 3^m
```
```
 nlg2 = mlg3
```
```
 n/m = lg3/lg2 = 1.585
```

 有n必须是m的1.585倍以上k向小值收敛。

*/
public class CollatzConjecture {

private static List<Long> arr = new ArrayList<>();
private static List<Integer> distributeArr = new ArrayList<>();
private static long ch2 = 0;
private static long ch3 = 0;

public static void main(String[] args) throws IOException {
    long n = 27L;
    chang(n);
}

private static void chang3(long k) {
    long i = k * 3 + 1;
    ch3++;
    distributeArr.add(3);
    chang(i);
}

private static void chang2(long k) {
    long i = k / 2;
    ch2++;
    distributeArr.add(2);
    if (i == 2) {
        System.out.println("i = " + i);
        //arr.add(i);
        System.out.println("arr = " + arr);
        System.out.println("arr_size = " + arr.size());
        System.out.println("distributeArr = " + distributeArr);
        System.out.println("distributeArr_size = " + distributeArr.size());

        System.out.println("ch2 = " + ch2);
        System.out.println("ch3 = " + ch3);
        System.out.println("p_ch2 = " + (float) ch2 /distributeArr.size());
        System.out.println("p_ch3 = " + (float) ch3 /distributeArr.size());
        float ch2_divide_ch3 = (float) ch2 / (float) ch3;
        System.out.println("ch2_divide_ch3 = " + ch2_divide_ch3);
        double v = Math.log10(3) / Math.log10(2);
        System.out.println("v = " + v);
        System.out.println("ch2_divide_ch3 > v 故数列必收敛");
        System.exit(1);
    }
    chang(i);
}

private static void chang(long m){
    arr.add(m);
    if (m % 2 == 0) {
        // 偶变换
        chang2(m);
    }else {
        // 奇变换
        chang3(m);
    }
}

}
代码运行结果：
i = 2
arr = [27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4]
arr_size = 110
distributeArr = [3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2]
distributeArr_size = 110
ch2 = 69
ch3 = 41
p_ch2 = 0.6272727
p_ch3 = 0.37272727
ch2_divide_ch3 = 1.6829268
v = 1.584962500721156
ch2_divide_ch3 > v 故数列必收敛
TODO 未完待完善 2021-9-12

标签：考拉,概率,猜想,System,ch2,ch3,println,distributeArr,out
来源： https://www.cnblogs.com/yqq-blog/p/15257321.html