1001 害死人不偿命的(3n+1)猜想 (15 分) (1ms 极速版)

卡拉兹(Callatz)猜想：

对任何一个正整数 n，如果它是偶数，那么把它砍掉一半；如果它是奇数，那么把 (3n+1) 砍掉一半。这样一直反复砍下去，最后一定在某一步得到 n=1。卡拉兹在 1950 年的世界数学家大会上公布了这个猜想，传说当时耶鲁大学师生齐动员，拼命想证明这个貌似很傻很天真的命题，结果闹得学生们无心学业，一心只证 (3n+1)，以至于有人说这是一个阴谋，卡拉兹是在蓄意延缓美国数学界教学与科研的进展……

我们今天的题目不是证明卡拉兹猜想，而是对给定的任一不超过 1000 的正整数 n，简单地数一下，需要多少步（砍几下）才能得到 n=1？

输入格式：

每个测试输入包含 1 个测试用例，即给出正整数 n 的值。

输出格式：

输出从 n 计算到 1 需要的步数。

输入样例：

3

输出样例：

5

程序如下：

#include <stdio.h>

int main() {
    unsigned int n, step = 0;
    scanf("%u", &n);
    while (n > 1) {
        n = n & 1 ? (n * 3 + 1) / 2 : n / 2;
        step++;
    }
    printf("%u", step);
    return 0;
}

第二种，

#include <stdio.h>

int main() {
    unsigned int array[1001] = {0, 0, 1, 5, 2, 4, 6, 11, 3, 13, 5, 10, 7, 7, 12, 12, 4, 9, 14, 14, 6, 6, 11, 11, 8, 16,
                                8, 70, 13,
                                13, 13, 67, 5, 18, 10, 10, 15, 15, 15, 23, 7, 69, 7, 20, 12, 12, 12, 66, 9, 17, 17, 17,
                                9, 9, 71, 71,
                                14, 22, 14, 22, 14, 14, 68, 68, 6, 19, 19, 19, 11, 11, 11, 65, 16, 73, 16, 11, 16, 16,
                                24, 24, 8, 16,
                                70, 70, 8, 8, 21, 21, 13,
                                21, 13, 59, 13, 13, 67, 67, 10, 75, 18, 18, 18, 18, 18, 56, 10, 26, 10, 64, 72, 72, 72,
                                45, 15, 10,
                                23, 23, 15, 15, 23, 23, 15, 61, 15, 31, 69, 69, 69, 31, 7, 77, 20, 20, 20, 20, 20, 28,
                                12, 58, 12,
                                28, 12, 12, 66, 66, 17, 74, 74, 74, 17, 17, 12, 12, 17, 25, 17, 55, 25, 25, 25, 36, 9,
                                63, 17, 17,
                                71, 71, 71, 44, 9, 33, 9, 79, 22, 22, 22, 52, 14, 22, 22, 22, 14, 14, 60, 60, 14, 30,
                                14, 30, 68, 68,
                                68, 30, 11, 76, 76, 76, 19, 19, 19, 76, 19, 14, 19, 27, 19, 19, 57, 57, 11, 27, 27, 27,
                                11, 11, 65,
                                65, 73, 19, 73, 35, 73, 73, 46, 46, 16, 35, 11, 11, 24, 24, 24, 81, 16, 54, 16, 81, 24,
                                24, 24, 35,
                                16, 16, 62, 62, 16, 16, 32, 32, 70, 32, 70, 43, 70, 70, 32, 32, 8, 78, 78, 78, 21, 21,
                                21, 51, 21,
                                78, 21, 16, 21, 21, 29, 29, 13, 21, 59, 59, 13, 13, 29, 29, 13, 29, 13, 40, 67, 67, 67,
                                29, 18, 21,
                                75, 75, 75, 75, 75, 37, 18, 48, 18, 75, 13, 13, 13, 29, 18, 26, 26, 26, 18, 18, 56, 56,
                                26, 83, 26,
                                26, 26, 26, 37, 37, 10, 18, 64, 64, 18, 18, 18, 91, 72, 34, 72, 18, 72, 72, 45, 45, 10,
                                72, 34, 34,
                                10, 10, 80, 80, 23, 80, 23, 80, 23, 23, 53, 53, 15, 80, 23, 23, 23, 23, 23, 34, 15, 31,
                                15, 31, 61,
                                61, 61, 31, 15, 15, 31, 31, 15, 15, 31, 31, 69, 42, 69, 39, 69, 69, 31, 31, 12, 23, 77,
                                77, 77, 77,
                                77, 77, 20, 39, 20, 50, 20, 20, 77, 77, 20, 15, 15, 15, 20, 20, 28, 28, 20, 28, 20, 85,
                                58, 58, 58,
                                85, 12, 85, 28, 28, 28, 28, 28, 23, 12, 39, 12, 36, 66, 66, 66, 28, 74, 20, 20, 20, 74,
                                74, 36, 36,
                                74, 20, 74, 36, 47, 47, 47, 63, 17, 74, 36, 36, 12, 12, 12, 28, 25, 82, 25, 82, 25, 25,
                                82, 82, 17,
                                25, 55, 55, 17, 17, 82, 82, 25, 25, 25, 20, 25, 25, 36, 36, 17, 33, 17, 17, 63, 63, 63,
                                90, 17, 33,
                                17, 90, 33, 33, 33, 63, 71, 17, 33, 33, 71, 71, 44, 44, 71, 41, 71, 25, 33, 33, 33, 41,
                                9, 25, 79,
                                79, 79, 79, 79, 41, 22, 79, 22, 79, 22, 22, 52, 52, 22, 22, 79,
                                79, 22, 22, 17, 17, 22, 17, 22, 33, 30, 30, 30, 87, 14, 30, 22, 22, 60, 60, 60, 30, 14,
                                87, 14, 22,
                                30, 30, 30, 57, 14, 30, 30, 30, 14, 14, 41, 41, 68, 38, 68,
                                22, 68, 68, 30, 30, 19, 22, 22, 22, 76, 76, 76, 22, 76, 38, 76, 76, 76, 76, 38, 38, 19,
                                49, 49, 49,
                                19, 19, 76, 76, 14, 38, 14, 46, 14, 14, 30, 30, 19, 84, 27,
                                27, 27, 27, 27, 46, 19, 84, 19, 84, 57, 57, 57, 84, 27, 19, 84, 84, 27, 27, 27, 27, 27,
                                22, 27, 22,
                                38, 38, 38, 84, 11, 35, 19, 19, 65, 65, 65, 27, 19, 92, 19,
                                65, 19, 19, 92, 92, 73, 35, 35, 35, 73, 73, 19, 19, 73, 35, 73, 92, 46, 46, 46, 62, 11,
                                43, 73, 73,
                                35, 35, 35, 43, 11, 43, 11, 27, 81, 81, 81, 27, 24, 81, 81,
                                81, 24, 24, 81, 81, 24, 81, 24, 43, 54, 54, 54, 108, 16, 24, 81, 81, 24, 24, 24, 43, 24,
                                19, 24, 19,
                                24, 24, 35, 35, 16, 32, 32, 32, 16, 16, 32, 32, 62, 24, 62, 89, 62, 62, 32, 32, 16, 89,
                                16, 16, 32,
                                32, 32, 62, 16, 59, 16, 32, 32, 32, 32, 89, 70, 16, 43, 43, 70, 70, 40, 40, 70, 24, 70,
                                97, 32, 32,
                                32, 40, 13, 24, 24, 24, 78, 78, 78, 97, 78, 24, 78, 40, 78, 78, 78, 78, 21, 78, 40, 40,
                                21, 21, 51,
                                51, 21, 51, 21, 67, 78, 78, 78, 48, 21, 40, 16, 16, 16, 16, 16, 48, 21, 32, 21, 86, 29,
                                29, 29, 86,
                                21, 29, 29, 29, 21, 21, 86, 86, 59, 86, 59, 29, 59, 59, 86, 86, 13, 21, 86, 86, 29, 29,
                                29, 56, 29,
                                29, 29, 29, 29, 29, 24, 24, 13, 40, 40, 40, 13, 13, 37, 37, 67, 21, 67, 94, 67, 67, 29,
                                29, 75, 94,
                                21, 21, 21, 21, 21, 113, 75, 94, 75, 21, 37, 37, 37, 94, 75, 75, 21, 21, 75, 75, 37, 37,
                                48, 94, 48,
                                32, 48, 48, 64, 64, 18, 45, 75, 75, 37, 37, 37, 75, 13, 45, 13, 37, 13, 13, 29, 29, 26,
                                83, 83, 83,
                                26, 26, 83, 83, 26, 83, 26, 45, 83, 83, 83, 75, 18, 83, 26, 26, 56, 56, 56, 83, 18, 110,
                                18, 56, 83,
                                83, 83, 26, 26, 26, 26, 26, 26, 26, 21, 21, 26, 21, 26, 21, 37, 37, 37, 83, 18, 34, 34,
                                34, 18, 18,
                                18, 91, 64, 34,
                                64, 26, 64, 64, 91, 91, 18, 64, 34, 34, 18, 18, 91, 91, 34, 18, 34, 26, 34, 34, 64, 64,
                                72, 61, 18,
                                18, 34, 34, 34, 34, 72};
    unsigned int n = 0;
    scanf("%u", &n);
    printf("%u", array[n]);
    return 0;
}