Question

注意：

1）对于s = n 我们有来自1,2,3 ...，n的元素，用于填充矩阵

2）如果没有，两个矩阵是不同的。列是不同的或如果他们没有。行是不同的

我试图找到类似的解决方案 s = 1 我们只能制作1矩阵

然后是s = 2 我们有两个矩阵 [1 2]订购1x2，另外订购2x1

列

表示s = 3，也就是两个矩阵订单1x3的[1 2 3]和订单3x1的列的另一个

但s = 4 我们有矩阵1x4,4x1和2x2

但我无法在此找到任何模式对于s = 1,2,3,4,5,6...

的所有值

需要帮助！

Answer 1

您提供的示例以及接下来的几个示例是：

的1x1
1x2,2x1
1x3,3x1
1x4,2x2,4x1
1x5,5x1
1x6,2x3,3x2,6x1
1x7,7x1
1x8,2x4,4x2,8x1

那么模式是什么？解决方案只是s的整数除数。当然，始终1和s本身，以及均匀划分s的每个整数。您可以找到算法来在线查找整数的所有因子，例如：Algorithm to find all the exact divisors of a given integer或此处：Best way to find all factors of a given number in C#

Answer 2

你需要可分的因子[不一定是素数]来获得数字对。

这是一个[工作] perl脚本。我不会写＆＃34;惯用语＆＃34; perl，但是，更像是一个C程序员，所以应该很容易将其视为伪代码来编写C程序：

#!/usr/bin/perl
# mtxcombo -- generate matrix combinations

master(@ARGV);
exit(0);

# master -- master control
sub master
{
    my(@argv) = @_;
    my($lim);
    my($s);

    $lim = shift(@argv);
    $lim //= 1000;

    for ($s = 1;  $s <= $lim;  ++$s) {
        domtx($s);
    }
}

sub domtx
{
    my($s) = @_;
    my($i);
    my($d);

    printf("%d:",$s);

    add(1,$s);

    for ($i = 2;  $i < $s;  ++$i) {
        # up to sqrt
        last if (($i * $i) > $s);

        if (($s % $i) == 0) {
            $d = int($s / $i);
            add($d,$i);
            next;
        }
    }

    printf("\n");
}

sub add
{
    my($x,$y) = @_;

    printf(" %dx%d",$x,$y);

    if ($x != $y) {
        printf(" %dx%d",$y,$x);
    }
}

这是<program> 100的程序输出：

1: 1x1
2: 1x2 2x1
3: 1x3 3x1
4: 1x4 4x1 2x2
5: 1x5 5x1
6: 1x6 6x1 3x2 2x3
7: 1x7 7x1
8: 1x8 8x1 4x2 2x4
9: 1x9 9x1 3x3
10: 1x10 10x1 5x2 2x5
11: 1x11 11x1
12: 1x12 12x1 6x2 2x6 4x3 3x4
13: 1x13 13x1
14: 1x14 14x1 7x2 2x7
15: 1x15 15x1 5x3 3x5
16: 1x16 16x1 8x2 2x8 4x4
17: 1x17 17x1
18: 1x18 18x1 9x2 2x9 6x3 3x6
19: 1x19 19x1
20: 1x20 20x1 10x2 2x10 5x4 4x5
21: 1x21 21x1 7x3 3x7
22: 1x22 22x1 11x2 2x11
23: 1x23 23x1
24: 1x24 24x1 12x2 2x12 8x3 3x8 6x4 4x6
25: 1x25 25x1 5x5
26: 1x26 26x1 13x2 2x13
27: 1x27 27x1 9x3 3x9
28: 1x28 28x1 14x2 2x14 7x4 4x7
29: 1x29 29x1
30: 1x30 30x1 15x2 2x15 10x3 3x10 6x5 5x6
31: 1x31 31x1
32: 1x32 32x1 16x2 2x16 8x4 4x8
33: 1x33 33x1 11x3 3x11
34: 1x34 34x1 17x2 2x17
35: 1x35 35x1 7x5 5x7
36: 1x36 36x1 18x2 2x18 12x3 3x12 9x4 4x9 6x6
37: 1x37 37x1
38: 1x38 38x1 19x2 2x19
39: 1x39 39x1 13x3 3x13
40: 1x40 40x1 20x2 2x20 10x4 4x10 8x5 5x8
41: 1x41 41x1
42: 1x42 42x1 21x2 2x21 14x3 3x14 7x6 6x7
43: 1x43 43x1
44: 1x44 44x1 22x2 2x22 11x4 4x11
45: 1x45 45x1 15x3 3x15 9x5 5x9
46: 1x46 46x1 23x2 2x23
47: 1x47 47x1
48: 1x48 48x1 24x2 2x24 16x3 3x16 12x4 4x12 8x6 6x8
49: 1x49 49x1 7x7
50: 1x50 50x1 25x2 2x25 10x5 5x10
51: 1x51 51x1 17x3 3x17
52: 1x52 52x1 26x2 2x26 13x4 4x13
53: 1x53 53x1
54: 1x54 54x1 27x2 2x27 18x3 3x18 9x6 6x9
55: 1x55 55x1 11x5 5x11
56: 1x56 56x1 28x2 2x28 14x4 4x14 8x7 7x8
57: 1x57 57x1 19x3 3x19
58: 1x58 58x1 29x2 2x29
59: 1x59 59x1
60: 1x60 60x1 30x2 2x30 20x3 3x20 15x4 4x15 12x5 5x12 10x6 6x10
61: 1x61 61x1
62: 1x62 62x1 31x2 2x31
63: 1x63 63x1 21x3 3x21 9x7 7x9
64: 1x64 64x1 32x2 2x32 16x4 4x16 8x8
65: 1x65 65x1 13x5 5x13
66: 1x66 66x1 33x2 2x33 22x3 3x22 11x6 6x11
67: 1x67 67x1
68: 1x68 68x1 34x2 2x34 17x4 4x17
69: 1x69 69x1 23x3 3x23
70: 1x70 70x1 35x2 2x35 14x5 5x14 10x7 7x10
71: 1x71 71x1
72: 1x72 72x1 36x2 2x36 24x3 3x24 18x4 4x18 12x6 6x12 9x8 8x9
73: 1x73 73x1
74: 1x74 74x1 37x2 2x37
75: 1x75 75x1 25x3 3x25 15x5 5x15
76: 1x76 76x1 38x2 2x38 19x4 4x19
77: 1x77 77x1 11x7 7x11
78: 1x78 78x1 39x2 2x39 26x3 3x26 13x6 6x13
79: 1x79 79x1
80: 1x80 80x1 40x2 2x40 20x4 4x20 16x5 5x16 10x8 8x10
81: 1x81 81x1 27x3 3x27 9x9
82: 1x82 82x1 41x2 2x41
83: 1x83 83x1
84: 1x84 84x1 42x2 2x42 28x3 3x28 21x4 4x21 14x6 6x14 12x7 7x12
85: 1x85 85x1 17x5 5x17
86: 1x86 86x1 43x2 2x43
87: 1x87 87x1 29x3 3x29
88: 1x88 88x1 44x2 2x44 22x4 4x22 11x8 8x11
89: 1x89 89x1
90: 1x90 90x1 45x2 2x45 30x3 3x30 18x5 5x18 15x6 6x15 10x9 9x10
91: 1x91 91x1 13x7 7x13
92: 1x92 92x1 46x2 2x46 23x4 4x23
93: 1x93 93x1 31x3 3x31
94: 1x94 94x1 47x2 2x47
95: 1x95 95x1 19x5 5x19
96: 1x96 96x1 48x2 2x48 32x3 3x32 24x4 4x24 16x6 6x16 12x8 8x12
97: 1x97 97x1
98: 1x98 98x1 49x2 2x49 14x7 7x14
99: 1x99 99x1 33x3 3x33 11x9 9x11
100: 1x100 100x1 50x2 2x50 25x4 4x25 20x5 5x20 10x10

找到所有大小的不同矩阵（N）的数量（元素的数量）？

2 个答案: