程序员的算法趣题Perl版（四）

第十一题 
用斐波那契数列中的每一个数除以其数位上所有数字之和，求出能整除的数。我这里设置的范围是前1000个数字。

#! perl

# 20180108

# this program is used to find out some numbers in Fibonacci , and the numbers can be divisible
# by the sum of its every single number;
use strict;

# the special Fibonacci;
my @fibonacci;
# the maximum of times that the recusive function is executed 
my $max = 1000;
&createFibonacci(1, 1, 0, \@fibonacci);

# print
foreach(@fibonacci) {

    print $_ . "\n";
}

sub createFibonacci {

    my $first = shift;
    my $second = shift;
    # the 
    my $count = shift;
    # the array point
    my $p = shift;
    my $third = $first + $second;

    # push if the number is matched
    push @$p, $third if &check($third);

    $count ++;
    # the length of array now;
    my $size = @$p;
    return 0 if($size == 11);

    return 0 if $count == $max;
    # if not contiue...
    &createFibonacci($second, $third, $count, $p);
}


sub check {

    my $num = shift;

    my $leng = length $num;
    my $sum = &sum($num, $leng);

    return 1 if ($num % $sum) == 0;

    0;
}

# this function is used to sum a number`s every single numbers;
sub sum {

    my $num = shift;
    my $leng = shift;
    my $sum = 0;

    for(my $i = 0; $i < $leng; $i ++) {

        return $num if $leng == 1;

        $sum += substr $num, $i, 1;
    }

    $sum;
}
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答案： 
2 
3 
5 
8 
21 
144 
2584 
14930352 
86267571272 
498454011879264 
160500643816367088

第十二题 
求在计算平方根的时候，最早让0-9全部出现的最小整数。

#! perl

# 20180109
# 20180110

use strict;

for(my $i = 2; $i < 5000; $i ++) {

    if(&check($i, 0)) {

        print "$i\n";
        last;
    }
}

sub check {

    # the number checked
    my $num = shift;
    # '0' means that includes integer, '1' means just decimal
    my $justDecimal = shift;
    # get the square root of a number
    my $sqrtR = sprintf "%10.10f", sqrt $num;
    # split with '.'
    my @allNum = split /\./, $sqrtR;
    # this array is used to check if the number is repeat
    my @arr;
    if($justDecimal) {

        # just split the decimal part
        @arr = split //, $allNum[1];
    } else {

        my @integerArr = split //, $allNum[0];
        my @decimalArr = split //, $allNum[1];
        # include integer, get 10 numbers from the left
        @arr = (@integerArr, @decimalArr)[0..9];
    }

    &isRepeat(\@arr);
}

sub isRepeat {

    # the point of the array
    my $p = shift;
    # key is numbers, value is times
    my %hash = ();
    my @uniqueArr = grep {
        # put the number which is found only once into the hash
        ++ $hash{$_} < 2;
        } @$p;

    # the array is repeat if the size of the array is not 10
    return 1 if $#uniqueArr + 1 == 10;
}
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答案： 
包含整数部分：1362 
只有小数部分：143

第十三题 
给字母赋值，求使下列算式成立的解有多少种。字母代表的数字不可以相等。

#! perl

# 20180114
# 20180116

# this guy is used to compute READ + WRITE + TALK = SKILL;

use Algorithm::Combinatorics qw(
                                combinations
                                combinations_with_repetition
                                variations
                                variations_with_repetition
                                tuples
                                tuples_with_repetition
                                permutations
                                circular_permutations
                                derangements
                                complete_permutations
                                partitions
                                subsets
                            );
use strict;

my $start = time;
my @numbers = (0..9);

my @result;
my $count = 0;

&sum(\@numbers, 10);

foreach (@result) {

    print "$_\n";
}

print "$count \n";

my $duration = time - $start;
print "$duration s\n";

sub sum {

    my $numbersP = shift;
    my $k = shift;

    # permutation
    my $iter = variations($numbersP, $k);

    while(my $item = $iter -> next) {

        &isRight($item);
    }
}

sub isRight {

    my @str_arr = @{@_[0]};

    my ($r, $e, $a, $d, $w, $i, $t, $l, $k, $s) = @str_arr;

    # The highest number of digits can not be zero.
    return 0 if $r == 0 || $w == 0 || $t == 0 || $s == 0;

    my $read = $r * 1000 + $e * 100 + $a * 10 + $d;
    my $write = $w * 10000 + $r * 1000 + $i * 100 + $t * 10 + $e;
    my $talk = $t * 1000 + $a * 100 + $l * 10 + $k;
    my $skill = $s * 10000 + $k * 1000 + $i * 100 + $l * 10 + $l;

    if ($read + $write + $talk == $skill) {

        push @result, "$read + $write + $talk = $skill";
        $count ++;
        return 1;
    }

    0
}
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答案： 
10种 
1632 + 41976 + 7380 = 50988 
2543 + 72065 + 6491 = 81099 
4905 + 24689 + 8017 = 37611 
5094 + 75310 + 1962 = 82366 
5096 + 35710 + 1982 = 42788 
5180 + 65921 + 2843 = 73944 
5270 + 85132 + 3764 = 94166 
7092 + 37510 + 1986 = 46588 
7092 + 47310 + 1986 = 56388 
9728 + 19467 + 6205 = 35400