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。
use strict;my @fibonacci;my $max = 1000;&createFibonacci(1, 1, 0, \@fibonacci);foreach(@fibonacci) { print $_ . "\n";}sub createFibonacci { my $first = shift; my $second = shift; my $count = shift; my $p = shift; my $third = $first + $second; push @$p, $third if &check($third); $count ++; my $size = @$p; return 0 if($size == 11); return 0 if $count == $max; &createFibonacci($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;}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。
use strict;for(my $i = 2; $i < 5000; $i ++) { if(&check($i, 0)) { print "$i\n"; last; }}sub check { my $num = shift; my $justDecimal = shift; my $sqrtR = sprintf "%10.10f", sqrt $num; my @allNum = split /\./, $sqrtR; my @arr; if($justDecimal) { @arr = split //, $allNum[1]; } else { my @integerArr = split //, $allNum[0]; my @decimalArr = split //, $allNum[1]; @arr = (@integerArr, @decimalArr)[0..9]; } &isRepeat(\@arr);}sub isRepeat { my $p = shift; my %hash = (); my @uniqueArr = grep { ++ $hash{$_} < 2; } @$p; 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。
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; 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; 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
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