Combinations with repetitions/Square digit chain: Difference between revisions
Combinations with repetitions/Square digit chain (view source)
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=={{header|D}}==
{{improve|D|See talk page}}
<syntaxhighlight lang="d">
// Count how many number chains for Natural Numbers < 10**K end with a value of 1.
//
Line 117:
writefln ("\n(k=%d) In the range 1 to %d\n%d translate to 1 and %d translate to 89\n", K, (cast (ulong) (10))^^K-1,z,(cast (ulong) (10))^^K-1-z);
}
</syntaxhighlight>
{{out}}
<pre>
Line 135:
//12024696404768024 translate to 1 and 87975303595231975 translate to 89
</pre>
=={{header|Go}}==
{{trans|Kotlin}}
<syntaxhighlight lang="go">package main
import (
"fmt"
"math"
)
func endsWithOne(n int) bool {
sum := 0
for {
for n > 0 {
digit := n % 10
sum += digit * digit
n /= 10
}
if sum == 1 {
return true
}
if sum == 89 {
return false
}
n = sum
sum = 0
}
}
func main() {
ks := [...]int{7, 8, 11, 14, 17}
for _, k := range ks {
sums := make([]int64, k*81+1)
sums[0] = 1
sums[1] = 0
for n := 1; n <= k; n++ {
for i := n * 81; i > 0; i-- {
for j := 1; j < 10; j++ {
s := j * j
if s > i {
break
}
sums[i] += sums[i-s]
}
}
}
count1 := int64(0)
for i := 1; i <= k*81; i++ {
if endsWithOne(i) {
count1 += sums[i]
}
}
limit := int64(math.Pow10(k)) - 1
fmt.Println("For k =", k, "in the range 1 to", limit)
fmt.Println(count1, "numbers produce 1 and", limit-count1, "numbers produce 89\n")
}
}</syntaxhighlight>
{{out}}
<pre>
For k = 7 in the range 1 to 9999999
1418853 numbers produce 1 and 8581146 numbers produce 89
For k = 8 in the range 1 to 99999999
14255666 numbers produce 1 and 85744333 numbers produce 89
For k = 11 in the range 1 to 99999999999
15091199356 numbers produce 1 and 84908800643 numbers produce 89
For k = 14 in the range 1 to 99999999999999
13770853279684 numbers produce 1 and 86229146720315 numbers produce 89
For k = 17 in the range 1 to 99999999999999999
12024696404768024 numbers produce 1 and 87975303595231975 numbers produce 89
</pre>
=={{header|jq}}==
{{trans|Wren}}
'''Works with jq''' (*)
'''Works with gojq, the Go implementation of jq'''
(*) For the given values of k up to and including 14, the C implementation of jq has sufficient
precision, but for k==17, the unbounded precision integer arithmetic
of gojq would be required. The output shown below is taken from a gojq run.
<syntaxhighlight lang="jq"># For gojq:
def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);
def endsWithOne:
. as $start
| { n: ., sum: 0 }
| until(.stop;
until(.n <= 0;
(.n % 10) as $digit
| .sum += $digit * $digit
| .n = (.n / 10 | floor)
)
| if .sum == 1 then .stop = 1
elif .sum == 89 then .stop = 0
else .n = .sum
| .sum = 0
end )
| .stop == 1 ;
def ks: [7, 8, 11, 14, 17];
ks[] as $k
| {sums: [1,0]}
| reduce range(1; $k+1) as $n (.;
reduce range( $n*81; 0; -1) as $i (.;
.emit = false
| .j = 0
| until(.emit or (.j == 9);
.j+=1
| (.j * .j) as $s
| if ($s > $i) then .emit = true
else .sums[$i] = .sums[$i] + .sums[$i-$s]
end) ))
| .count1 = 0
| reduce range(1; 1 + $k*81) as $i (.; if $i|endsWithOne then .count1 = .count1 + .sums[$i] else . end)
| ((10|power($k)) - 1) as $limit
| "For k = \($k) in the range 1 to \($limit)",
"\(.count1) numbers produce 1 and \($limit - .count1) numbers produce 89.\n"</syntaxhighlight>
{{out}}
<pre>
For k = 7 in the range 1 to 9999999
1418853 numbers produce 1 and 8581146 numbers produce 89.
For k = 8 in the range 1 to 99999999
14255666 numbers produce 1 and 85744333 numbers produce 89.
For k = 11 in the range 1 to 99999999999
15091199356 numbers produce 1 and 84908800643 numbers produce 89.
For k = 14 in the range 1 to 99999999999999
13770853279684 numbers produce 1 and 86229146720315 numbers produce 89.
For k = 17 in the range 1 to 99999999999999999
12024696404768024 numbers produce 1 and 87975303595231975 numbers produce 89.
</pre>
=={{header|Julia}}==
<syntaxhighlight lang="julia">using Combinatorics
function iterate(m::Integer)
while m != 1 && m != 89
s = 0
while m > 0 # compute sum of squares of digits
m, d = divrem(m, 10)
s += d ^ 2
end
m = s
end
return m
end
function testitersquares(numdigits)
items = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
onecount, eightyninecount = 0, 0
for combo in with_replacement_combinations(items, numdigits)
if any(x -> x != 0, combo)
pcount = Int(factorial(length(combo)) /
prod(y -> factorial(sum(x -> x == y, combo)), unique(combo)))
if iterate(sum(combo)) == 89
eightyninecount += pcount
else
onecount += pcount
end
end
end
println("For k = $numdigits, in the range 1 to $("9" ^ numdigits),\n" *
"$onecount numbers produce 1 and $eightyninecount numbers produce 89.\n")
end
for i in [7, 8, 11, 14, 17]
testitersquares(i)
end
</syntaxhighlight>{{out}}
<pre>
For k = 2, in the range 1 to 99,
19 numbers produce 1 and 80 numbers produce 89.
For k = 7, in the range 1 to 9999999,
1418853 numbers produce 1 and 8581146 numbers produce 89.
For k = 8, in the range 1 to 99999999,
14255666 numbers produce 1 and 85744333 numbers produce 89.
For k = 11, in the range 1 to 99999999999,
15091199356 numbers produce 1 and 84908800643 numbers produce 89.
For k = 14, in the range 1 to 99999999999999,
13770853279684 numbers produce 1 and 86229146720315 numbers produce 89.
For k = 17, in the range 1 to 99999999999999999,
12024696404768024 numbers produce 1 and 87975303595231975 numbers produce 89.
</pre>
=={{header|Kotlin}}==
To achieve reasonable performance, the Kotlin entry for the [[Iterated digits squaring]] task already used a similar approach to that required by this task for k = 8.
So the following generalizes that code to deal with values of k up to 17 (which requires 64 bit integers) and to count numbers where the squared digits sum sequence eventually ends in 1 rather than 89, albeit the sum of both must of course be 10 ^ k - 1.
<syntaxhighlight lang="scala">// version 1.1.51
fun endsWithOne(n: Int): Boolean {
var digit: Int
var sum = 0
var nn = n
while (true) {
while (nn > 0) {
digit = nn % 10
sum += digit * digit
nn /= 10
}
if (sum == 1) return true
if (sum == 89) return false
nn = sum
sum = 0
}
}
fun main(args: Array<String>) {
val ks = intArrayOf(7, 8, 11, 14, 17)
for (k in ks) {
val sums = LongArray(k * 81 + 1)
sums[0] = 1
sums[1] = 0
var s: Int
for (n in 1 .. k) {
for (i in n * 81 downTo 1) {
for (j in 1 .. 9) {
s = j * j
if (s > i) break
sums[i] += sums[i - s]
}
}
}
var count1 = 0L
for (i in 1 .. k * 81) if (endsWithOne(i)) count1 += sums[i]
val limit = Math.pow(10.0, k.toDouble()).toLong() - 1
println("For k = $k in the range 1 to $limit")
println("$count1 numbers produce 1 and ${limit - count1} numbers produce 89\n")
}
}</syntaxhighlight>
{{out}}
<pre>
For k = 7 in the range 1 to 9999999
1418853 numbers produce 1 and 8581146 numbers produce 89
For k = 8 in the range 1 to 99999999
14255666 numbers produce 1 and 85744333 numbers produce 89
For k = 11 in the range 1 to 99999999999
15091199356 numbers produce 1 and 84908800643 numbers produce 89
For k = 14 in the range 1 to 99999999999999
13770853279684 numbers produce 1 and 86229146720315 numbers produce 89
For k = 17 in the range 1 to 99999999999999999
12024696404768024 numbers produce 1 and 87975303595231975 numbers produce 89
</pre>
=={{header|Nim}}==
{{trans|Kotlin}}
<syntaxhighlight lang="nim">import math, strformat
func endsWithOne(n: Natural): bool =
var n = n
while true:
var sum = 0
while n > 0:
let digit = n mod 10
sum += digit * digit
n = n div 10
if sum == 1: return true
if sum == 89: return false
n = sum
const Ks = [7, 8, 11, 14, 17]
for k in Ks:
var sums = newSeq[int64](k * 81 + 1) # Initialized to 0s.
sums[0] = 1
for n in 1..k:
for i in countdown(n * 81, 1):
for j in 1..9:
let s = j * j
if s > i: break
sums[i] += sums[i - s]
var count1 = 0i64
for i in 1..k*81:
if i.endsWithOne(): count1 += sums[i]
let limit = 10^k - 1
echo &"For k = {k} in the range 1 to {limit}"
echo &"{count1} numbers produce 1 and {limit - count1} numbers produce 89\n"</syntaxhighlight>
{{out}}
<pre>For k = 7 in the range 1 to 9999999
1418853 numbers produce 1 and 8581146 numbers produce 89
For k = 8 in the range 1 to 99999999
14255666 numbers produce 1 and 85744333 numbers produce 89
For k = 11 in the range 1 to 99999999999
15091199356 numbers produce 1 and 84908800643 numbers produce 89
For k = 14 in the range 1 to 99999999999999
13770853279684 numbers produce 1 and 86229146720315 numbers produce 89
For k = 17 in the range 1 to 99999999999999999
12024696404768024 numbers produce 1 and 87975303595231975 numbers produce 89</pre>
=={{header|Perl}}==
{{trans|Raku}}
<syntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
use Math::AnyNum qw(:overload);
sub comma { reverse ((reverse shift) =~ s/(.{3})/$1,/gr) =~ s/^,//r }
sub endsWithOne {
my($n) = @_;
my $digit;
my $sum = 0;
my $nn = $n;
while () {
while ($nn > 0) {
$digit = $nn % 10;
$sum += $digit**2;
$nn = int $nn / 10;
}
return 1 if $sum == 1;
return 0 if $sum == 89;
$nn = $sum;
$sum = 0;
}
}
my @ks = <7 8 11 14 17>;
for my $k (@ks) {
my @sums = <1 0>;
my $s;
for my $n (1 .. $k) {
for my $i (reverse 1 .. $n*81) {
for my $j (1 .. 9) {
no warnings 'uninitialized';
last if ($s = $j**2) > $i;
$sums[$i] += $sums[$i-$s];
}
}
}
my $count1 = 0;
for my $i (1 .. $k*81) { $count1 += $sums[$i] if endsWithOne($i) }
my $limit = 10**$k - 1;
say "For k = $k in the range 1 to " . comma $limit;
say comma($count1) . ' numbers produce 1 and ' . comma($limit-$count1) . " numbers produce 89\n";
}</syntaxhighlight>
{{out}}
<pre>For k = 7 in the range 1 to 9,999,999
1,418,853 numbers produce 1 and 8,581,146 numbers produce 89
For k = 8 in the range 1 to 99,999,999
14,255,666 numbers produce 1 and 85,744,333 numbers produce 89
For k = 11 in the range 1 to 99,999,999,999
15,091,199,356 numbers produce 1 and 84,908,800,643 numbers produce 89
For k = 14 in the range 1 to 99,999,999,999,999
13,770,853,279,684 numbers produce 1 and 86,229,146,720,315 numbers produce 89
For k = 17 in the range 1 to 99,999,999,999,999,999
12,024,696,404,768,024 numbers produce 1 and 87,975,303,595,231,975 numbers produce 89</pre>
=={{header|Phix}}==
{{trans|Wren}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">endsWithOne</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">total</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">digit</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">total</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">digit</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">digit</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">total</span><span style="color: #0000FF;">==</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">true</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">total</span><span style="color: #0000FF;">==</span><span style="color: #000000;">89</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #004600;">false</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">total</span>
<span style="color: #000000;">total</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">ks</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">11</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">14</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17</span><span style="color: #0000FF;">}</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">count1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">si</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
<span style="color: #000000;">limit</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">ki</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ks</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ks</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ki</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sums</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">*</span><span style="color: #000000;">81</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sums</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">sums</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">k</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">81</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">j</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">></span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sums</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">sums</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">s</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">*</span><span style="color: #000000;">81</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">endsWithOne</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">mpz_set_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">si</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sums</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">si</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_sub_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">si</span><span style="color: #0000FF;">,</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count1</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">limit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">comma_fill</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">count1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">comma_fill</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">si</span><span style="color: #0000FF;">,</span><span style="color: #000000;">comma_fill</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"For k = %d in the range 1 to %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s numbers produce 1 and %s numbers produce 89\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
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<pre>
For k = 7 in the range 1 to 9,999,999
1,418,853 numbers produce 1 and 8,581,146 numbers produce 89
For k = 8 in the range 1 to 99,999,999
14,255,666 numbers produce 1 and 85,744,333 numbers produce 89
For k = 11 in the range 1 to 99,999,999,999
15,091,199,356 numbers produce 1 and 84,908,800,643 numbers produce 89
For k = 14 in the range 1 to 99,999,999,999,999
13,770,853,279,684 numbers produce 1 and 86,229,146,720,315 numbers produce 89
For k = 17 in the range 1 to 99,999,999,999,999,999
12,024,696,404,768,024 numbers produce 1 and 87,975,303,595,231,975 numbers produce 89
</pre>
Also, [[Iterated_digits_squaring#Phix]] produces some of the same numbers (just not so high).
=={{header|Raku}}==
(formerly Perl 6)
{{trans|Kotlin}}
<syntaxhighlight lang="raku" line>use v6;
sub endsWithOne($n --> Bool) {
my $digit;
my $sum = 0;
my $nn = $n;
loop {
while ($nn > 0) {
$digit = $nn % 10;
$sum += $digit²;
$nn = $nn div 10;
}
($sum == 1) and return True;
($sum == 89) and return False;
$nn = $sum;
$sum = 0;
}
}
my @ks = (7, 8, 11, 14, 17);
for @ks -> $k {
my @sums is default(0) = 1,0;
my $s;
for (1 .. $k) -> $n {
for ($n*81 ... 1) -> $i {
for (1 .. 9) -> $j {
$s = $j²;
if ($s > $i) { last };
@sums[$i] += @sums[$i-$s];
}
}
}
my $count1 = 0;
for (1 .. $k*81) -> $i { if (endsWithOne($i)) {$count1 += @sums[$i]} }
my $limit = 10**$k - 1;
say "For k = $k in the range 1 to $limit";
say "$count1 numbers produce 1 and ",$limit-$count1," numbers produce 89";
}</syntaxhighlight>
{{out}}
<pre>For k = 7 in the range 1 to 9999999
1418853 numbers produce 1 and 8581146 numbers produce 89
For k = 8 in the range 1 to 99999999
14255666 numbers produce 1 and 85744333 numbers produce 89
For k = 11 in the range 1 to 99999999999
15091199356 numbers produce 1 and 84908800643 numbers produce 89
For k = 14 in the range 1 to 99999999999999
13770853279684 numbers produce 1 and 86229146720315 numbers produce 89
For k = 17 in the range 1 to 99999999999999999
12024696404768024 numbers produce 1 and 87975303595231975 numbers produce 89</pre>
=={{header|Ruby}}==
<
# Count how many number chains for Natural Numbers < 10**K end with a value of 1.
#
Line 160 ⟶ 667:
}
puts "\nk=(#{K}) in the range 1 to #{10**K-1}\n#{z} numbers produce 1 and #{10**K-1-z} numbers produce 89"
</syntaxhighlight>
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<pre>
Line 177 ⟶ 684:
#(k=17) in the range 1 to 99999999999999999
#12024696404768024 numbers produce 1 and 87975303595231975 numbers produce 89
</pre>
=={{header|Wren}}==
{{trans|Kotlin}}
{{libheader|Wren-big}}
As Wren doesn't have 64 bit integers, it is necessary to use BigInt here to process k = 17.
<syntaxhighlight lang="wren">import "./big" for BigInt
var endsWithOne = Fn.new { |n|
var sum = 0
while (true) {
while (n > 0) {
var digit = n % 10
sum = sum + digit * digit
n = (n/10).floor
}
if (sum == 1) return true
if (sum == 89) return false
n = sum
sum = 0
}
}
var ks = [7, 8, 11, 14, 17]
for (k in ks) {
var sums = List.filled(k * 81 + 1, 0)
sums[0] = 1
sums[1] = 0
for (n in 1..k) {
for (i in n*81..1) {
for (j in 1..9) {
var s = j * j
if (s > i) break
sums[i] = sums[i] + sums[i-s]
}
}
}
var count1 = BigInt.zero
for (i in 1..k*81) if (endsWithOne.call(i)) count1 = count1 + sums[i]
var limit = BigInt.ten.pow(k) - 1
System.print("For k = %(k) in the range 1 to %(limit)")
System.print("%(count1) numbers produce 1 and %(limit - count1) numbers produce 89\n")
}</syntaxhighlight>
{{out}}
<pre>
For k = 7 in the range 1 to 9999999
1418853 numbers produce 1 and 8581146 numbers produce 89
For k = 8 in the range 1 to 99999999
14255666 numbers produce 1 and 85744333 numbers produce 89
For k = 11 in the range 1 to 99999999999
15091199356 numbers produce 1 and 84908800643 numbers produce 89
For k = 14 in the range 1 to 99999999999999
13770853279684 numbers produce 1 and 86229146720315 numbers produce 89
For k = 17 in the range 1 to 99999999999999999
12024696404768024 numbers produce 1 and 87975303595231975 numbers produce 89
</pre>
=={{header|zkl}}==
{{trans|Ruby}}
<syntaxhighlight lang="zkl">fcn countNumberChains(K){
F:=(K+1).pump(List,fcn(n){ (1).reduce(n,'*,1) }); #Some small factorials
g:=fcn(n){
Line 192 ⟶ 758:
n,G:=K*81+1,n.pump(List,g);
N:=n.pump(List,'wrap(n){ n=g(n); while(n>1){ n=G[n] } n });
z:=([0..9].pump(List,fcn(n){ n*n }):Utils.Helpers.combosKW(K,_)) #combos of (0,1,4,9,16,25,36,49,64,81)
.reduce('wrap(z,ds){ #Iterate over unique digit combinations
if(N[ds.sum(0)]==0) return(z); #Count only ones
nn:=Dictionary(); #Determine how many numbers this digit combination corresponds to
ds.pump(Void,nn.incV); #and (eg (0,0,0,0,0,1,9)-->(0:5, 1:1, 9:1)
z +
'wrap(gn,n){ gn/F[n] },F[K]);
},0);
println("\nk=(%d) in the range 1 to %,d".fmt(K,(10).pow(K)-1));
println("%,d numbers produce 1 and %,d numbers produce 89".fmt(z,(10).pow(K)-1-z));
z
}</syntaxhighlight>
combosKW(k,sequence) is lazy, which, in this case, is quite a bit faster than the non-lazy version.
<
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<pre>
| |||