Largest palindrome product
- Task
Task description is taken from Project Euler (https://projecteuler.net/problem=4)
A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.
Find the largest palindrome made from the product of two 3-digit numbers.
Go
Though, unlike Wren, can deal with 18 digit integers. Note also that it's a lot quicker in Go to reverse a number arithmetically than to reverse its string equivalent. <lang go>package main
import "fmt"
func reverse(n uint64) uint64 {
r := uint64(0)
for n > 0 {
r = n%10 + r*10
n /= 10
}
return r
}
func main() {
pow := uint64(10)
nextN:
for n := 2; n < 10; n++ {
low := pow*9 + 1
pow *= 10
high := pow - 1
fmt.Printf("Largest palindromic product of two %d-digit integers: ", n)
for i := high; i >= low; i-- {
for j := high; j >= low; j-- {
p := i * j
if p%10 != 9 {
continue
}
if p == reverse(p) {
fmt.Printf("%d x %d = %d\n", i, j, p)
continue nextN
}
}
}
}
}</lang>
- Output:
Largest palindromic product of two 2-digit integers: 99 x 91 = 9009 Largest palindromic product of two 3-digit integers: 993 x 913 = 906609 Largest palindromic product of two 4-digit integers: 9999 x 9901 = 99000099 Largest palindromic product of two 5-digit integers: 99979 x 99681 = 9966006699 Largest palindromic product of two 6-digit integers: 999999 x 999001 = 999000000999 Largest palindromic product of two 7-digit integers: 9999979 x 9467731 = 94677111177649 Largest palindromic product of two 8-digit integers: 99999999 x 99990001 = 9999000000009999 Largest palindromic product of two 9-digit integers: 999999969 x 998396971 = 998396940049693899
Raku
<lang perl6>use Prime::Factor;
.say for (1..9).hyper(:1batch).map: {.&lpp} ;
multi lpp ($oom where {$_ +& 1}) {
my $f = +(9 x ($oom + 1)); my $o = (1 + $oom) / 2; my $pal = +(9 x $o ~ 0 x $o * 2 ~ 9 x $o); sprintf "Largest palindromic product of two %2d-digit integers: %d × %d = %d", $oom + 1, $pal div $f, $f, $pal
}
multi lpp ($oom where {$_ +^ 1}) {
my $f = 9 x $oom;
my $p;
(+(1 ~ (0 x $oom)) .. +(9 ~ (9 x $oom))).reverse.map({ +($_ ~ .flip) }).map: -> $pal {
for my @factors = $pal.&divisors.grep({.chars == ($oom + 1)}).sort(-*) {
next unless $pal div $_ ∈ @factors;
$p = sprintf("Largest palindromic product of two %2d-digit integers: %d × %d = %d", $oom + 1, $pal div $_, $_, $pal) and last;
}
last if $p;
}
$p
}</lang>
Largest palindromic product of two 2-digit integers: 91 × 99 = 9009 Largest palindromic product of two 3-digit integers: 913 × 993 = 906609 Largest palindromic product of two 4-digit integers: 9901 × 9999 = 99000099 Largest palindromic product of two 5-digit integers: 99681 × 99979 = 9966006699 Largest palindromic product of two 6-digit integers: 999001 × 999999 = 999000000999 Largest palindromic product of two 7-digit integers: 9997647 × 9998017 = 99956644665999 Largest palindromic product of two 8-digit integers: 99990001 × 99999999 = 9999000000009999 Largest palindromic product of two 9-digit integers: 999920317 × 999980347 = 999900665566009999 Largest palindromic product of two 10-digit integers: 9999900001 × 9999999999 = 99999000000000099999
Ring
<lang ring> load "stdlib.ring" see "working..." + nl
prodOld = 0 limitStart = 100 limitEnd = 999
for n = limitStart to limitEnd
for m = limitStart to limitEnd
prodNew = n*m
if prodNew > prodOld and palindrome(string(prodNew))
prodOld = prodNew
first = n
second = m
ok
next
next
see "The largest palindrome is:" + nl see "" + first + " * " + second + " = " + prodOld + nl see "done..." + nl </lang>
- Output:
working... The largest palindrome is: 913 * 993 = 906609 done...
Wren
<lang ecmascript>var pow = 10 for (n in 2..7) {
var low = pow * 9 + 1
pow = pow * 10
var high = pow - 1
System.write("Largest palindromic product of two %(n)-digit integers: ")
var nextN = false
for (i in high..low) {
for (j in high..low) {
var p = i * j
if (p%10 != 9) continue
var s = p.toString
if (s == s[-1..0]) {
System.print("%(i) x %(j) = %(p)")
nextN = true
break
}
}
if (nextN) break
}
}</lang>
- Output:
Largest palindromic product of two 2-digit integers: 99 x 91 = 9009 Largest palindromic product of two 3-digit integers: 993 x 913 = 906609 Largest palindromic product of two 4-digit integers: 9999 x 9901 = 99000099 Largest palindromic product of two 5-digit integers: 99979 x 99681 = 9966006699 Largest palindromic product of two 6-digit integers: 999999 x 999001 = 999000000999 Largest palindromic product of two 7-digit integers: 9999979 x 9467731 = 94677111177649