# Distinct palindromes within decimal numbers

Distinct palindromes within decimal numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Find all distinct palindromes contained as substrings in decimal representation of n. Note that for the purpose of the initial function, a single digit will be considered a palindrome.

1. Find all the palindromes including single digits in the integers from 100 to 125, inclusive.
2. Determine which if any of the following decimal integers contain palindromes of 2 digits or more:
``` 9, 169, 12769, 1238769, 123498769, 12346098769, 1234572098769,
123456832098769, 12345679432098769, 1234567905432098769, 123456790165432098769,
83071934127905179083, 1320267947849490361205695
```
Also see

## Factor

Works with: Factor version 0.99 2021-02-05

<lang factor>USING: formatting io kernel math math.ranges present prettyprint sequences sequences.extras sets ;

dpal ( n -- seq )
```   present all-subseqs members [ dup reverse = ] filter ;
```

! task 1 "Number Palindromes" print 100 125 [a..b] [ dup pprint bl bl bl bl bl dpal . ] each nl

! task 2 "Number Has no >= 2 digit-palindromes?" print { 9 169 12769 1238769 123498769 12346098769 1234572098769

``` 123456832098769 12345679432098769 1234567905432098769
123456790165432098769 83071934127905179083
1320267947849490361205695 }
```

[ dup dpal [ length 2 < ] reject empty? "%-25d %u\n" printf ] each</lang>

Output:
```Number  Palindromes
100     { "1" "0" "00" }
101     { "1" "0" "101" }
102     { "1" "0" "2" }
103     { "1" "0" "3" }
104     { "1" "0" "4" }
105     { "1" "0" "5" }
106     { "1" "0" "6" }
107     { "1" "0" "7" }
108     { "1" "0" "8" }
109     { "1" "0" "9" }
110     { "1" "0" "11" }
111     { "1" "11" "111" }
112     { "1" "2" "11" }
113     { "1" "3" "11" }
114     { "1" "4" "11" }
115     { "1" "5" "11" }
116     { "1" "6" "11" }
117     { "1" "7" "11" }
118     { "1" "8" "11" }
119     { "1" "9" "11" }
120     { "1" "2" "0" }
121     { "1" "2" "121" }
122     { "1" "2" "22" }
123     { "1" "2" "3" }
124     { "1" "2" "4" }
125     { "1" "2" "5" }

Number                    Has no >= 2 digit-palindromes?
9                         t
169                       t
12769                     t
1238769                   t
123498769                 t
12346098769               t
1234572098769             t
123456832098769           t
12345679432098769         t
1234567905432098769       t
123456790165432098769     t
83071934127905179083      t
1320267947849490361205695 f
```

## Julia

<lang julia>function allpalindromes(a::Vector{T}) where T

```   pals = Vector{Vector{T}}([[x] for x in a])
len = length(a)
len < 2 && return pals
a == reverse(a) && push!(pals, a)
len == 2 && return pals
for i in 2:len
left = a[1:i]
left == reverse(left) && push!(pals, left)
end
return unique(vcat(pals, allpalindromes(a[2:end])))
```

end

println("Number Palindromes") for n in 100:125

```   println(" ", rpad(n, 7), sort(allpalindromes(digits(n))))
```

end

palindrome2plusfree(n) = (a = allpalindromes(digits(n)); all(x -> length(x) == 1, a))

println("\nNumber Has no >= 2 digit palindromes") for n in [9, 169, 12769, 1238769, 123498769, 12346098769, 1234572098769, 123456832098769,

```   12345679432098769, 1234567905432098769, 123456790165432098769, 83071934127905179083, 1320267947849490361205695]
```

end

</lang>
Output:
```Number  Palindromes
100    [[0], [0, 0], [1]]
101    [[0], [1], [1, 0, 1]]
102    [[0], [1], [2]]
103    [[0], [1], [3]]
104    [[0], [1], [4]]
105    [[0], [1], [5]]
106    [[0], [1], [6]]
107    [[0], [1], [7]]
108    [[0], [1], [8]]
109    [[0], [1], [9]]
110    [[0], [1], [1, 1]]
111    [[1], [1, 1], [1, 1, 1]]
112    [[1], [1, 1], [2]]
113    [[1], [1, 1], [3]]
114    [[1], [1, 1], [4]]
115    [[1], [1, 1], [5]]
116    [[1], [1, 1], [6]]
117    [[1], [1, 1], [7]]
118    [[1], [1, 1], [8]]
119    [[1], [1, 1], [9]]
120    [[0], [1], [2]]
121    [[1], [1, 2, 1], [2]]
122    [[1], [2], [2, 2]]
123    [[1], [2], [3]]
124    [[1], [2], [4]]
125    [[1], [2], [5]]

Number                    Has no >= 2 digit palindromes
9                         true
169                       true
12769                     true
1238769                   true
123498769                 true
12346098769               true
1234572098769             true
123456832098769           true
12345679432098769         true
1234567905432098769       true
123456790165432098769     true
83071934127905179083      true
1320267947849490361205695 false
```

## Phix

```procedure show_all_palindromes(string s, integer longest=0)
sequence res = {}
for i=1 to length(s) do
if longest=0 then
res = append(res,{1,s[i..i]})
end if
for j=0 to iff(i>1 and s[i-1]=s[i]?2:1) do
integer rev = j,
fwd = 1
while rev<i and i+fwd<=length(s) and s[i-rev]=s[i+fwd] do
if longest=0 then
res = append(res,{rev+fwd+1,s[i-rev..i+fwd]})
end if
rev += 1
fwd += 1
end while
if longest>0 then
longest = max(longest,rev+fwd-1)
end if
end for
end for
if longest then
printf(1,"%-26s %t\n",{s,longest<3})
else
printf(1," %s    %s\n",{s,join(vslice(unique(res),2))})
end if
end procedure

printf(1,"Number  Palindromes\n")
papply(apply(true,sprintf,{{"%d"},tagset(125,100)}),show_all_palindromes)

constant tests = split_any("""9, 169, 12769, 1238769, 123498769, 12346098769,
1234572098769, 123456832098769, 12345679432098769, 1234567905432098769,
123456790165432098769, 83071934127905179083, 1320267947849490361205695"""," ,\n")
printf(1,"\nNumber           Has no >2 digit palindromes\n")
papply(true,show_all_palindromes,{tests,1})
```
Output:
```Number  Palindromes
100    0 1 00
101    0 1 101
102    0 1 2
103    0 1 3
104    0 1 4
105    0 1 5
106    0 1 6
107    0 1 7
108    0 1 8
109    0 1 9
110    0 1 11
111    1 11 111
112    1 2 11
113    1 3 11
114    1 4 11
115    1 5 11
116    1 6 11
117    1 7 11
118    1 8 11
119    1 9 11
120    0 1 2
121    1 2 121
122    1 2 22
123    1 2 3
124    1 2 4
125    1 2 5

Number           Has no >2 digit palindromes
9                          true
169                        true
12769                      true
1238769                    true
123498769                  true
12346098769                true
1234572098769              true
123456832098769            true
12345679432098769          true
1234567905432098769        true
123456790165432098769      true
83071934127905179083       true
1320267947849490361205695  false
```

## Raku

A minor modification of the Longest palindromic substrings task. As such, works for any string, not just integers. <lang perl6>use Sort::Naturally;

sub getpal (\$str) {

```   my @chars = \$str.comb;
my @pal = flat @chars,
(1 ..^ @chars).map: -> \idx {
my @s;
for 1, 2 {
my int (\$rev, \$fwd) = \$_, 1;
loop {
quietly last if (\$rev > idx) || (@chars[idx - \$rev] ne @chars[idx + \$fwd]);
\$rev = \$rev + 1;
\$fwd = \$fwd + 1;
}
@s.push: @chars[idx - \$rev ^..^ idx + \$fwd].join if \$rev + \$fwd > 2;
last if @chars[idx - 1] ne @chars[idx];
}
next unless +@s;
@s
}
@pal.unique.sort({.chars, .&naturally});
```

}

say 'All palindromic substrings including (bizarrely enough) single characters:'; put "\$_ => ", getpal \$_ for 100..125; put "\nDo these strings contain a minimum two character palindrome?"; printf "%25s => %s\n", \$_, getpal(\$_).tail.chars > 1 for flat

```   9, 169, 12769, 1238769, 123498769, 12346098769, 1234572098769,
123456832098769, 12345679432098769, 1234567905432098769,
123456790165432098769, 83071934127905179083, 1320267947849490361205695,
<Do these strings contain a minimum two character palindrome?></lang>
```
Output:
```All palindromic substrings including (bizarrely enough) single characters:
100 => 0 1 00
101 => 0 1 101
102 => 0 1 2
103 => 0 1 3
104 => 0 1 4
105 => 0 1 5
106 => 0 1 6
107 => 0 1 7
108 => 0 1 8
109 => 0 1 9
110 => 0 1 11
111 => 1 11 111
112 => 1 2 11
113 => 1 3 11
114 => 1 4 11
115 => 1 5 11
116 => 1 6 11
117 => 1 7 11
118 => 1 8 11
119 => 1 9 11
120 => 0 1 2
121 => 1 2 121
122 => 1 2 22
123 => 1 2 3
124 => 1 2 4
125 => 1 2 5

Do these strings contain a minimum two character palindrome?
9 => False
169 => False
12769 => False
1238769 => False
123498769 => False
12346098769 => False
1234572098769 => False
123456832098769 => False
12345679432098769 => False
1234567905432098769 => False
123456790165432098769 => False
83071934127905179083 => False
1320267947849490361205695 => True
Do => False
these => True
strings => False
contain => False
a => False
minimum => True
two => False
character => True
palindrome? => False```

## REXX

This REXX version can handle strings or numbers,   a hexadecimal string is included in the examples. <lang>/*REXX program finds distinct palindromes contained in substrings (of decimal numbers). */ parse arg LO HI mL \$\$ /*obtain optional arguments from the CL*/ if LO= | LO="," then LO= 100 /*Not specified? Then use the default.*/ if HI= | HI="," then HI= 125 /* " " " " " " */ if mL= | mL="," then mL= 2 /* " " " " " " */ if \$\$= | \$\$="," then \$\$= 9 169 12769 1238769 12346098769 1234572098769 123456832098769,

```                           12345679432098769 1234567905432098769 123456790165432098769  ,
1320267947849490361205695            /* special numbers.*/
```

w= length(HI) /*max width of LO ──► HI for alignment.*/

```      do j=LO  to HI;  #= Dpal(j, 1)            /*get # distinct palindromes, minLen=1 */
say right(j, w)  ' has '  #    " palindrome"s(#)': '    \$
end   /*j*/
```

w= length( word(\$\$, words(\$\$) ) ) /*find the length of the last special #*/ if words(\$\$)==0 then exit 0 /*No special words/numbers? Then exit.*/ say

```      do j=1  for words(\$\$);  z= word(\$\$, j)
#= Dpal(z, mL);    w= max(w, length(z) )  /*get # distinct palindromes, minLen=mL*/
_= left(':', #>0); @has= ' has ';                     @of='of length'
say right(z, w)    @has   #   " palindrome"s(#,,' ')  @of  mL  "or more"_  space(\$)
end   /*j*/
```

exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ s: if arg(1)==1 then return arg(3); return word( arg(2) 's', 1) /*──────────────────────────────────────────────────────────────────────────────────────*/ Dpal: procedure expose @. !. \$ w; parse arg x, mL; \$=;  !.= 0; #= 0; L= length(x)

```        do   j=1  for L                         /*test for primality for all substrings*/
do k=1  to  L-j+1                     /*search for substrings (including  X).*/
y= strip( substr(x, j, k) )           /*extract a substring from the X string*/
if length(y)<mL | y\==reverse(y)  then iterate   /*too short or ¬palindromic?*/
if \!.y  then do;  \$= \$ right(y, w);  !.y= 1;  #= # + 1;  end
end   /*k*/
end     /*j*/
return #</lang>
```
output   when using the default inputs:
```100  has  3  palindromes:     1   0  00
101  has  3  palindromes:     1 101   0
102  has  3  palindromes:     1   0   2
103  has  3  palindromes:     1   0   3
104  has  3  palindromes:     1   0   4
105  has  3  palindromes:     1   0   5
106  has  3  palindromes:     1   0   6
107  has  3  palindromes:     1   0   7
108  has  3  palindromes:     1   0   8
109  has  3  palindromes:     1   0   9
110  has  3  palindromes:     1  11   0
111  has  3  palindromes:     1  11 111
112  has  3  palindromes:     1  11   2
113  has  3  palindromes:     1  11   3
114  has  3  palindromes:     1  11   4
115  has  3  palindromes:     1  11   5
116  has  3  palindromes:     1  11   6
117  has  3  palindromes:     1  11   7
118  has  3  palindromes:     1  11   8
119  has  3  palindromes:     1  11   9
120  has  3  palindromes:     1   2   0
121  has  3  palindromes:     1 121   2
122  has  3  palindromes:     1   2  22
123  has  3  palindromes:     1   2   3
124  has  3  palindromes:     1   2   4
125  has  3  palindromes:     1   2   5

9  has  0  palindromes of length 2 or more
169  has  0  palindromes of length 2 or more
12769  has  0  palindromes of length 2 or more
1238769  has  0  palindromes of length 2 or more
12346098769  has  0  palindromes of length 2 or more
1234572098769  has  0  palindromes of length 2 or more
123456832098769  has  0  palindromes of length 2 or more
12345679432098769  has  0  palindromes of length 2 or more
1234567905432098769  has  0  palindromes of length 2 or more
123456790165432098769  has  0  palindromes of length 2 or more
83071934127905179083  has  0  palindromes of length 2 or more
deadbeef  has  1  palindrome  of length 2 or more: ee
1320267947849490361205695  has  3  palindromes of length 2 or more: 202 494 949
```

## Wren

Library: Wren-seq
Library: Wren-fmt
Library: Wren-sort

<lang ecmascript>import "/seq" for Lst import "/fmt" for Fmt import "/sort" for Sort

var substrings = Fn.new { |s|

```   var ss = []
var n = s.count
for (i in 0...n) {
for (j in 1..n-i) ss.add(s[i...i + j])
}
return ss
```

}

System.print("Number Palindromes") for (i in 100..125) {

```   var pals = []
var ss = substrings.call(i.toString)
for (s in ss) {
}
pals = Lst.distinct(pals)
var cmp = Fn.new { |i, j| (i.count - j.count).sign }
Sort.insertion(pals, cmp) // sort by length
Fmt.print("\$d   \$3s", i, pals)
```

}

var nums = [

```   "9", "169", "12769", "1238769", "123498769", "12346098769", "1234572098769",
"123456832098769", "12345679432098769", "1234567905432098769", "123456790165432098769",
"83071934127905179083", "1320267947849490361205695"
```

] System.print("\nNumber Has no >= 2 digit palindromes") for (num in nums) {

```   var ss = substrings.call(num).where { |s| s.count > 1 }
var none = !ss.any { |s| s == s[-1..0] }
Fmt.print("\$-25s \$s", num, none)
```

}</lang>

Output:
```Number  Palindromes
100     1   0  00
101     1   0 101
102     1   0   2
103     1   0   3
104     1   0   4
105     1   0   5
106     1   0   6
107     1   0   7
108     1   0   8
109     1   0   9
110     1   0  11
111     1  11 111
112     1   2  11
113     1   3  11
114     1   4  11
115     1   5  11
116     1   6  11
117     1   7  11
118     1   8  11
119     1   9  11
120     1   2   0
121     1   2 121
122     1   2  22
123     1   2   3
124     1   2   4
125     1   2   5

Number                    Has no >= 2 digit palindromes
9                         true
169                       true
12769                     true
1238769                   true
123498769                 true
12346098769               true
1234572098769             true
123456832098769           true
12345679432098769         true
1234567905432098769       true
123456790165432098769     true
83071934127905179083      true
1320267947849490361205695 false
```