Distinct palindromes within decimal numbers
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.
- Task
- Find all the palindromes including single digits in the integers from 100 to 125, inclusive.
- 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
-
- OEIS entry: A262188 (Task 1).
- OEIS entry: A151997 (Task 2).
Palindrome_detection
Longest_palindromic_substrings
N_1's_followed_by_a_3
Factor
<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] println(rpad(n, 26), palindrome2plusfree(n))
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