Self-describing numbers
LRCVS 08.05.11
Self-describing numbers:
There are several integers numbers called "self-describing".
Integers with the property that, when digit positions are labeled 0 to N-1, the digit in each position is equal to the number of times that that digit appears in the number.
For example 2020 is a four digit self describing number.
Position "0" has value 2 and there is two 0 in the number. Position "1" has value 0 because there are not 1's in the number. Position "2" has value 2 and there is two 2. And the position "3" has value 0 and there are zero 3's.
Self-describing numbers < 100.000.000 : 1210 - 2020 - 21200 - 3211000 - 42101000
.......................................... The following example is written in Basic ..........................................
lang "qb"
Dim x, r, b, c, n, m As Integer
Dim a, d As String
Dim v(10), w(10) As Integer
Cls
For x = 1 To 5000000
- a$ = ltrim$(Str$(x))
- b = Len(a$)
- For c = 1 To b
- d$ = Mid$(a$, c, 1)
- v(Val(d$)) = v(Val(d$)) + 1
- w(c - 1) = Val(d$)
- Next c
- r = 0
- For n = 0 To 10
- If v(n) = w(n) Then r = r + 1
- v(n) = 0
- w(n) = 0
- Next n
- For c = 1 To b
- If r = 11 Then Print x; " Yes,is autodescriptive number"
Next x
Print "End"
sleep
end
.........................................................................
This example is written in another language Logo (FMSLogo)
........................................................................
TO XX
BT
MAKE "AA (ARRAY 10 0) MAKE "BB (ARRAY 10 0)
- FOR [Z 0 9][SETITEM :Z :AA "0 SETITEM :Z :BB "0 ]
- FOR [A 1 50000][
- MAKE "B COUNT :A
- MAKE "Y 0
- MAKE "X 0
- MAKE "R 0
- MAKE "J 0
- MAKE "K 0
- FOR [A 1 50000][
- FOR [C 1 :B][MAKE "D ITEM :C :A
- SETITEM :C - 1 :AA :D
- MAKE "X ITEM :D :BB
- MAKE "Y :X + 1
- SETITEM :D :BB :Y
- MAKE "R 0]
- FOR [Z 0 9][MAKE "J ITEM :Z :AA
- MAKE "K ITEM :Z :BB
- IF :J = :K [MAKE "R :R + 1]]
IF :R = 10 [PR :A]
- FOR [Z 0 9][SETITEM :Z :AA "0 SETITEM :Z :BB "0 ]]
PR [END]
END