Taxicab numbers: Difference between revisions

=={{header|Fortran}}==

<lang fortran>

! A non-bruteforce approach

PROGRAM POOKA

IMPLICIT NONE

!

! PARAMETER definitions

!

INTEGER , PARAMETER :: NVARS = 25

!

! Local variables

!

REAL :: f1

REAL :: f2

INTEGER :: hits

INTEGER :: s

INTEGER :: TAXICAB

hits = 0

s = 0

f1 = SECOND()

DO WHILE ( hits<NVARS )

s = s + 1

hits = hits + TAXICAB(s)

END DO

f2 = SECOND()

PRINT * , 'elapsed time = ' , f2 - f1 , 'For ' , NVARS , ' Variables'

STOP

END PROGRAM POOKA

FUNCTION TAXICAB(N)

IMPLICIT NONE

!

! Dummy arguments

!

INTEGER :: N

INTEGER :: TAXICAB

INTENT (IN) N

!

! Local variables

!

INTEGER :: holder

INTEGER :: oldx

INTEGER :: oldy

INTEGER :: s

INTEGER :: x

INTEGER :: y

real*8,parameter :: xpon=(1.0D0/3.0D0)

!

x = 0

holder = 0

oldx = 0

oldy = 0

TAXICAB = 0

y = INT(N**xpon)

DO WHILE ( x<=y )

s = x**3 + y**3

IF( s<N )THEN

x = x + 1

ELSE IF( s>N )THEN

y = y - 1

ELSE

IF( holder==s )THEN ! Print the last value and this one that correspond

WRITE(6 , 34)s , '(' , x**3 , y**3 , ')' , '(' , oldx**3 , oldy**3 , ')'

34 FORMAT(1x , i12 , 10x , 1A1 , i12 , 2x , i12 , 1A1 , 10x , 1A1 , i12 , 2x ,&

& i12 , 1A1)

TAXICAB = 1 ! Indicate that we found a Taxi Number

END IF

holder = s ! Set to the number that appears a potential cab number

oldx = x ! Retain the values for the 2 cubes

oldy = y

x = x + 1 ! Keep looking

y = y - 1

END IF

END DO

RETURN

END FUNCTION TAXICAB

</lang>

{{out}}

<pre> Print first 25 numbers

1729 ( 729 1000) ( 1 1728)

4104 ( 729 3375) ( 8 4096)

13832 ( 5832 8000) ( 8 13824)

20683 ( 6859 13824) ( 1000 19683)

32832 ( 5832 27000) ( 64 32768)

39312 ( 3375 35937) ( 8 39304)

40033 ( 4096 35937) ( 729 39304)

46683 ( 19683 27000) ( 27 46656)

64232 ( 17576 46656) ( 4913 59319)

65728 ( 29791 35937) ( 1728 64000)

110656 ( 46656 64000) ( 64 110592)

110808 ( 19683 91125) ( 216 110592)

134379 ( 54872 79507) ( 1728 132651)

149389 ( 24389 125000) ( 512 148877)

165464 ( 54872 110592) ( 8000 157464)

171288 ( 13824 157464) ( 4913 166375)

195841 ( 10648 185193) ( 729 195112)

216027 ( 10648 205379) ( 27 216000)

216125 ( 91125 125000) ( 125 216000)

262656 ( 46656 216000) ( 512 262144)

314496 ( 27000 287496) ( 64 314432)

320264 ( 32768 287496) ( 5832 314432)

327763 ( 132651 195112) ( 27000 300763)

373464 ( 157464 216000) ( 216 373248)

402597 ( 175616 226981) ( 74088 328509)

elapsed time = 4.68750000E-02 For 25 Variables

</pre>