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Law of cosines - triples: Difference between revisions
Added Fortran solution candidate
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{ 13 13 13 }
}
</pre>
=={{header|Fortran}}==
<lang fortran>MODULE LAW_OF_COSINES
IMPLICIT NONE
CONTAINS
! Calculate the third side of a triangle using the cosine rule
REAL FUNCTION COSINE_SIDE(SIDE_A, SIDE_B, ANGLE)
INTEGER, INTENT(IN) :: SIDE_A, SIDE_B
REAL(8), INTENT(IN) :: ANGLE
COSINE_SIDE = SIDE_A**2 + SIDE_B**2 - 2*SIDE_A*SIDE_B*COS(ANGLE)
COSINE_SIDE = COSINE_SIDE**0.5
END FUNCTION COSINE_SIDE
! Convert an angle in degrees to radians
REAL(8) FUNCTION DEG2RAD(ANGLE)
REAL(8), INTENT(IN) :: ANGLE
REAL(8), PARAMETER :: PI = 4.0D0*DATAN(1.D0)
DEG2RAD = ANGLE*(PI/180)
END FUNCTION DEG2RAD
! Sort an array of integers
FUNCTION INT_SORTED(ARRAY) RESULT(SORTED)
INTEGER, DIMENSION(:), INTENT(IN) :: ARRAY
INTEGER, DIMENSION(SIZE(ARRAY)) :: SORTED, TEMP
INTEGER :: MAX_VAL, DIVIDE
SORTED = ARRAY
TEMP = ARRAY
DIVIDE = SIZE(ARRAY)
DO WHILE (DIVIDE .NE. 1)
MAX_VAL = MAXVAL(SORTED(1:DIVIDE))
TEMP(DIVIDE) = MAX_VAL
TEMP(MAXLOC(SORTED(1:DIVIDE))) = SORTED(DIVIDE)
SORTED = TEMP
DIVIDE = DIVIDE - 1
END DO
END FUNCTION INT_SORTED
! Append an integer to the end of an array of integers
SUBROUTINE APPEND(ARRAY, ELEMENT)
INTEGER, DIMENSION(:), ALLOCATABLE, INTENT(INOUT) :: ARRAY
INTEGER, DIMENSION(:), ALLOCATABLE :: TEMP
INTEGER :: ELEMENT
INTEGER :: I, ISIZE
IF (ALLOCATED(ARRAY)) THEN
ISIZE = SIZE(ARRAY)
ALLOCATE(TEMP(ISIZE+1))
DO I=1, ISIZE
TEMP(I) = ARRAY(I)
END DO
TEMP(ISIZE+1) = ELEMENT
DEALLOCATE(ARRAY)
CALL MOVE_ALLOC(TEMP, ARRAY)
ELSE
ALLOCATE(ARRAY(1))
ARRAY(1) = ELEMENT
END IF
END SUBROUTINE APPEND
! Check if an array of integers contains a subset
LOGICAL FUNCTION CONTAINS_ARR(ARRAY, ELEMENT)
INTEGER, DIMENSION(:), INTENT(IN) :: ARRAY
INTEGER, DIMENSION(:) :: ELEMENT
INTEGER, DIMENSION(SIZE(ELEMENT)) :: TEMP, SORTED_ELEMENT
INTEGER :: I, COUNTER, J
COUNTER = 0
ELEMENT = INT_SORTED(ELEMENT)
DO I=1,SIZE(ARRAY),SIZE(ELEMENT)
TEMP = ARRAY(I:I+SIZE(ELEMENT)-1)
DO J=1,SIZE(ELEMENT)
IF (ELEMENT(J) .EQ. TEMP(J)) THEN
COUNTER = COUNTER + 1
END IF
END DO
IF (COUNTER .EQ. SIZE(ELEMENT)) THEN
CONTAINS_ARR = .TRUE.
RETURN
END IF
END DO
CONTAINS_ARR = .FALSE.
END FUNCTION CONTAINS_ARR
! Count and print cosine triples for the given angle in degrees
INTEGER FUNCTION COSINE_TRIPLES(MIN_NUM, MAX_NUM, ANGLE, PRINT_RESULTS) RESULT(COUNTER)
INTEGER, INTENT(IN) :: MIN_NUM, MAX_NUM
REAL(8), INTENT(IN) :: ANGLE
LOGICAL, INTENT(IN) :: PRINT_RESULTS
INTEGER, DIMENSION(:), ALLOCATABLE :: CANDIDATES
INTEGER, DIMENSION(3) :: CANDIDATE
INTEGER :: A, B
REAL :: C
COUNTER = 0
DO A = MIN_NUM, MAX_NUM
DO B = MIN_NUM, MAX_NUM
C = COSINE_SIDE(A, B, DEG2RAD(ANGLE))
IF (C .GT. MAX_NUM .OR. MOD(C, 1.) .NE. 0) THEN
CYCLE
END IF
CANDIDATE(1) = A
CANDIDATE(2) = B
CANDIDATE(3) = C
IF (.NOT. CONTAINS_ARR(CANDIDATES, CANDIDATE)) THEN
COUNTER = COUNTER + 1
CALL APPEND(CANDIDATES, CANDIDATE(1))
CALL APPEND(CANDIDATES, CANDIDATE(2))
CALL APPEND(CANDIDATES, CANDIDATE(3))
IF (PRINT_RESULTS) THEN
WRITE(*,'(A,I0,A,I0,A,I0,A)') " (", CANDIDATE(1), ", ", CANDIDATE(2), ", ", CANDIDATE(3), ")"
END IF
END IF
END DO
END DO
END FUNCTION COSINE_TRIPLES
END MODULE LAW_OF_COSINES
! Program prints the cosine triples for the angles 90, 60 and 120 degrees
! by using the cosine rule to find the third side of each candidate and
! checking that this is an integer. Candidates are appended to an array
! after the sides have been sorted into ascending order
! the array is repeatedly checked to ensure there are no duplicates.
PROGRAM LOC
USE LAW_OF_COSINES
REAL(8), DIMENSION(3) :: TEST_ANGLES = (/90., 60., 120./)
INTEGER :: I, COUNTER
DO I = 1,SIZE(TEST_ANGLES)
WRITE(*, '(F0.0, A)') TEST_ANGLES(I), " degree triangles: "
COUNTER = COSINE_TRIPLES(1, 13, TEST_ANGLES(I), .TRUE.)
WRITE(*,'(A, I0)') "TOTAL: ", COUNTER
WRITE(*,*) NEW_LINE('A')
END DO
END PROGRAM LOC</lang>
<pre>
90. degree triangles:
(3, 4, 5)
(5, 12, 13)
(6, 8, 10)
TOTAL: 3
60. degree triangles:
(1, 1, 1)
(2, 2, 2)
(3, 3, 3)
(3, 7, 8)
(4, 4, 4)
(5, 5, 5)
(6, 6, 6)
(7, 7, 7)
(3, 7, 8)
(8, 8, 8)
(9, 9, 9)
(10, 10, 10)
(11, 11, 11)
(12, 12, 12)
(13, 13, 13)
TOTAL: 15
120. degree triangles:
(3, 5, 7)
(7, 8, 13)
TOTAL: 2
</pre>
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