Çözüldü Bölünebilme - Programlama

Bilgisayar programlama (kodlama) ile ilgilenen öğrenciler için https://codingfleet.com/code-generator/fortran/ adresindeki yapay zekânın
"If the three-digit natural number a6b is divisible by 12, write a Fortran program to list the different values to be taken by the digit a." sorusuna verdiği çok açıklamalı Fortran çözümü:

https://i72.servimg.com/u/f72/19/97/10/39/coding10.png

Here's a Fortran program to find the different values for the digit 'a' in a three-digit number a6b such that the number is divisible by 12.
A number a6b can be written as 100*a + 60 + b. For a number to be divisible by 12, it must be divisible by both 3 and 4.
Divisibility by 4: The number formed by the last two digits (6b) must be divisible by 4. Possible values for 6b that are divisible by 4 are 60, 64, 68. So, b can be 0, 4, or 8.
Divisibility by 3: The sum of the digits (a + 6 + b) must be divisible by 3.
The program will iterate through all possible values for a (from 1 to 9, as it's a three-digit number) and b (from 0 to 9). For each combination, it forms the number a6b and checks if it's divisible by 12. It then collects the unique a values that satisfy the condition.

Program:

Kod:

PROGRAM FindAValues
  IMPLICIT NONE

  INTEGER :: a, b, number
  ! An array to keep track of unique 'a' values found.
  ! found_a(i) will be .TRUE. if 'i' is a possible value for 'a'.
  LOGICAL, DIMENSION(1:9) :: found_a
  INTEGER :: i

  ! Initialize all entries in found_a to .FALSE.
  DO i = 1, 9
    found_a(i) = .FALSE.
  END DO

  WRITE(*,*) 'Searching for values of ''a'' in a6b divisible by 12...'

  ! Loop for 'a' (the first digit, must be between 1 and 9)
  DO a = 1, 9
    ! Loop for 'b' (the last digit, must be between 0 and 9)
    DO b = 0, 9
      ! Construct the three-digit number a6b
      number = a * 100 + 6 * 10 + b

      ! Check if the number is divisible by 12
      IF (MOD(number, 12) == 0) THEN
        ! If divisible, mark this 'a' value as found
        ! We only need to mark it once, so check if it's already .TRUE.
        IF (.NOT. found_a(a)) THEN
          found_a(a) = .TRUE.
          ! Optionally, print the full number for verification
          ! WRITE(*,*) 'Found number: ', number, ' (a=', a, ', b=', b, ')'
        END IF
      END IF
    END DO
  END DO

  ! Print the different values of 'a' that were found
  WRITE(*,*) '' ! New line for better formatting
  WRITE(*,*) 'The different values to be taken by the digit ''a'' are:'
  DO i = 1, 9
    IF (found_a(i)) THEN
      WRITE(*,*) i
    END IF
  END DO

END PROGRAM FindAValues

Explanation:
1. PROGRAM FindAValues: Declares the start of the Fortran program.
2. IMPLICIT NONE: A good practice in Fortran to prevent implicit type declarations, which can lead to errors. All variables must be explicitly declared.
3. INTEGER :: a, b, number: Declares integer variables a, b, and number.
4. LOGICAL, DIMENSION(1:9) :: found_a: Declares a logical array found_a of size 9. found_a(i) will be TRUE if i is a possible value for a, and FALSE otherwise. This helps in collecting unique a values.
5. Initialization Loop: The first DO i = 1, 9 loop initializes all elements of found_a to .FALSE..
6. Outer Loop (DO a = 1, 9): This loop iterates through all possible values for the digit a. Since a6b is a three-digit number, a cannot be 0.
7. Inner Loop (DO b = 0, 9): This loop iterates through all possible values for the digit b.
8. number = a * 100 + 6 * 10 + b: Constructs the three-digit number a6b based on the current a and b values.
9. IF (MOD(number, 12) == 0) THEN: This is the core condition check. MOD(number, 12) calculates the remainder when number is divided by 12. If the remainder is 0, the number is divisible by 12.
10. IF (.NOT. found_a(a)) THEN ... END IF: If a number a6b is found to be divisible by 12, and the current a value hasn't been recorded yet (.NOT. found_a(a)), then found_a(a) is set to .TRUE.. This ensures each unique a value is recorded only once.
11. Printing Results: After checking all combinations, the program iterates through found_a from 1 to 9. If found_a(i) is .TRUE., it means i is a valid digit for a, and it's printed.