CSCE150 Fortran Lab11

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CSCE150 Fortran Lab11
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outline

• recursive problems and recursive procedures
• Fibonacci numbers
• Tower of Hanoi
• character manipulations
• exercise 1
• exercise 2

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recursive problems

• a recursive problem
• the solution of the problem can be derived from
  the solutions of a smaller size of the same
  problem

• Fibonacci numbers
• 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, .

Fib(0)
Fib(1)
Fib(2) Fib(1) Fib(0)
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recursive procedures

• a recursive problem can be solved using a
  recursive procedure
• a recursive procedure is one that invokes itself
  directly or indirectly
• ordinary subroutines and functions in Fortran can
  not invoke themselves
• however, by adding a special term, Fortran allows
  a procedure to be declared RECURSIVE
• page 518 old textbook
• page 569 new textbook

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recursive procedures

• RECURSIVE SUBROUTINE sub (argu_list)
• END SUBROUTINE
• or
• RECURSIVE FUNCTION fun (argu_list) RESULT
  (answer)
• END FUNCTION

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• when defining recursive functions
• a special dummy argument is used whenever we want
  to specify a value to return
• the name of this special dummy argument is
  specified in a RESULT clause in the function
  declaration
• the actual name of the function is used whenever
  we want the function to invoke itself

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sample program

• calculate the nth Fibonacci number recursively

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FUNCTION

• PROGRAM Fibonacci
• IMPLICIT NONE
• INTEGER num, fib
• WRITE(,) This program is to calculate the nth
  Fibonacci number.
• WRITE(,) Please type in the value of n
  (nonnegative integer)
• READ(,) num
• IF (numlt0) THEN
• WRITE(,) The number you input must be gt 0!
• ELSE
• WRITE(,) The result is , fib(num)
• END IF
• END PROGRAM Fibonacci

invoke the function
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• RECURSIVE FUNCTION fib ( n ) RESULT ( answer )
• INTEGER, INTENT (IN) n
• INTEGER answer
• IF ( n gt 1 ) THEN
• answer fib(n-1)fib(n-2)
• ELSE IF (n1) THEN
• answer 1
• ELSE IF (n0) THEN
• answer 0
• END IF
• END FUNCTION fib

invoke itself
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SUBROUTINE

• PROGRAM Fibonacci
• IMPLICIT NONE
• INTEGER num, answer
• WRITE(,) This program is to calculate the nth
  Fibonacci number.
• WRITE(,) Please type in the value of n
  (nonnegative integer)
• READ(,) num
• IF (numlt0) THEN
• WRITE(,) The number you input must be gt 0!
• ELSE
• CALL fib(num, answer)
• WRITE(,) The result is , answer
• END IF
• END PROGRAM Fibonacci

invoke the subroutine
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• RECURSIVE SUBROUTINE fib ( n, answer )
• INTEGER, INTENT (IN) n
• INTEGER, INTENT (OUT) answer
• INTEGER answer1, answer2
• IF ( n gt 1 ) THEN
• CALL fib(n-1, answer1)
• CALL fib(n-2, answer2)
• answer answer1answer2
• ELSE IF (n1) THEN
• answer 1
• ELSE IF (n0) THEN
• answer 0
• END IF
• END SUBROUTINE fib

invoke itself
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Towers of Hanoi
Goal Move disks from peg A to peg B. Rule May
only move one disk at a time, onto a bigger disk
or an empty peg.
1
2
3
A
B
C
source
dest
inter
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Some initial steps
2
3
1
A
B
C
3
2
1
A
B
C
source
dest
inter
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Breaking the goal into subgoals
1
3
2
A
B
C
1
3
2
A
B
C
source
dest
inter
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Some final steps
3
2
1
A
B
C
2
3
1
A
B
C
source
dest
inter
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Implementation of Towers of Hanoi
PROGRAM TOH !Moves n disks (ngt0) from peg source
to peg dest using peg inter as !intermediate. IMPL
ICIT NONE INTEGER n CHARACTER (len1)
A'A', B'B', C'C' WRITE(,) Please type in
the value of n READ(,) n IF (nlt0)
THEN WRITE(,) n must be gt 0! ELSE CALL
Hanoi (n, A, B, C) END IF END PROGRAM
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• RECURSIVE SUBROUTINE Hanoi (n, source, dest,
  inter)
• IMPLICIT NONE
• INTEGER n
• CHARACTER (len1) source, dest, inter
• IF (ngt0) THEN
• CALL Hanoi (n-1, source, inter, dest)
• WRITE(,) Move disk from peg, source, to
  peg, dest
• CALL Hanoi (n-1, inter, dest, source)
• END IF
• END SUBROUTINE

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characters in computers

• How many characters are supported in computers?
• ASCII character set
• page 719-old textbook (871-new textbook),
  Appendix A
• How to express each character?
• each character is saved as a 8 bits sequence
  according to its index in the ASCII character set
• for example
• a is saved as 0110 0001 (97 in decimal)
• A is saved as 0100 0001 (65 in decimal)
• 5 is saved as 0011 1001 (53 in decimal)

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character manipulations

• a character string is an array of characters
• for example
• aAbB is a character string, which consists of 4
  characters continuously
• aAbB is saved as 0110 0001 0100 0001 0110
  0010 0100 0010
• We have lots of functions to handle characters
  and character strings.
• ACHAR, IACHAR, LEN, LEN_TRIM, TRIM (150-old
  textbook, 159-new textbook)
• More in Chapter 10 (429-old textbook, 457-new
  textbook)

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• TRIM(str1) returns str1 with trailing blanks
  removed

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• LEN(str1) returns length of str1
• LEN_TRIM(str1) returns length of str1, excluding
  any trailing blanks

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• ACHAR(int1) returns the character corresponding
  to int1 in the ASCII collating sequence

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• IACHAR(char1) returns the integer corresponding
  to char1 in the ASCII collating sequence

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• concatenation operator // combines two or more
  strings or substrings into a single larger string

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exercise 1

• the combinatorial coefficient C(n, r) is defined
  recursively as follows
• write a program to calculate the combinatorial
  coefficient, given n and r, by using a recursive
  function or a recursive subroutine

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exercise 2

• write a Fortran program
• it works on two strings
• the first string is Today is Tuesday.
• the second string is Today is November 20,
  2007.
• concatenates two strings to get a new string
  Today is Tuesday, November 20, 2007.
• then changes all the uppercase letters to
  lowercase letters
• prints out the original strings and the new
  strings
• Hint refer to the example on page 151 of old
  textbook (160 new textbook)