Implemented Ternary Search Algorithm

DIRECTORY.md

@@ -6,6 +6,7 @@
 ## Searches
 * [linear_search](/modules/searches/linear_search.f90)
 * [recursive_linear_search](/modules/searches/recursive_linear_search.f90)
+* [ternary_search](/modules/searches/ternary_search_module.f90)
 ## Sorts
 * [bubble_sort](/modules/sorts/bubble_sort.f90)
 * [recursive_bubble_sort](/modules/sorts/recursive_bubble_sort.f90)

examples/maths/factorial.f90

@@ -7,7 +7,7 @@ program factorial_program
     use factorial_module
     implicit none
 
-    Print*, factorial(5)
-    Print*, recursive_factorial(5)
+    Print *, factorial(5)
+    Print *, recursive_factorial(5)
 
 end program factorial_program

examples/searches/example_linear_search.f90

@@ -8,12 +8,12 @@ program linear_search_program
 
     integer, dimension(5) :: array
 
-    array = (/ 540, 6, 10, 100, 3 /)
+    array = (/540, 6, 10, 100, 3/)
 
     !! Search for the number 6 in array.
-    print*, "Target = 6: ", linear_search(array, 6) !! Prints 2.
+    print *, "Target = 6: ", linear_search(array, 6) !! Prints 2.
 
     !! Search for the number 5 in array.
-    print*, "Target = 5: ", linear_search(array, 5) !! Prints -1 because item 5 is not found.
+    print *, "Target = 5: ", linear_search(array, 5) !! Prints -1 because item 5 is not found.
 
 end program linear_search_program

examples/searches/example_ternary_search_array_based.f90

@@ -0,0 +1,20 @@
+! Example Program: Array-based Ternary Search
+! This program demonstrates how to use the array-based ternary search algorithm
+! implemented in the `ternary_search` module to find a target element in a sorted array.
+
+program example_ternary_search_array
+    use ternary_search
+    implicit none
+    integer :: result           ! Holds the index of the found target
+    integer, dimension(10) :: arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]     ! Sorted Test Array
+    integer :: target           ! Target value to search for
+
+    target = 17
+    result = ternary_search_array(arr, target, 1, size(arr))
+
+    if (result /= -1) then
+        print *, "Target found at index:", result
+    else
+        print *, "Target not found."
+    end if
+end program example_ternary_search_array

examples/searches/example_ternary_search_function_based.f90

@@ -0,0 +1,74 @@
+!> Example Program: Function-based Ternary Search for Minimum and Maximum
+!!
+!!  Created by: Ramy-Badr-Ahmed (https://github.com/Ramy-Badr-Ahmed)
+!!  in Pull Request: #24
+!!  https://github.com/TheAlgorithms/Fortran/pull/24
+!!
+!!  Please mention me (@Ramy-Badr-Ahmed) in any issue or pull request
+!!  addressing bugs/corrections to this file. Thank you!
+!!
+!! This program demonstrates how to use the function-based ternary search algorithm
+!! from the `ternary_search` module to find the minimum and maximum of unimodal functions.
+
+program ternary_search_function_based
+    use ternary_search
+    implicit none
+
+    ! Define the variables
+    integer, parameter :: dp = kind(0.0d0)  ! Define double precision kind
+    real(8) :: result_min, result_max       ! Results for minimum and maximum values
+    real(8) :: min_point, max_point         ! Points where minimum and maximum occur
+    real(8) :: left, right, tol             ! Left and right bounds, and tolerance
+
+    interface
+        ! Function with a minimum (example function - defined externally)
+        real(8) function f_min(x)
+            real(8), intent(in) :: x
+        end function f_min
+
+        ! Function with a maximum (example function - defined externally)
+        real(8) function f_max(x)
+            real(8), intent(in) :: x
+        end function f_max
+    end interface
+
+    ! The boundary values can vary depending on the problem context.
+    ! In this example, they are chosen arbitrarily.
+    left = 0.0d0
+    right = 10.0d0
+
+    ! The tolerance value defines how close the left and right bounds must be for the search to terminate.
+    tol = 1.0e-6_dp
+
+    ! Call the ternary search to find the minimum point of f_min
+    min_point = ternary_search_minimum(f_min, left, right, tol)
+    result_min = f_min(min_point)
+
+    ! Call the ternary search to find the maximum point of f_max
+    max_point = ternary_search_maximum(f_max, left, right, tol)
+    result_max = f_max(max_point)
+
+    print *, "Minimum of the function f_min is at x =", min_point, "with value =", result_min
+    print *, "Maximum of the function f_max is at x =", max_point, "with value =", result_max
+
+end program ternary_search_function_based
+
+! Define the unimodal function f_min with a minimum near x = 5.0
+! The quadratic term (x - 5.0)**2 defines a parabola that is concave upward with a minimum at x = 5.0
+! and values increasing as x moves away from 5.
+! The cosine term introduces oscillations, affecting the exact location of the minimum slightly away from 5.0.
+
+real(8) function f_min(x)
+    real(8), intent(in) :: x
+    f_min = (x - 5.0d0)**2 + cos(x)      ! Example of a quadratic function with a cosine oscillation
+end function f_min
+
+! Define the unimodal function f_max with a maximum near x = 5.0
+! The quadratic term -(x - 5.0)**2 defines a parabola that is concave downward with a maximum at x = 5.0
+! and values decreasing as x moves away from 5.
+! The cosine term introduces oscillations, affecting the exact location of the maximum slightly away from 5.0.
+
+real(8) function f_max(x)
+    real(8), intent(in) :: x
+    f_max = -(x - 5.0d0)**2 + cos(x)     ! Example of a quadratic function with a cosine oscillation
+end function f_max

examples/searches/recursive_linear_search.f90

@@ -8,12 +8,12 @@ program recursive_linear_search_example
 
     integer, dimension(5) :: array
 
-    array = (/ 306, 1005, 5, 62, 0 /)
+    array = (/306, 1005, 5, 62, 0/)
 
     !! Search for the number 62 in the array
-    print*, "Target = 62: ", recursive_linear_search(array, size(array), 62) !! Prints 4.
+    print *, "Target = 62: ", recursive_linear_search(array, size(array), 62) !! Prints 4.
 
     !! Search for the number 10 in the array
-    print*, "Target = 10: ", recursive_linear_search(array, size(array), 10) !! Prints -1 because item 10 is not found.
+    print *, "Target = 10: ", recursive_linear_search(array, size(array), 10) !! Prints -1 because item 10 is not found.
 
 end program recursive_linear_search_example

examples/sorts/example_recursive_bubble_sort.f90

@@ -11,11 +11,11 @@ program recursive_bubble_sort_example
     !! Fill the array with random numbers.
     call random_number(array)
 
-    print*, "Before:", array
+    print *, "Before:", array
 
     !! Bubble sort subroutine call.
     call recursive_bubble_sort(array, size(array))
 
-    print*, "After:", array
+    print *, "After:", array
 
 end program recursive_bubble_sort_example

examples/sorts/example_usage_bubble_sort.f90

@@ -11,11 +11,11 @@ program bubble_sort_example
     !! Fill the array with random numbers
     call random_number(array)
 
-    print*, "Before:", array
+    print *, "Before:", array
 
     !! Call the bubble_sort subroutine to sort the array
     call bubble_sort(array)
 
-    print*, "After:", array
+    print *, "After:", array
 
 end program bubble_sort_example

examples/sorts/example_usage_gnome_sort.f90

@@ -9,7 +9,7 @@ program test_gnome_sort
     integer :: n, i
 
     ! Initialize the test array
-    array = (/ -5, 2, 9, 1, 5, 6, -7, 8, 15, -20 /)
+    array = (/-5, 2, 9, 1, 5, 6, -7, 8, 15, -20/)
     n = size(array)
 
     ! Call gnome_sort from the module to sort the array

examples/sorts/example_usage_heap_sort.f90

@@ -10,7 +10,7 @@ program test_heap_sort
     integer, dimension(n) :: array(n)   ! Test array
 
     ! Initialize the test array
-    array = (/ 12, 11, 13, 5, 6, 7, 3, 9, -1, 2, -12, 1 /)
+    array = (/12, 11, 13, 5, 6, 7, 3, 9, -1, 2, -12, 1/)
 
     ! Print the original array
     print *, "Original array:"

examples/sorts/example_usage_merge_sort.f90

@@ -9,7 +9,7 @@ program test_merge_sort
     integer :: n, i
 
     ! Initialize the test array
-    array = (/ -2, 3, -10, 11, 99, 100000, 100, -200 /)
+    array = (/-2, 3, -10, 11, 99, 100000, 100, -200/)
     n = size(array)
 
     ! Call merge_sort from the module to sort the array

examples/sorts/example_usage_quick_sort.f90

@@ -9,7 +9,7 @@ program test_quick_sort
     integer :: n, i
 
     ! Initialize the test array
-    array = (/ 10, 7, 8, 9, 1, 5, -2, 12, 0, -5 /)
+    array = (/10, 7, 8, 9, 1, 5, -2, 12, 0, -5/)
     n = size(array)
 
     ! Print the original array

examples/sorts/example_usage_radix_sort.f90

@@ -13,7 +13,7 @@ program test_radix_sort
 
     ! Test for base 10
     print *, "Testing Radix Sort with base 10:"
-    array = (/ 170, 45, 75, 90, 802, 24, 2, 66, 15, 40 /)
+    array = (/170, 45, 75, 90, 802, 24, 2, 66, 15, 40/)
     n = size(array)
     call radix_sort(array, n, base10)
     print *, "Sorted array in base 10:"
@@ -23,7 +23,7 @@ program test_radix_sort
 
     ! Test for base 2
     print *, "Testing Radix Sort with base 2:"
-    array = (/ 1010, 1101, 1001, 1110, 0010, 0101, 1111, 0110, 1000, 0001 /) ! Binary values whose decimal: (/ 10, 13, 9, 14, 2, 5, 15, 6, 8, 1 /)
+    array = (/1010, 1101, 1001, 1110, 0010, 0101, 1111, 0110, 1000, 0001/) ! Binary values whose decimal: (/ 10, 13, 9, 14, 2, 5, 15, 6, 8, 1 /)
     n = size(array)
     call radix_sort(array, n, base2)
     print *, "Sorted binary array in Decimal:"
@@ -33,7 +33,7 @@ program test_radix_sort
 
     ! Test for base 16
     print *, "Testing Radix Sort with base 16:"
-    array = (/ 171, 31, 61, 255, 16, 5, 211, 42, 180, 0 /)  ! Hexadecimal values as decimal
+    array = (/171, 31, 61, 255, 16, 5, 211, 42, 180, 0/)  ! Hexadecimal values as decimal
     n = size(array)
     call radix_sort(array, n, base16)
     print *, "Sorted hexadecimal array in Decimal:"

modules/maths/factorial.f90

@@ -19,7 +19,7 @@ function factorial(number) result(factorial_number)
 
         factorial_number = 1
         do while (counter > 1)
-            factorial_number = factorial_number * counter
+            factorial_number = factorial_number*counter
             counter = counter - 1
         end do
 
@@ -33,7 +33,7 @@ recursive function recursive_factorial(number) result(factorial_number)
         if (number .lt. 1) then
             factorial_number = 1
         else
-            factorial_number = number * recursive_factorial(number - 1)
+            factorial_number = number*recursive_factorial(number - 1)
         end if
 
     end function recursive_factorial

modules/searches/linear_search.f90

@@ -8,7 +8,7 @@ module linear_search_module
 
     !! This function searches for a target in a given collection.
     !! Returns the index of the found target or -1 if target is not found.
-    function linear_search (collection, target) result(target_index)
+    function linear_search(collection, target) result(target_index)
         integer, dimension(:), intent(in) :: collection   !! A collection for elements of type integer
         integer, intent(in)               :: target       !! Target value to be searched.
         integer                           :: target_index !! Target's index in the collection to return.

modules/searches/recursive_linear_search.f90

@@ -26,9 +26,9 @@ recursive function recursive_linear_search(collection, index, target) result(tar
             target_index = index
         else
             !! Recursively search in the remaining part of the collection
-            target_index = recursive_linear_search(collection, index-1, target)
+            target_index = recursive_linear_search(collection, index - 1, target)
         end if
 
     end function recursive_linear_search
 
-end module recursive_linear_search_module
+end module recursive_linear_search_module