Data update

Task/McNuggets-problem/Fortran/mcnuggets-problem.f

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+program mcnugget
+  ! Program to find non-McNugget numbers (up to 100) that cannot be expressed as
+  ! 6x + 9y + 20z (with x, y, z non-negative integers). This version uses dynamic
+  ! programming to mark expressible numbers and then uses FINDLOC on a logical mask
+  ! (derived by applying .NOT. to the expressible array) to obtain the largest
+  ! non-expressible number.
+
+  implicit none
+  integer, parameter :: n = 100
+  logical :: expressible(0:n)  ! Mark if each number 0:n is expressible.
+  integer :: max_val           ! To store the largest non-expressible number.
+  integer :: i, j            ! Loop indices.
+  integer :: denoms(3)         ! Array of denominations: 6, 9, 20.
+  integer, allocatable :: loc(:)
+  ! 'loc' will store the indices returned by FINDLOC.
+
+  !--------------------------------------------------------------------
+  ! Initialize the denominations and print them.
+  !--------------------------------------------------------------------
+  denoms = [6, 9, 20]
+  print *, 'Nugget pacet sizes: ', denoms
+
+  !--------------------------------------------------------------------
+  ! Initialize all numbers as non-expressible except 0.
+  ! 0 is expressible (with x = y = z = 0).
+  !--------------------------------------------------------------------
+  expressible = .false.
+  expressible(0) = .true.
+
+  !--------------------------------------------------------------------
+  ! Dynamic programming:
+  ! For each denomination, if a number i is expressible then mark
+  ! i + denomination as expressible (provided it does not exceed n).
+  !--------------------------------------------------------------------
+  do j = 1, 3
+    do i = 0, n - denoms(j)
+      if (expressible(i)) then
+        expressible(i + denoms(j)) = .true.
+      end if
+    end do
+  end do
+
+  !--------------------------------------------------------------------
+  ! Instead of looping to count and store non-expressible numbers,
+  ! we use the FINDLOC intrinsic to get the largest index for which
+  ! the number is NOT expressible.
+  !
+  ! The expression (.not. expressible) creates a logical mask that is .true.
+  ! when a number is non-expressible. FINDLOC with BACK=.TRUE. searches the
+  ! array in reverse order (from n down to 0), thus returning the maximum index.
+  !--------------------------------------------------------------------
+  loc = findloc(.not. expressible, .true., back = .true.)
+  if (size(loc) > 0) then
+    max_val = loc(1)  ! Retrieve the largest non-expressible number.
+  else
+    max_val = 0       ! In the unlikely event that every number is expressible.
+  end if
+
+  !--------------------------------------------------------------------
+  ! Output the result (only the largest non-McNugget number).
+  !--------------------------------------------------------------------
+  print *, 'Maximum non-McNuggets number is ', max_val
+
+end program mcnugget