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  1. function nthPartition(m, n)
  2.     implicit none
  3.     character * 32 :: nthPartition
  4.     integer :: m, n, i, j, L, v(32)
  5.     integer, allocatable :: A(:, :)
  6.  
  7.     allocate(A(m, m))
  8.     A = 0
  9.     A(1, 1:min(m, 5)) = 1
  10.     do i = 2, m
  11.         do j = 1, 5
  12.             A(i, j + 1:) = A(i, j + 1:) + A(i - 1, :m - j)
  13.         end do
  14.     end do
  15.  
  16.     do L = 1, m
  17.         if (n <= A(L, m)) exit
  18.         if (L < m) then
  19.             n = n - A(L, m)
  20.         else
  21.             nthPartition = '0'
  22.             deallocate(A)
  23.             return
  24.         end if
  25.     end do
  26.  
  27.     do i = 1, L
  28.         do j = 1, 5
  29.             if (i < L) then
  30.                 if (n <= A(L - i, m - j)) exit
  31.                 n = n - A(L - i, m - j)
  32.             else
  33.                 if (j == m) exit
  34.             end if
  35.         end do
  36.  
  37.         v(i) = j
  38.         m = m - j
  39.     end do
  40.  
  41.     write(nthPartition, '(32(i0))') v(1:L)
  42.     deallocate(A)
  43. end function
  44.  
  45. program main
  46.     implicit none
  47.     integer :: Q(2, 16) = reshape((/ &
  48.          (/2, 1/), (/2, 2/), (/2, 3/), &
  49.          (/20, 1/), (/20, 2/), (/20, 3/), (/20, 400096/), (/20, 400097/), &
  50.          (/32, 1/), (/32, 2/), (/32, 3/), (/32, 1000/), (/32, 1000000/), &
  51.          (/32, 1000000000/), (/32, 1333610936/), (/32, 1333610937/) &
  52.     /), (/2, 16/))
  53.  
  54.     character * 32 :: nthPartition
  55.     integer :: i, m, n
  56.  
  57.     do i = 1, size(Q, 2)
  58.         m = Q(1, i); n = Q(2, i)
  59.         print '("(", (i0), ", ", (i0), ") → ", (a))', m, n, nthPartition(m, n)
  60.     end do
  61. end program
Success #stdin #stdout 0s 5320KB
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(2, 1) → 2                               
(2, 2) → 11                              
(2, 3) → 0                               
(20, 1) → 5555                            
(20, 2) → 14555                           
(20, 3) → 15455                           
(20, 400096) → 11111111111111111111            
(20, 400097) → 0                               
(32, 1) → 2555555                         
(32, 2) → 3455555                         
(32, 3) → 3545555                         
(32, 1000) → 34355354                        
(32, 1000000) → 11532334334                     
(32, 1000000000) → 2141111311212411131             
(32, 1333610936) → 11111111111111111111111111111111
(32, 1333610937) → 0
https://ideone.com/CnJ0S9
language:
Fortran (gfortran 8.3)
created:
6 days ago
visibility:
secret

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