=== Prim from a with a binary heap ===
step 1  pop a:0  add (root)  total  0  updates b:inf->4 h:inf->8 
        heap: b:4 h:8 
step 2  pop b:4  add ab(4)   total  4  updates c:inf->8 
        heap: c:8 h:8 
step 3  pop c:8  add bc(8)   total 12  updates d:inf->7 f:inf->4 i:inf->2 
        heap: i:2 f:4 d:7 h:8 
step 4  pop i:2  add ci(2)   total 14  updates g:inf->6 h:8->7 
        heap: f:4 g:6 d:7 h:7 h:8 
step 5  pop f:4  add cf(4)   total 18  updates e:inf->10 g:6->2 
        heap: g:2 g:6 d:7 h:7 h:8 e:10 
step 6  pop g:2  add fg(2)   total 20  updates h:7->1 
        heap: h:1 g:6 d:7 h:7 h:8 e:10 
step 7  pop h:1  add gh(1)   total 21  updates - 
        heap: g:6 d:7 h:7 h:8 e:10 
      pop g:6  stale, discarded
step 8  pop d:7  add cd(7)   total 28  updates e:10->9 
        heap: h:7 h:8 e:9 e:10 
      pop h:7  stale, discarded
      pop h:8  stale, discarded
step 9  pop e:9  add de(9)   total 37  updates - 
        heap: e:10 
      pop e:10  stale, discarded
tree: ab(4) bc(8) cd(7) de(9) cf(4) fg(2) gh(1) ci(2)
total weight 37; heap pushes 13, pops 13, stale pops 4

=== Prim from i with a binary heap ===
step 1  pop i:0  add (root)  total  0  updates c:inf->2 g:inf->6 h:inf->7 
        heap: c:2 g:6 h:7 
step 2  pop c:2  add ic(2)   total  2  updates b:inf->8 d:inf->7 f:inf->4 
        heap: f:4 g:6 d:7 h:7 b:8 
step 3  pop f:4  add cf(4)   total  6  updates e:inf->10 g:6->2 
        heap: g:2 g:6 d:7 h:7 b:8 e:10 
step 4  pop g:2  add fg(2)   total  8  updates h:7->1 
        heap: h:1 g:6 d:7 h:7 b:8 e:10 
step 5  pop h:1  add gh(1)   total  9  updates a:inf->8 
        heap: g:6 d:7 h:7 a:8 b:8 e:10 
      pop g:6  stale, discarded
step 6  pop d:7  add cd(7)   total 16  updates e:10->9 
        heap: h:7 a:8 b:8 e:9 e:10 
      pop h:7  stale, discarded
step 7  pop a:8  add ha(8)   total 24  updates b:8->4 
        heap: b:4 b:8 e:9 e:10 
step 8  pop b:4  add ab(4)   total 28  updates - 
        heap: b:8 e:9 e:10 
      pop b:8  stale, discarded
step 9  pop e:9  add de(9)   total 37  updates - 
        heap: e:10 
      pop e:10  stale, discarded
tree: ha(8) ab(4) ic(2) cd(7) de(9) cf(4) fg(2) gh(1)
total weight 37; heap pushes 13, pops 13, stale pops 4
