%! no DSC

/max2 {
    dup % a b b
    3 2 roll % b b a
    dup % b b a a
    3 1 roll % b a b a
    lt { exch} if
    pop
} def

/btd {
    /tree exch def
    /st tree length def
    /depth st array def
    /diameter st array def
    0 1 st 1 sub {
        dup
        depth exch 0 put
        diameter exch 0 put
    } for
    st 1 sub 1 neg 0 {
        /i exch def
        tree i get 0 ne {
            /a i 2 mul 1 add def
            /b a 1 add def
            b st lt {
                depth i depth a get depth b get max2 1 add put
                diameter i
                depth a get depth b get add
                diameter a get
                diameter b get
                max2 max2 put
            } {
                depth i 1 put
            } ifelse
        } if
    } for
    diameter 0 get
} def

[ 1
  2 5
  3 4 6 7
  0 0 0 0 0 0 8 10
  0 0 0 0 0 0 0  0 0 0 0 0 9 0 0 0 ]
btd
=