How to determine whether a binary tree is complete?

Question

A complete binary tree is defined as a binary tree in which every level, except possibly the deepest, is completely filled. At deepest level, all nodes must be as far left a

Answer 1

Similar to:

height(t) = if (t==NULL) then 0 else 1+max(height(t.left),height(t.right))

You have:

perfect(t) = if (t==NULL) then 0 else { 
                  let h=perfect(t.left)
                  if (h != -1 && h==perfect(t.right)) then 1+h else -1
             }

Where perfect(t) returns -1 if the leaves aren't all at the same depth, or any node has only one child; otherwise, it returns the height.

Edit: this is for "complete" = "A perfect binary tree is a full binary tree in which all leaves are at the same depth or same level.1 (This is ambiguously also called a complete binary tree.)" (Wikipedia).

Here's a recursive check for: "A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible.". It returns (-1,false) if the tree isn't complete, otherwise (height,full) if it is, with full==true iff it's perfect.

complete(t) = if (t==NULL) then (0,true) else { 
                  let (hl,fl)=complete(t.left)
                  let (hr,fr)=complete(t.right)                      
                  if (fl && hl==hr) then (1+h,fr)
                  else if (fr && hl==hr+1) then (1+h,false)
                  else (-1,false)
              }