A binary tree is left-complete of height h if all possible nodes of depth h-1 are present and all nodes at depth h are in the leftmost possible positions

size, complete binary tree

1     0

2       0
       /
      1

3       0
       / \
      1   2

4       0
       / \
      1   2
     /
    3

6       0
       / \
      1   2
     / \ /
    3  4 5

7       0
       / \
      1   2
     / \ / \
    3  4 5  6

10       _ 0 _
        /     \
      1         2
     / \       / \
    3   4     5   6
   / \  /
  7  8 9

15       _ 0 _
        /     \
      1         2
     / \       / \
    3   4     5    6
   / \  /\   / \  / \
  7  8 9 10 11 12 13 14

16                ________ 0 _______
                /                   \
           __ 1 __                 __ 2 __
          /       \               /       \
        3           4           5           6
       / \         / \         / \         / \
     7     8     9    10    11    12    13    14
    / 
   15

31                ________ 0 _______
                /                   \
           __ 1 __                 __ 2 __
          /       \               /       \
        3           4           5           6
       / \         / \         / \         / \
     7     8     9    10    11    12    13    14
    / \   / \   / \   / \   / \   / \   / \   / \
   15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 


Height, range of sizes

-1       0..0
0        1..1
1        2..3
2        4..7
3        8..15
4       16..31
5       32..63
6       64..127
7      128..255
8      256..511
9      512..1023
10    1024..2047
11    2048..4095
12    4096..8191
13    8192..16383
14   16384..32767
15   32768..65537
16   65536..131071
17  131072..262143
18  262144..523287
19  524288..1048575
20 1048576..(2 million +)
..
30 (1 billion +)..(2 billion +)