Enter size of tree to create     [1000]: 
Enter # of random trees to create[100000]: 
Enter # trees per heartbeat      [10000]: 
Shuffle values before adding     [true]?: 
Verify searches work             [false]?: 
Show 1st tree                    [false]?: 

Collecting Statistics: 
Processed: 
  10000
  20000
  30000
  40000
  50000
  60000
  70000
  80000
  90000
  100000
  Done


Height |   #Trees    | 
----------------------------------------------------------------------
    16 |          43 | 
    17 |         966 | **
    18 |        5579 | *************
    19 |       14661 | **********************************
    20 |       21314 | **************************************************
    21 |       21134 | *************************************************
    22 |       16082 | *************************************
    23 |        9845 | ***********************
    24 |        5486 | ************
    25 |        2761 | ******
    26 |        1215 | **
    27 |         561 | *
    28 |         220 | 
    29 |          83 | 
    30 |          36 | 
    31 |           9 | 
    32 |           5 | 

Minimum Possible Height = 8.96723
Minimum Actual Height   = 16
Average Actual Height   = 21.0394
Maximum Actual Height   = 32
Maximum Possible Height = 999
Avg Compares for Search = 11 (truncated)

Time = 29.479 seconds; processing speed = 3392 trees/second

------------------------------------------------------------------------------

Enter size of tree to create     [1000]: 10000
Enter # of random trees to create[100000]: 1000000
Enter # trees per heartbeat      [10000]: 100000
Shuffle values before adding     [true]?: 
Verify searches work             [false]?: 
Show 1st tree                    [false]?: 

Collecting Statistics: 
Processed: 
  100000
  200000
  300000
  400000
  500000
  600000
  700000
  800000
  900000
  1000000
  Done


Height |   #Trees    | 
----------------------------------------------------------------------
    24 |          18 | 
    25 |         949 | 
    26 |       12208 | ***
    27 |       57676 | **************
    28 |      134769 | *********************************
    29 |      193509 | ************************************************
    30 |      198608 | **************************************************
    31 |      160151 | ****************************************
    32 |      108700 | ***************************
    33 |       65271 | ****************
    34 |       35518 | ********
    35 |       17801 | ****
    36 |        8356 | **
    37 |        3771 | 
    38 |        1604 | 
    39 |         682 | 
    40 |         267 | 
    41 |          95 | 
    42 |          36 | 
    43 |           7 | 
    44 |           1 | 
    45 |           2 | 
    46 |           1 | 

Minimum Possible Height = 12.2879
Minimum Actual Height   = 24
Average Actual Height   = 30.2145
Maximum Actual Height   = 46
Maximum Possible Height = 9999
Avg Compares for Search = 16 (truncated)

Time = 3063.72 seconds; processing speed = 326 trees/second

------------------------------------------------------------------------------

Some data taken from previous versions of ICS-46 in Java

Enter size of tree to create       : 10000
Enter # of random trees to create  : 1000000

Collecting Statistics: 

Height |   #Trees    | 
----------------------------------------------------------------------
    24 |          18 | 
    25 |         906 | 
    26 |       12360 | ***
    27 |       57584 | **************
    28 |      135007 | **********************************
    29 |      193358 | ************************************************
    30 |      198349 | **************************************************
    31 |      160260 | ****************************************
    32 |      109076 | ***************************
    33 |       65045 | ****************
    34 |       35396 | ********
    35 |       17637 | ****
    36 |        8549 | **
    37 |        3703 | 
    38 |        1643 | 
    39 |         665 | 
    40 |         282 | 
    41 |          97 | 
    42 |          41 | 
    43 |          16 | 
    44 |           5 | 
    45 |           2 | 
    46 |           1 | 

Minimum Possible Height = 12.287856641840545
Minimum Actual Height   = 24
Average Actual Height   = 30.214161
Maximum Actual Height   = 46
Maximum Possible Height = 9999
Avg Compares for Search = 16 (truncated)

Time = 1341.13 seconds; processing speed = 745 trees/second

------------------------------------------------------------------------------

Enter size of tree to create       : 10000
Enter # of random trees to create  : 3000000

Collecting Statistics: 

Height |   #Trees    | 
----------------------------------------------------------------------
    24 |          48 | 
    25 |        2816 | 
    26 |       36641 | ***
    27 |      173110 | **************
    28 |      404628 | *********************************
    29 |      580334 | ************************************************
    30 |      596070 | **************************************************
    31 |      479814 | ****************************************
    32 |      326389 | ***************************
    33 |      194708 | ****************
    34 |      106582 | ********
    35 |       53511 | ****
    36 |       25438 | **
    37 |       11558 | 
    38 |        5032 | 
    39 |        1998 | 
    40 |         838 | 
    41 |         314 | 
    42 |         105 | 
    43 |          42 | 
    44 |          16 | 
    45 |           6 | 
    46 |           2 | 

Minimum Possible Height = 12.287856641840545
Minimum Actual Height   = 24
Average Actual Height   = 30.21550166666667
Maximum Actual Height   = 46
Maximum Possible Height = 9999
Avg Compares for Search = 16 (truncated)

Time = 4135.146 seconds; processing speed = 725 trees/second

------------------------------------------------------------------------------

Enter size of tree to create       : 10000
Enter # of random trees to create  : 5000000

Collecting Statistics: 

Height |   #Trees    | 
----------------------------------------------------------------------
    24 |          67 | 
    25 |        4707 | 
    26 |       61134 | ***
    27 |      289110 | **************
    28 |      674927 | *********************************
    29 |      965701 | ************************************************
    30 |      992753 | **************************************************
    31 |      800114 | ****************************************
    32 |      544052 | ***************************
    33 |      325608 | ****************
    34 |      177491 | ********
    35 |       89025 | ****
    36 |       42452 | **
    37 |       19076 | 
    38 |        8282 | 
    39 |        3347 | 
    40 |        1332 | 
    41 |         554 | 
    42 |         177 | 
    43 |          61 | 
    44 |          19 | 
    45 |           5 | 
    46 |           4 | 
    47 |           2 | 

Minimum Possible Height = 12.287856641840545
Minimum Actual Height   = 24
Average Actual Height   = 30.2152332
Maximum Actual Height   = 47
Maximum Possible Height = 9999
Avg Compares for Search = 16 (truncated)

Time = 6786.836 seconds; processing speed = 736 trees/second

------------------------------------------------------------------------------

I actually figured out a formula that computes the number of sequences that
yield a binary search tree with N values and of height H. From this formula
I computed the exact average height of a tree with N nodes.

N     Average Height
1     0.0
2     1.0
4     2.3333333333333335
8     4.017460317460317
16    6.039095184259206
32    8.280329890049611
64    10.67962444037314
128   13.190811301631685

This was a far as I was able compute: with N = 128, there are 128! sequences
generated, beyond which swammped my computer. Note that 128! is

3856204823625804217356770659234636406174931095902235902788284032763734025751655
4356068616858850736153403005183305891634759217293226249885776611495524503935776
0034644709279247692495585280000000000000000000000000000000

The average height is approximated by 2*Log2(N)-1. The best bst with N nodes has
height Log2(N)-1. So the average height is about 2 * the best (+1).