TopCoder Statistics - Problem Statement

Problem Statement

A binary tree is a rooted tree in which each node has at most one left child and at most one right child.

Each N-node tree in this problem will have its nodes labeled 0 to N-1. For a fixed tree left(v) and right(v) will denote the numbers of the left and right child of node v. The special value None is used if node v does not have that child.

Consider the following three mutually recursive functions:


function PreInPost(v):
    print(v)
    if left(v) is not None: InPostPre(left(v))
    if right(v) is not None: InPostPre(right(v))

function InPostPre(v):
    if left(v) is not None: PostPreIn(left(v))
    print(v)
    if right(v) is not None: PostPreIn(right(v))

function PostPreIn(v):
    if left(v) is not None: PreInPost(left(v))
    if right(v) is not None: PreInPost(right(v))
    print(v)

Each of these three functions has the property that if you call it with the argument equal to the root of the tree, it will output each of the tree's nodes exactly once. (As the three functions call each other in a cycle, we are cycling through printing the tree in pre-order, in-order, and post-order. Hence the function names.)

You are given the int[]s PIP and IPP. PIP contains the order in which the call PreInPost(root) printed the nodes of a tree. IPP contains the order in which the call InPostPre(root) printed the nodes of the same tree.

Count all distinct trees that match the given information. Return that count modulo (10^9 + 7).

Definition

Class:: PreInPostOrder
Method:: reconstruct
Parameters:: int[], int[]
Returns:: int
Method signature:: int reconstruct(int[] PIP, int[] IPP)
(be sure your method is public)

Notes

Remember that you are counting binary trees with N nodes, where N is the number of elements in PIP. The nodes are labelled 0 to N-1.
Two trees count as identical if and only if the functions left() and right() that describe them are identical.

Constraints

PIP will have between 1 and 70 elements, inclusive.
PIP will be a permutation of 0 to N-1, where N is the number of elements in PIP.
IPP will have the same number of elements as PIP.
IPP will be a permutation of 0 to N-1, where N is the number of elements in IPP.

Examples

{0, 1, 2}

{0, 2, 1}

Returns: 1

The only tree that matches these looks as follows: 0 \ 1 \ 2
{1, 2, 0}

{1, 0, 2}

Returns: 1

The only matching tree has the same shape as in the previous example, only the order of node labels is different.
{1, 2, 0}

{0, 1, 2}

Returns: 0

No such tree.
{2, 1, 3, 0}

{0, 3, 1, 2}

Returns: 2

In both matching trees we have left(2)=1 and right(1)=0. One of the two matching trees has left(0)=3, the other has right(0)=3.
{0, 3, 4, 2, 1, 7, 8, 6, 5, 10, 9}

{2, 3, 4, 1, 0, 6, 7, 8, 9, 10, 5}

Returns: 18
{0, 3, 4, 2, 1}

{0, 2, 4, 3, 1}

Returns: 2
{0, 2, 1, 3, 4}

{2, 1, 0, 4, 3}

Returns: 1
{0, 1, 3, 4, 2}

{0, 2, 4, 3, 1}

Returns: 2
{0, 1, 3, 4, 2}

{2, 3, 4, 1, 0}

Returns: 3
{0, 3, 4, 7, 6, 5, 8, 2, 1, 9}

{2, 3, 6, 7, 8, 5, 4, 1, 0, 9}

Returns: 2
{0, 3, 2, 1, 5, 6, 7, 8, 9, 4}

{0, 2, 3, 4, 6, 5, 7, 9, 8, 1}

Returns: 8
{0, 2, 1, 3, 6, 7, 8, 5, 4, 9}

{2, 3, 1, 0, 5, 7, 6, 8, 9, 4}

Returns: 3
{0, 1, 3, 4, 5, 6, 7, 8, 2, 9}

{2, 4, 3, 5, 8, 7, 6, 1, 0, 9}

Returns: 7
{0, 1, 3, 4, 7, 8, 10, 12, 11, 13, 9, 6, 5, 14, 2}

{2, 4, 3, 6, 9, 12, 11, 10, 13, 8, 7, 14, 5, 1, 0}

Returns: 12
{0, 2, 1, 3, 6, 5, 4, 8, 9, 10, 13, 12, 11, 14, 7}

{2, 3, 1, 0, 5, 6, 7, 8, 9, 12, 13, 14, 11, 10, 4}

Returns: 4
{0, 1, 3, 6, 7, 5, 4, 2, 10, 9, 8, 12, 13, 14, 11}

{2, 3, 5, 7, 6, 4, 1, 0, 9, 10, 11, 12, 13, 14, 8}

Returns: 56
{0, 3, 6, 5, 4, 7, 8, 2, 1, 11, 12, 14, 13, 10, 9}

{2, 3, 5, 6, 4, 7, 8, 1, 0, 10, 12, 11, 14, 13, 9}

Returns: 12
{0, 2, 1, 4, 6, 5, 8, 9, 12, 13, 16, 17, 15, 14, 18, 11, 10, 7, 19, 3}

{0, 2, 3, 4, 6, 7, 8, 9, 11, 12, 15, 16, 17, 18, 14, 13, 10, 5, 19, 1}

Returns: 3
{0, 3, 5, 4, 6, 9, 11, 10, 13, 12, 15, 14, 8, 7, 16, 19, 18, 17, 2, 1}

{0, 2, 5, 4, 3, 8, 11, 12, 13, 10, 9, 15, 14, 16, 7, 6, 18, 19, 17, 1}

Returns: 16
{0, 3, 6, 7, 5, 4, 8, 10, 11, 9, 12, 2, 1, 14, 15, 16, 17, 13, 19, 18}

{2, 5, 6, 7, 4, 3, 9, 11, 10, 8, 12, 13, 16, 15, 14, 17, 1, 0, 19, 18}

Returns: 72
{0, 3, 6, 7, 8, 9, 5, 4, 10, 2, 1, 11, 14, 16, 15, 17, 19, 18, 13, 12}

{2, 5, 7, 6, 9, 8, 4, 3, 10, 11, 1, 0, 13, 16, 17, 15, 14, 19, 18, 12}

Returns: 36
{0, 1, 3, 6, 7, 10, 11, 14, 15, 16, 18, 19, 20, 21, 17, 13, 12, 22, 9, 8, 5, 4, 23, 24, 2}

{0, 2, 5, 7, 6, 9, 10, 11, 13, 15, 14, 17, 19, 18, 20, 21, 16, 22, 12, 8, 4, 3, 23, 24, 1}

Returns: 64
{0, 3, 2, 1, 6, 7, 8, 11, 12, 13, 14, 15, 18, 17, 16, 20, 19, 10, 9, 21, 22, 23, 5, 4, 24}

{2, 3, 1, 0, 5, 7, 6, 10, 12, 11, 13, 15, 14, 17, 18, 19, 20, 16, 21, 9, 8, 23, 22, 24, 4}

Returns: 12
{0, 3, 4, 6, 5, 7, 8, 2, 1, 10, 11, 12, 15, 17, 16, 14, 13, 18, 19, 9, 22, 21, 20, 24, 23}

{2, 4, 3, 6, 5, 7, 8, 9, 11, 10, 14, 15, 17, 16, 18, 13, 12, 19, 1, 0, 21, 22, 23, 24, 20}

Returns: 32
{0, 1, 3, 4, 5, 2, 8, 7, 6, 10, 11, 14, 15, 16, 13, 12, 18, 19, 20, 17, 21, 22, 23, 24, 9}

{2, 3, 4, 5, 1, 0, 7, 8, 9, 11, 10, 13, 14, 15, 16, 17, 18, 20, 19, 12, 23, 22, 21, 24, 6}

Returns: 96
{0, 1, 3, 4, 7, 8, 9, 11, 14, 15, 18, 20, 19, 22, 23, 24, 25, 21, 17, 16, 26, 13, 12, 27, 28, 10, 6, 5, 2, 29}

{2, 3, 6, 7, 10, 13, 15, 14, 17, 18, 20, 21, 22, 24, 23, 25, 19, 16, 26, 12, 11, 27, 28, 9, 8, 5, 4, 1, 0, 29}

Returns: 72
{0, 3, 4, 5, 8, 9, 10, 11, 14, 15, 16, 17, 19, 18, 13, 12, 21, 22, 20, 7, 6, 24, 25, 23, 2, 1, 26, 29, 28, 27}

{2, 3, 5, 4, 7, 9, 8, 11, 10, 13, 14, 15, 17, 16, 19, 18, 20, 22, 21, 12, 23, 24, 25, 6, 26, 1, 0, 28, 29, 27}

Returns: 24
{0, 3, 4, 5, 7, 6, 2, 1, 9, 10, 12, 13, 14, 16, 17, 15, 18, 20, 19, 11, 23, 24, 22, 21, 25, 26, 27, 28, 29, 8}

{2, 4, 3, 7, 6, 5, 8, 11, 12, 15, 16, 17, 14, 13, 19, 20, 18, 10, 9, 22, 23, 24, 25, 21, 28, 27, 26, 29, 1, 0}

Returns: 24
{0, 3, 6, 7, 5, 4, 9, 10, 8, 2, 1, 12, 13, 14, 16, 15, 17, 19, 18, 11, 22, 23, 24, 25, 27, 26, 28, 21, 20, 29}

{2, 5, 6, 7, 8, 9, 10, 4, 3, 11, 12, 15, 16, 14, 13, 18, 19, 17, 1, 0, 21, 22, 24, 23, 27, 28, 26, 25, 29, 20}

Returns: 252
{0, 2, 1, 4, 7, 10, 11, 13, 12, 15, 17, 16, 19, 20, 22, 21, 24, 27, 28, 29, 31, 30, 26, 25, 23, 32, 18, 14, 9, 8, 33, 34, 6, 5, 3}

{2, 3, 4, 6, 9, 11, 10, 13, 14, 15, 17, 18, 19, 22, 23, 24, 26, 27, 29, 28, 31, 30, 25, 21, 20, 32, 16, 12, 8, 7, 33, 34, 5, 1, 0}

Returns: 576
{0, 3, 2, 1, 5, 8, 9, 7, 6, 11, 12, 13, 14, 16, 15, 18, 21, 20, 19, 23, 24, 25, 26, 27, 22, 28, 29, 17, 10, 31, 30, 32, 4, 34, 33}

{2, 3, 4, 7, 8, 9, 10, 12, 11, 13, 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 26, 19, 28, 29, 15, 14, 6, 5, 31, 30, 32, 1, 0, 34, 33}

Returns: 108
{0, 3, 2, 1, 5, 4, 8, 11, 13, 12, 14, 17, 16, 15, 19, 20, 18, 21, 10, 9, 23, 22, 25, 24, 26, 27, 7, 6, 29, 31, 30, 33, 32, 34, 28}

{2, 3, 4, 5, 1, 0, 7, 10, 11, 13, 12, 16, 17, 18, 19, 20, 15, 14, 21, 22, 23, 9, 8, 25, 24, 27, 26, 28, 31, 32, 33, 30, 29, 34, 6}

Returns: 864
{0, 3, 5, 4, 6, 9, 8, 7, 11, 10, 12, 13, 15, 16, 17, 14, 2, 1, 19, 20, 23, 25, 24, 26, 27, 22, 21, 28, 31, 30, 29, 32, 18, 34, 33}

{2, 5, 6, 4, 3, 8, 9, 10, 11, 7, 12, 14, 16, 15, 17, 13, 18, 20, 19, 22, 25, 24, 23, 27, 26, 21, 28, 30, 31, 32, 29, 1, 0, 34, 33}

Returns: 90
{0, 1, 2, 4, 6, 5, 8, 9, 12, 14, 13, 16, 18, 17, 20, 21, 22, 25, 27, 26, 29, 30, 28, 31, 32, 24, 23, 33, 19, 34, 35, 15, 36, 37, 11, 10, 7, 38, 39, 3}

{1, 0, 3, 6, 7, 9, 8, 11, 14, 15, 18, 19, 20, 22, 21, 24, 27, 28, 29, 30, 26, 25, 31, 32, 33, 23, 17, 16, 34, 35, 13, 12, 36, 37, 10, 5, 4, 38, 39, 2}

Returns: 1536
{0, 3, 5, 4, 6, 8, 7, 10, 9, 12, 13, 16, 17, 15, 14, 19, 20, 21, 24, 27, 28, 29, 30, 31, 32, 33, 26, 25, 35, 36, 34, 38, 37, 39, 23, 22, 18, 11, 2, 1}

{0, 2, 3, 5, 4, 8, 7, 6, 10, 11, 12, 15, 16, 17, 18, 20, 19, 21, 23, 26, 28, 27, 30, 29, 31, 33, 32, 34, 35, 36, 25, 24, 38, 39, 37, 22, 14, 13, 9, 1}

Returns: 144
{0, 2, 1, 3, 6, 7, 8, 9, 10, 5, 4, 12, 14, 13, 16, 17, 15, 20, 21, 19, 18, 23, 25, 24, 27, 28, 26, 29, 31, 30, 33, 32, 34, 35, 22, 36, 37, 38, 39, 11}

{2, 3, 1, 0, 5, 8, 7, 6, 9, 10, 11, 14, 15, 17, 16, 13, 12, 19, 20, 21, 22, 25, 26, 27, 28, 24, 23, 31, 32, 33, 30, 29, 35, 34, 18, 37, 36, 39, 38, 4}

Returns: 144
{0, 3, 5, 4, 6, 7, 8, 10, 9, 2, 1, 12, 15, 14, 13, 18, 19, 17, 16, 20, 21, 24, 23, 22, 11, 27, 28, 30, 29, 31, 32, 33, 35, 34, 26, 25, 37, 38, 39, 36}

{2, 3, 5, 6, 4, 7, 9, 10, 8, 11, 14, 15, 13, 12, 17, 18, 19, 16, 21, 20, 23, 24, 22, 1, 0, 26, 28, 27, 30, 31, 29, 34, 35, 33, 32, 36, 38, 37, 39, 25}

Returns: 1152
{0, 1, 2, 4, 7, 10, 12, 11, 14, 15, 17, 16, 19, 22, 25, 26, 28, 29, 31, 30, 33, 34, 36, 35, 32, 27, 24, 23, 37, 38, 21, 20, 39, 18, 40, 13, 9, 8, 41, 42, 6, 5, 43, 44, 3}

{1, 0, 3, 6, 9, 10, 12, 13, 14, 17, 18, 19, 21, 24, 25, 27, 29, 28, 31, 32, 33, 35, 36, 34, 30, 26, 23, 22, 37, 38, 20, 39, 16, 15, 40, 11, 41, 8, 7, 42, 43, 5, 4, 44, 2}

Returns: 3240
{0, 2, 1, 3, 6, 8, 7, 10, 13, 16, 17, 18, 20, 19, 21, 22, 23, 15, 14, 25, 26, 24, 27, 29, 28, 30, 32, 31, 12, 11, 34, 35, 33, 36, 37, 9, 39, 38, 40, 41, 5, 4, 43, 44, 42}

{2, 3, 1, 0, 5, 8, 9, 12, 15, 17, 16, 19, 20, 18, 23, 22, 21, 24, 25, 26, 14, 13, 28, 29, 27, 30, 32, 31, 33, 35, 34, 11, 10, 36, 37, 7, 6, 39, 38, 40, 41, 42, 43, 44, 4}

Returns: 6912
{0, 1, 4, 7, 6, 5, 8, 11, 10, 9, 13, 16, 15, 14, 17, 18, 19, 22, 25, 26, 27, 24, 23, 30, 31, 29, 28, 33, 36, 35, 34, 38, 40, 39, 37, 32, 21, 20, 41, 12, 42, 3, 2, 44, 43}

{1, 0, 3, 6, 7, 8, 5, 4, 10, 11, 12, 13, 15, 16, 17, 14, 19, 18, 21, 24, 25, 26, 27, 23, 22, 29, 30, 31, 32, 33, 35, 36, 37, 40, 39, 38, 34, 28, 41, 20, 9, 42, 43, 44, 2}

Returns: 4992
{0, 3, 6, 7, 8, 9, 5, 4, 11, 12, 10, 14, 13, 15, 18, 19, 20, 21, 17, 16, 23, 24, 25, 26, 29, 28, 27, 22, 2, 1, 31, 33, 32, 34, 35, 36, 37, 38, 30, 39, 41, 43, 42, 44, 40}

{2, 5, 6, 8, 7, 9, 10, 11, 12, 4, 3, 14, 13, 15, 17, 19, 18, 21, 20, 22, 24, 23, 25, 26, 28, 29, 27, 16, 30, 31, 33, 34, 32, 37, 36, 35, 38, 1, 0, 40, 43, 42, 41, 44, 39}

Returns: 1458
{0, 3, 4, 6, 7, 9, 8, 11, 14, 15, 16, 18, 19, 21, 24, 26, 25, 28, 29, 30, 33, 36, 37, 40, 41, 42, 39, 38, 43, 44, 35, 34, 32, 31, 27, 45, 23, 22, 46, 20, 17, 13, 12, 47, 10, 5, 2, 1, 48, 49}

{2, 5, 7, 6, 9, 10, 13, 15, 14, 17, 20, 23, 26, 27, 28, 30, 29, 32, 33, 35, 36, 39, 40, 42, 41, 43, 38, 37, 44, 34, 31, 25, 24, 45, 22, 21, 46, 19, 18, 16, 12, 11, 47, 8, 4, 3, 48, 1, 0, 49}

Returns: 3888
{0, 3, 4, 5, 7, 6, 9, 11, 10, 13, 14, 16, 15, 18, 19, 20, 21, 22, 24, 26, 25, 27, 30, 31, 32, 34, 33, 35, 37, 38, 39, 36, 29, 28, 23, 17, 40, 41, 42, 12, 44, 43, 45, 46, 47, 8, 48, 2, 1, 49}

{2, 4, 3, 7, 8, 11, 12, 14, 13, 16, 17, 18, 20, 19, 23, 26, 25, 24, 29, 31, 30, 34, 33, 32, 36, 38, 37, 39, 35, 28, 27, 22, 21, 15, 42, 41, 40, 10, 9, 44, 45, 43, 47, 46, 6, 5, 48, 49, 1, 0}

Returns: 12
{0, 3, 4, 5, 6, 9, 10, 12, 11, 8, 7, 14, 15, 16, 19, 20, 21, 22, 23, 18, 17, 25, 27, 26, 29, 30, 31, 28, 32, 34, 33, 35, 24, 36, 37, 39, 38, 13, 40, 41, 2, 1, 43, 44, 45, 42, 46, 48, 49, 47}

{2, 4, 3, 5, 8, 9, 11, 12, 10, 13, 16, 15, 14, 18, 19, 20, 22, 21, 23, 24, 25, 27, 28, 29, 30, 31, 26, 32, 34, 35, 33, 17, 36, 38, 39, 37, 7, 6, 41, 40, 42, 43, 45, 44, 1, 0, 47, 48, 49, 46}

Returns: 1440
{0, 3, 5, 4, 6, 9, 11, 10, 12, 13, 14, 8, 7, 17, 20, 21, 19, 18, 22, 23, 25, 26, 28, 27, 30, 29, 32, 31, 24, 33, 34, 16, 15, 36, 35, 2, 1, 38, 41, 40, 39, 43, 44, 45, 46, 47, 42, 49, 48, 37}

{2, 5, 4, 3, 8, 11, 12, 10, 9, 14, 13, 7, 6, 16, 19, 20, 21, 22, 18, 17, 24, 27, 28, 26, 25, 30, 31, 32, 29, 23, 34, 33, 35, 36, 15, 37, 40, 41, 42, 44, 43, 46, 45, 47, 39, 38, 49, 48, 1, 0}

Returns: 12096
{0, 2, 1, 4, 6, 5, 8, 9, 12, 14, 13, 16, 17, 20, 23, 24, 26, 28, 27, 30, 31, 33, 35, 34, 37, 40, 41, 39, 38, 42, 36, 43, 44, 32, 45, 46, 29, 47, 25, 48, 22, 21, 49, 50, 19, 18, 15, 51, 52, 11, 10, 53, 54, 7, 3}

{0, 2, 3, 4, 6, 7, 8, 11, 14, 15, 16, 17, 19, 20, 22, 25, 26, 28, 29, 32, 35, 36, 37, 39, 40, 41, 42, 38, 34, 33, 43, 44, 31, 30, 45, 46, 27, 47, 24, 23, 48, 49, 21, 50, 18, 13, 12, 51, 52, 53, 10, 9, 54, 5, 1}

Returns: 3456
{0, 3, 4, 5, 7, 6, 9, 8, 11, 12, 14, 17, 20, 21, 22, 23, 25, 26, 27, 28, 31, 33, 32, 35, 34, 36, 37, 39, 38, 30, 29, 42, 41, 40, 24, 19, 18, 44, 43, 45, 16, 15, 46, 47, 48, 13, 49, 50, 10, 2, 1, 51, 54, 53, 52}

{2, 4, 3, 7, 6, 5, 9, 10, 13, 16, 19, 20, 22, 21, 24, 26, 25, 27, 30, 33, 32, 31, 35, 36, 34, 39, 38, 37, 29, 28, 41, 42, 40, 23, 43, 44, 18, 17, 45, 46, 15, 14, 47, 48, 12, 11, 49, 50, 8, 51, 1, 0, 53, 54, 52}

Returns: 1920
{0, 3, 4, 5, 6, 8, 7, 9, 12, 13, 11, 10, 15, 16, 14, 19, 21, 20, 23, 22, 24, 25, 28, 29, 30, 32, 33, 34, 35, 31, 38, 37, 36, 40, 42, 41, 43, 39, 27, 26, 45, 44, 18, 17, 46, 2, 1, 48, 49, 51, 50, 52, 47, 53, 54}

{2, 5, 4, 3, 7, 8, 6, 11, 12, 13, 14, 15, 16, 10, 9, 18, 21, 20, 19, 23, 22, 25, 24, 27, 28, 31, 33, 32, 34, 35, 30, 29, 37, 38, 39, 42, 41, 40, 43, 36, 44, 45, 26, 46, 17, 47, 49, 48, 51, 50, 52, 1, 0, 54, 53}

Returns: 2592
{0, 3, 4, 5, 2, 1, 7, 10, 9, 8, 11, 14, 15, 16, 13, 12, 18, 19, 17, 20, 23, 22, 21, 25, 26, 29, 30, 31, 28, 27, 32, 33, 24, 36, 37, 38, 39, 41, 40, 35, 34, 43, 42, 6, 46, 47, 48, 51, 50, 49, 53, 52, 54, 45, 44}

{2, 3, 5, 4, 6, 9, 10, 11, 8, 7, 13, 14, 16, 15, 17, 18, 19, 12, 22, 23, 24, 26, 25, 28, 30, 29, 31, 27, 33, 32, 21, 20, 35, 36, 38, 37, 39, 41, 40, 42, 43, 34, 1, 0, 45, 47, 46, 50, 51, 49, 48, 53, 54, 52, 44}

Returns: 3888
{0, 2, 1, 4, 7, 10, 11, 14, 15, 18, 19, 21, 22, 23, 25, 28, 29, 31, 30, 33, 34, 35, 37, 40, 41, 43, 44, 46, 48, 47, 50, 51, 49, 45, 52, 42, 39, 38, 53, 54, 55, 36, 32, 27, 26, 24, 56, 20, 17, 16, 57, 13, 12, 58, 9, 8, 6, 5, 59, 3}

{0, 2, 3, 4, 6, 7, 9, 11, 10, 13, 15, 14, 17, 18, 20, 21, 24, 25, 27, 29, 28, 31, 32, 34, 33, 36, 39, 42, 45, 46, 48, 49, 51, 50, 47, 44, 43, 52, 41, 40, 53, 38, 37, 54, 55, 35, 30, 26, 23, 22, 56, 19, 16, 57, 58, 12, 8, 59, 5, 1}

Returns: 36864
{0, 2, 1, 5, 6, 7, 10, 11, 12, 14, 15, 16, 17, 20, 21, 23, 22, 26, 27, 25, 24, 29, 30, 31, 34, 33, 32, 37, 39, 38, 42, 41, 40, 44, 47, 46, 45, 50, 49, 48, 51, 43, 52, 53, 36, 35, 54, 28, 19, 18, 56, 55, 13, 57, 58, 59, 9, 8, 4, 3}

{2, 1, 0, 4, 6, 5, 7, 9, 11, 10, 13, 15, 14, 16, 19, 20, 23, 22, 21, 25, 27, 26, 28, 30, 29, 33, 34, 32, 31, 36, 39, 38, 37, 41, 42, 43, 46, 47, 45, 44, 49, 50, 51, 48, 40, 53, 52, 54, 35, 24, 55, 56, 18, 17, 12, 58, 57, 59, 8, 3}

Returns: 192
{0, 2, 1, 4, 3, 6, 8, 7, 11, 12, 13, 10, 9, 15, 17, 16, 18, 20, 19, 22, 23, 25, 24, 21, 28, 29, 30, 33, 32, 31, 34, 35, 38, 37, 36, 39, 42, 43, 44, 45, 47, 46, 49, 50, 48, 41, 40, 52, 53, 55, 54, 56, 57, 51, 27, 26, 14, 58, 59, 5}

{2, 1, 0, 4, 5, 8, 7, 6, 10, 11, 13, 12, 14, 17, 16, 15, 20, 21, 22, 23, 25, 24, 19, 18, 27, 30, 29, 28, 32, 33, 34, 31, 37, 38, 39, 36, 35, 41, 42, 43, 45, 44, 47, 48, 49, 50, 46, 51, 52, 54, 55, 53, 56, 57, 40, 26, 9, 59, 58, 3}

Returns: 1080
{0, 3, 4, 6, 7, 8, 9, 11, 10, 12, 5, 15, 18, 19, 17, 16, 14, 13, 20, 21, 23, 24, 25, 22, 28, 29, 27, 26, 31, 32, 34, 33, 35, 36, 37, 30, 2, 1, 39, 40, 41, 43, 42, 44, 46, 45, 38, 47, 49, 51, 50, 53, 52, 54, 56, 55, 57, 59, 58, 48}

{2, 5, 7, 6, 9, 8, 11, 12, 10, 4, 3, 14, 15, 17, 18, 19, 16, 13, 22, 23, 24, 25, 21, 20, 27, 28, 29, 30, 31, 33, 34, 32, 35, 37, 36, 26, 38, 39, 42, 43, 41, 40, 45, 46, 44, 1, 0, 48, 51, 52, 53, 50, 49, 55, 56, 54, 57, 59, 58, 47}

Returns: 161280
{0, 3, 4, 7, 10, 12, 11, 14, 16, 15, 18, 19, 22, 23, 25, 24, 27, 28, 31, 32, 35, 37, 36, 39, 40, 43, 46, 48, 47, 50, 51, 52, 53, 49, 45, 44, 54, 55, 42, 41, 56, 57, 38, 34, 33, 30, 29, 58, 26, 21, 20, 59, 60, 17, 61, 13, 9, 8, 62, 6, 5, 2, 1, 63, 64}

{2, 4, 3, 6, 9, 12, 13, 14, 16, 17, 18, 21, 23, 22, 25, 26, 28, 27, 30, 32, 31, 34, 35, 37, 38, 40, 39, 42, 45, 48, 49, 52, 51, 50, 53, 47, 46, 44, 43, 54, 55, 56, 41, 57, 36, 33, 58, 29, 24, 59, 20, 19, 60, 15, 61, 11, 10, 8, 7, 62, 5, 63, 1, 0, 64}

Returns: 10368
{0, 3, 2, 1, 4, 6, 8, 7, 9, 12, 13, 16, 17, 15, 14, 19, 22, 24, 23, 26, 27, 28, 30, 29, 32, 33, 34, 35, 36, 38, 37, 40, 39, 42, 43, 46, 45, 44, 47, 41, 31, 25, 50, 49, 48, 51, 21, 20, 53, 52, 54, 55, 56, 57, 18, 58, 59, 11, 10, 61, 60, 64, 63, 62, 5}

{2, 3, 1, 0, 5, 6, 8, 7, 11, 13, 12, 15, 16, 17, 18, 21, 24, 25, 27, 26, 30, 31, 32, 34, 33, 37, 38, 36, 35, 40, 41, 42, 43, 45, 46, 47, 44, 39, 29, 28, 23, 22, 49, 50, 48, 51, 52, 53, 20, 19, 55, 54, 57, 56, 14, 58, 59, 60, 61, 10, 9, 63, 64, 62, 4}

Returns: 27648
{0, 3, 4, 2, 1, 6, 5, 9, 10, 11, 8, 7, 13, 14, 16, 17, 19, 18, 15, 22, 23, 25, 24, 26, 28, 29, 31, 32, 30, 33, 36, 37, 35, 34, 39, 40, 38, 43, 46, 45, 44, 47, 42, 41, 49, 50, 51, 54, 57, 56, 55, 59, 58, 53, 52, 48, 27, 21, 20, 60, 61, 64, 63, 62, 12}

{2, 3, 4, 5, 6, 1, 0, 8, 10, 9, 11, 12, 15, 16, 19, 18, 17, 14, 13, 21, 24, 25, 23, 22, 27, 28, 30, 31, 32, 29, 35, 37, 36, 38, 39, 40, 34, 33, 42, 43, 45, 46, 44, 47, 48, 49, 50, 53, 54, 56, 57, 58, 59, 55, 52, 51, 41, 26, 20, 61, 60, 63, 64, 62, 7}

Returns: 114048
{0, 3, 4, 2, 1, 6, 8, 7, 11, 12, 13, 10, 9, 15, 16, 14, 17, 20, 21, 23, 22, 24, 19, 18, 26, 25, 28, 31, 32, 30, 29, 34, 33, 36, 35, 27, 5, 39, 40, 41, 43, 42, 44, 45, 47, 46, 50, 49, 48, 51, 38, 37, 53, 54, 57, 59, 58, 60, 61, 62, 56, 55, 64, 63, 52}

{2, 4, 3, 5, 8, 7, 6, 10, 13, 12, 11, 14, 16, 15, 9, 19, 22, 23, 21, 20, 24, 18, 17, 26, 27, 30, 32, 31, 29, 28, 34, 35, 36, 33, 25, 1, 0, 38, 41, 40, 39, 43, 44, 42, 47, 46, 45, 49, 50, 51, 48, 52, 53, 56, 59, 58, 57, 60, 62, 61, 55, 54, 64, 63, 37}

Returns: 5376
{0, 3, 4, 7, 10, 11, 14, 15, 16, 19, 20, 23, 24, 27, 29, 28, 31, 32, 34, 35, 37, 36, 39, 40, 43, 44, 45, 47, 48, 50, 51, 54, 55, 57, 59, 58, 60, 56, 61, 53, 52, 62, 49, 46, 42, 41, 63, 38, 64, 33, 30, 26, 25, 22, 21, 65, 66, 18, 17, 13, 12, 67, 9, 8, 68, 69, 6, 5, 2, 1}

{0, 2, 4, 3, 6, 9, 11, 10, 13, 14, 16, 15, 18, 20, 19, 22, 23, 26, 27, 29, 30, 33, 34, 37, 38, 40, 39, 42, 44, 43, 46, 47, 49, 50, 53, 56, 59, 58, 57, 60, 55, 54, 61, 52, 51, 62, 48, 45, 63, 41, 36, 35, 64, 32, 31, 28, 25, 24, 65, 21, 66, 17, 12, 67, 68, 8, 7, 69, 5, 1}

Returns: 2592
{0, 3, 5, 4, 6, 7, 9, 10, 11, 14, 15, 16, 17, 19, 20, 21, 22, 24, 23, 26, 25, 28, 31, 32, 33, 35, 34, 37, 38, 41, 43, 42, 44, 45, 47, 50, 51, 52, 49, 48, 53, 55, 54, 46, 40, 39, 57, 56, 58, 36, 60, 59, 61, 30, 29, 62, 63, 64, 27, 18, 13, 12, 66, 65, 8, 67, 2, 1, 68, 69}

{2, 5, 6, 4, 3, 8, 10, 9, 13, 14, 16, 15, 18, 21, 20, 19, 24, 23, 22, 26, 27, 28, 30, 32, 31, 35, 36, 38, 37, 40, 43, 44, 42, 41, 46, 49, 51, 50, 52, 48, 47, 54, 55, 53, 45, 56, 57, 39, 58, 34, 33, 60, 61, 59, 62, 29, 64, 63, 25, 17, 65, 66, 12, 11, 7, 67, 68, 1, 0, 69}

Returns: 600
{0, 3, 4, 5, 2, 1, 8, 9, 7, 6, 11, 13, 12, 16, 17, 19, 18, 20, 23, 24, 22, 21, 26, 27, 29, 28, 30, 33, 36, 37, 38, 41, 40, 39, 42, 43, 45, 44, 35, 34, 48, 49, 50, 47, 46, 32, 31, 52, 53, 51, 55, 54, 57, 59, 58, 60, 56, 25, 15, 14, 62, 63, 64, 65, 66, 61, 67, 69, 68, 10}

{2, 5, 4, 3, 1, 0, 7, 8, 9, 10, 13, 12, 11, 15, 16, 18, 19, 17, 22, 23, 24, 25, 28, 29, 27, 26, 32, 35, 38, 37, 36, 40, 41, 39, 42, 44, 45, 43, 34, 33, 47, 48, 50, 49, 46, 51, 52, 53, 31, 30, 55, 56, 59, 58, 57, 60, 54, 21, 20, 61, 63, 62, 65, 64, 66, 14, 67, 69, 68, 6}

Returns: 139968
{0, 3, 6, 7, 5, 4, 9, 10, 11, 12, 15, 16, 14, 13, 17, 8, 20, 22, 21, 23, 19, 18, 24, 25, 28, 27, 26, 30, 33, 32, 31, 29, 35, 34, 37, 38, 36, 2, 1, 40, 41, 39, 43, 42, 45, 48, 47, 46, 51, 53, 52, 54, 50, 49, 56, 57, 55, 58, 60, 59, 62, 64, 63, 65, 66, 61, 68, 67, 69, 44}

{2, 5, 6, 7, 8, 9, 10, 12, 11, 14, 16, 15, 17, 13, 4, 3, 19, 20, 22, 21, 23, 24, 18, 27, 28, 29, 30, 32, 33, 31, 26, 25, 35, 36, 38, 37, 34, 39, 40, 41, 1, 0, 43, 44, 47, 48, 46, 45, 50, 53, 54, 52, 51, 55, 56, 57, 49, 60, 61, 64, 63, 62, 65, 66, 59, 58, 68, 69, 67, 42}

Returns: 93312
{3, 4, 1, 0, 2}

{0, 3, 1, 2, 4}

Returns: 0
{3, 2, 1, 4, 7, 8, 5, 9, 0, 6}

{9, 7, 2, 6, 1, 3, 4, 5, 0, 8}

Returns: 0
{2, 4, 14, 6, 12, 11, 1, 13, 9, 10, 5, 8, 0, 3, 7}

{13, 0, 12, 7, 10, 2, 14, 3, 1, 4, 11, 8, 6, 9, 5}

Returns: 0
{19, 3, 2, 18, 1, 10, 14, 12, 6, 4, 16, 0, 17, 15, 5, 8, 7, 9, 11, 13}

{5, 9, 19, 18, 13, 3, 6, 7, 16, 11, 1, 10, 17, 2, 0, 14, 4, 8, 15, 12}

Returns: 0
{14, 5, 8, 9, 4, 1, 18, 23, 3, 17, 12, 2, 24, 13, 22, 11, 6, 7, 0, 10, 15, 21, 16, 19, 20}

{1, 5, 16, 18, 6, 10, 22, 9, 19, 7, 23, 12, 17, 15, 4, 21, 11, 2, 13, 24, 20, 0, 14, 8, 3}

Returns: 0
{25, 29, 24, 11, 14, 6, 21, 22, 16, 13, 15, 18, 27, 8, 28, 9, 2, 0, 3, 12, 23, 7, 19, 1, 20, 10, 17, 4, 26, 5}

{24, 5, 23, 27, 20, 26, 22, 10, 7, 21, 1, 8, 25, 12, 6, 0, 17, 14, 29, 16, 2, 4, 19, 15, 18, 9, 11, 28, 13, 3}

Returns: 0
{25, 24, 10, 13, 3, 2, 4, 5, 7, 31, 18, 14, 16, 11, 19, 12, 15, 23, 30, 34, 9, 27, 33, 28, 0, 26, 22, 21, 17, 20, 8, 32, 29, 6, 1}

{9, 23, 34, 28, 0, 5, 24, 15, 29, 16, 7, 22, 14, 31, 4, 8, 12, 20, 18, 21, 1, 27, 13, 33, 2, 3, 11, 26, 17, 10, 30, 25, 19, 32, 6}

Returns: 0
{38, 19, 4, 20, 36, 31, 34, 2, 23, 21, 25, 11, 14, 30, 24, 12, 39, 17, 26, 8, 22, 32, 35, 7, 37, 15, 10, 13, 5, 3, 9, 6, 18, 16, 28, 33, 29, 27, 1, 0}

{5, 10, 9, 27, 28, 33, 21, 7, 36, 20, 8, 13, 6, 37, 1, 18, 22, 16, 35, 32, 34, 15, 24, 30, 12, 17, 2, 23, 38, 19, 0, 25, 11, 29, 14, 3, 26, 31, 4, 39}

Returns: 0
{37, 33, 13, 44, 15, 10, 40, 0, 30, 23, 18, 14, 26, 28, 11, 24, 34, 17, 3, 32, 9, 39, 41, 36, 42, 35, 7, 29, 2, 19, 43, 1, 22, 5, 38, 16, 6, 21, 31, 8, 4, 25, 20, 12, 27}

{0, 23, 14, 19, 24, 43, 29, 39, 22, 38, 36, 28, 8, 27, 16, 1, 25, 34, 30, 26, 7, 20, 17, 35, 13, 3, 40, 12, 18, 31, 2, 42, 33, 41, 32, 9, 5, 11, 15, 44, 37, 10, 4, 21, 6}

Returns: 0
{19, 11, 9, 17, 18, 14, 8, 42, 41, 46, 4, 36, 30, 2, 32, 29, 0, 34, 35, 44, 22, 23, 16, 15, 13, 33, 45, 5, 24, 25, 10, 49, 39, 21, 37, 7, 48, 6, 47, 38, 3, 20, 12, 1, 31, 26, 43, 27, 28, 40}

{25, 4, 10, 16, 40, 3, 33, 17, 24, 11, 9, 14, 37, 21, 5, 47, 6, 20, 0, 42, 43, 29, 48, 15, 32, 34, 18, 45, 1, 44, 30, 31, 22, 36, 27, 7, 26, 41, 38, 19, 2, 39, 28, 49, 8, 46, 23, 13, 35, 12}

Returns: 0
{11, 10, 37, 33, 40, 8, 32, 5, 31, 4, 45, 46, 47, 15, 54, 51, 49, 17, 24, 53, 39, 43, 6, 19, 1, 35, 9, 29, 3, 44, 28, 22, 20, 26, 2, 25, 21, 41, 52, 23, 42, 13, 34, 16, 48, 36, 38, 7, 0, 18, 12, 50, 30, 27, 14}

{44, 32, 49, 7, 50, 20, 25, 10, 31, 15, 47, 19, 41, 3, 9, 38, 2, 27, 34, 33, 17, 35, 42, 4, 45, 40, 28, 22, 54, 30, 13, 0, 48, 14, 8, 12, 37, 36, 39, 1, 18, 11, 43, 24, 6, 23, 53, 16, 5, 51, 21, 52, 46, 26, 29}

Returns: 0
{21, 3, 59, 36, 4, 44, 24, 5, 32, 22, 48, 16, 6, 43, 2, 8, 53, 41, 12, 20, 42, 17, 33, 52, 13, 23, 49, 15, 51, 58, 25, 27, 0, 11, 28, 26, 19, 29, 57, 30, 56, 18, 45, 7, 14, 9, 46, 40, 55, 34, 38, 50, 10, 1, 37, 54, 39, 31, 47, 35}

{34, 35, 59, 8, 0, 27, 36, 38, 53, 41, 32, 19, 55, 12, 31, 40, 1, 25, 6, 24, 49, 58, 46, 44, 47, 43, 37, 5, 4, 28, 3, 23, 48, 50, 33, 29, 15, 18, 14, 57, 11, 13, 7, 42, 52, 21, 16, 17, 9, 20, 45, 30, 26, 56, 51, 2, 54, 39, 10, 22}

Returns: 0
{58, 26, 11, 63, 43, 27, 57, 55, 48, 21, 0, 30, 39, 19, 46, 15, 53, 31, 44, 1, 6, 9, 29, 25, 10, 62, 5, 64, 4, 3, 45, 56, 28, 40, 61, 2, 36, 20, 59, 49, 18, 14, 34, 41, 23, 51, 50, 22, 35, 16, 7, 24, 38, 17, 13, 60, 37, 47, 32, 52, 42, 54, 8, 12, 33}

{59, 11, 40, 22, 43, 2, 1, 38, 33, 8, 25, 56, 0, 12, 45, 17, 46, 6, 18, 53, 37, 31, 64, 50, 10, 9, 15, 63, 47, 48, 32, 51, 60, 4, 39, 16, 24, 58, 52, 3, 14, 30, 36, 21, 42, 34, 54, 41, 55, 49, 13, 29, 57, 44, 61, 7, 23, 20, 19, 26, 62, 5, 35, 28, 27}

Returns: 0
{19, 5, 62, 42, 3, 12, 26, 35, 69, 43, 2, 58, 48, 51, 54, 7, 45, 49, 8, 30, 38, 32, 33, 0, 34, 36, 22, 55, 1, 64, 37, 14, 67, 11, 15, 10, 68, 61, 66, 24, 56, 16, 65, 27, 46, 13, 52, 57, 21, 17, 53, 31, 60, 40, 50, 6, 39, 18, 28, 44, 59, 29, 25, 4, 9, 63, 20, 23, 47, 41}

{67, 44, 0, 34, 41, 22, 49, 60, 18, 64, 36, 68, 53, 40, 26, 55, 24, 9, 69, 56, 37, 19, 25, 48, 1, 27, 58, 39, 23, 4, 11, 52, 10, 45, 6, 38, 13, 59, 61, 5, 28, 15, 8, 2, 46, 50, 14, 7, 33, 21, 16, 29, 17, 47, 51, 32, 31, 54, 43, 63, 12, 65, 42, 35, 30, 66, 20, 62, 57, 3}

Returns: 0
{0,3,6,7,9,8,10,11,5,4,13,14,12,15,2,1,17,18,20,21,19,22,24,25,26,23,16,29,32,33,31,30,35,36,37,34,38,40,41,39,42,45,44,43,46,49,52,51,50,53,56,55,54,48,47,58,60,59,62,61,65,64,63,67,68,69,66,57,28,27}

{2,5,6,8,9,7,10,11,12,13,14,4,3,15,16,19,21,20,18,17,23,24,25,26,22,1,0,28,31,32,33,34,35,37,36,30,29,39,40,41,38,44,45,46,43,42,48,51,52,53,50,49,55,56,54,57,60,61,62,59,58,64,65,66,68,67,69,63,47,27}

Returns: 13996800
{0,1,3,4,5,6,8,9,10,12,14,13,16,17,19,21,20,23,26,27,29,30,31,32,34,37,38,40,39,42,43,44,45,47,50,53,54,56,55,58,59,60,62,61,57,52,51,63,64,65,49,48,46,41,36,35,66,33,28,67,25,24,68,22,18,15,69,11,7,2}

{0,2,3,5,4,7,8,9,11,14,15,18,19,21,22,25,28,29,31,30,33,36,38,37,40,41,42,44,43,46,49,52,54,53,56,57,58,61,62,60,59,55,63,51,50,64,65,48,47,45,39,66,35,34,32,27,26,67,24,23,68,20,17,16,13,12,69,10,6,1}

Returns: 52488000
{0,3,4,6,9,10,8,7,12,13,14,11,5,17,18,19,16,15,21,24,23,22,26,29,30,28,27,31,32,33,25,34,20,35,38,39,40,41,37,36,42,45,46,48,49,50,47,51,44,43,53,54,56,55,57,52,2,1,59,60,61,62,58,65,66,64,63,68,69,67}

{2,5,6,8,9,10,11,12,13,14,7,4,3,16,17,18,19,20,23,24,25,28,29,30,27,26,31,33,32,22,21,34,15,37,40,39,38,41,42,36,35,44,47,48,49,50,46,45,51,52,53,55,56,54,57,43,58,59,61,60,62,1,0,64,65,66,67,68,69,63}

Returns: 94058496
{0,1,3,5,4,2}

{0,2,3,5,4,1}

Returns: 4

0 0 0 0 \ \ \ \ 1 1 1 1 \ \ \ \ 2 2 2 2 \ / \ / \ / 3 3 5 3 4 3 \ \ \ \ 4 4 5 4 / / 5 5
{0, 1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, 33, 34, 36, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 64, 66, 67, 69, 68, 65, 62, 59, 56, 53, 50, 47, 44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5, 2 }

{0, 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 67, 64, 61, 58, 55, 52, 49, 46, 43, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1 }

Returns: 10485760
{0, 3, 24, 38, 65, 17, 5, 47, 55, 18, 27, 40, 36, 30, 7, 6, 51, 67, 44, 4, 33, 8, 68, 20, 49, 50, 60, 43, 25, 52, 63, 64, 45, 46, 22, 58, 23, 53, 35, 11, 10, 14, 21, 37, 34, 13, 2, 1, 12, 41, 42, 26, 15, 56, 59, 57, 69, 31, 39, 16, 66, 61, 19, 54, 62, 48, 29, 32, 9, 28 }

{2, 17, 38, 24, 65, 18, 55, 47, 5, 3, 7, 40, 36, 27, 30, 44, 51, 67, 6, 33, 68, 8, 4, 11, 43, 50, 49, 60, 45, 63, 52, 64, 25, 20, 46, 58, 23, 22, 53, 35, 13, 14, 37, 34, 21, 10, 9, 26, 41, 42, 31, 59, 56, 69, 57, 15, 12, 39, 61, 66, 16, 48, 54, 62, 29, 19, 32, 1, 0, 28 }

Returns: 26244

Statistics

Problem Statement for "PreInPostOrder"

Problem Statement

Definition

Notes

Constraints

Examples