This article is part 5 of the series Level based Representation of a Binary Tree

So, your task is to write the load function. Can you think about how to do it?

Suppose, you are given an index and level based representation of a binary tree. can you tell, what is the index of its left child and what is the index of its right index?

Let's see some examples :

Node index | Left child index | Right child index |
---|---|---|

0 | 1 | 2 |

1 | 3 | 4 |

1 | 5 | 6 |

3 | 7 | 8 |

4 | 9 | 10 |

Do you see the pattern? It is easy to see:

Node index | Left child index | Right child index |
---|---|---|

k | 2*k+1 | 2*k+2 |

Now that we regonize the pattern, we can write:

```
def loadByIndex(data: List[Union[int, None]], kk: int):
# if the node does not exist in the list
if kk >= len(data):
return None
# find the value stored in current Node
value = data[kk]
# if the item is None, there is no node at this position
if value is None:
return None
# load the left child subtree
left = loadByIndex(data, kk * 2 + 1)
# load the right child subtree
right = loadByIndex(data, kk * 2 + 2)
# create the new tree
return Node(value, left, right)
```

So, using this function we can easily load the tree:

```
def load( data : List[Union[int,None]] ) -> Node :
return loadByIndex(data,0)
```

Now, let's see that it works

```
$ python -m unittest tests.load
.....
----------------------------------------------------------------------
Ran 5 tests in 0.002s
OK
```

Yes, we solved the first task. However, can we write a better code

We write a helper function that is used only in the load function, let's move this function as inner function of load

```
def load(data: List[Union[int, None]])
def loadByIndex(data: List[Union[int, None]], kk: int):
# if the node does not exist in the list
if kk >= len(data):
return None
# find the value stored in current Node
value = data[kk]
# if the item is None, there is no node at this position
if value is None:
return None
# load the left child subtree
left = loadByIndex(data, kk * 2 + 1)
# load the right child subtree
right = loadByIndex(data, kk * 2 + 2)
# create the new tree
return Node(value, left, right)
return loadByIndex(data,0)
```

It seems the code is verbose. Let's fix it. first, there is no need to move data to the function as it is available by defualt from the outer function.

```
def load(data: List[Union[int, None]]):
def loadByIndex(kk: int):
# if the node does not exist in the list
if kk >= len(data):
return None
# find the value stored in current Node
value = data[kk]
# if the item is None, there is no node at this position
if value is None:
return None
# load the left child subtree
left = loadByIndex(kk * 2 + 1)
# load the right child subtree
right = loadByIndex(kk * 2 + 2)
# create the new tree
return Node(value, left, right)
return loadByIndex(0)
```

Now, that we have tests, we can be confident in refactoring the code.

```
def load(data: List[Union[int, None]]):
def loadByIndex(kk: int):
# if the node does not exist in the list
if kk >= len(data) or data[kk] is None:
return None
# load Node, the left node located kk*2+1 and right node located at kk*2+2
return Node(data[kk], loadByIndex(kk * 2 + 1), loadByIndex(kk * 2 + 2) )
```

Let's run the unittest again, and check that new changes we made in the code still works

```
$ python -m unittest tests.load
.....
----------------------------------------------------------------------
Ran 5 tests in 0.002s
OK
```

Now, can you write the tests for the dump functions and implement it?