## Akamai Interview Question

SDE-2s**Country:**India

**Interview Type:**Phone Interview

6

4 8

3 5 7 9

{3547986}

{LLILLII} // I dont find any use for this information , probably can be used for data verification

{0 - n-1}

top=n-1

constructBTree(post[n])

{

top=n-1;

root=post[top];

if(size(post) == 1)

return root;

if(z)

leftTop=top-1;

while(root < post[leftTop] && leftTop != 0)

leftTop--;

if(leftTop != 0)

root->left = constructBTree(post[0....leftTop-1]);

else

root->left = null;

if(leftTop < top-1)

root->right = constructBTree(post[leftTop....top-1]);

else

root->right = null;

}

If I am correct, we will be given a post order tree like below:

LLILLII or LLILLILLIII.

For this they have given a condition that a node can have 0 or 2 children compulsory.

Algo for constructing a BinaryTreeNode in Java Language :

```
BinaryTreeFromPostOrder(char[] A, int i){
if(A == null){
return null;
}
BinaryTreeNode new Node = new BinaryTreeNode();
newNode.setData(A[i]);
newNode.setLeft(null);
newNode.setRight(null);
if(A[i] == 'L'){
return newNode;
}
i = i - 1;
newNode.setRight(BuildTreeFromPostOrder(A,i));
i = i - 1;
newNode.setLeft(BuildTreeFromPostOrder(A,i));
return newNode;
}
```

Call this method with BinaryTreeFromPostOrder(A, A.length-1);

Let me know if I did any thing wrong or if I understood the question wrongly.

Thanks,

Ranjith

If you are give the postfix in an array in the form like

a[]={i,i,n,i,n,n} and another array that denotes the node like

b[]={2,3,4,5,6,7} then you can make the binary tree using recursion as:

```
tree *makeBinaryTree(char a[],int b[],int *index,int n)
{
int indx=*index;
if(indx==n)
return NULL;
tree *n=makeNewNode(a[indx]);
*index++;
if(b[indx]=='i')
{
n->left=makeBinaryTree(n,a,b,index);
n->right=makeBinaryTree(n,a,b,index);
}
return n;
}
```

hi vgeek it seems that makeBinaryTree() is missing one more parameter, i.e., the 1st parameter, seems tree* type.

this is wrong.

lets take an example L L i (L=leaf and i=intermediate node)

first it creates new node for arr[0] (L), next again arr[1] here it is not 'i', so it returns

```
if given array is post-order then start processing from end of the array and first insert right child and then left child
if given array is pre-order then start processing from start of the array and first insert left child and then right child
initially sz = length of array - 1 (for given post-order array)
void insert(node **root, char arr[], int &sz)
{
*root = new node;
(*root)->data = arr[sz];
(*root)->left = (*root)->right = NULL;
if(arr[sz] == 'i')
{
insert(&(*root)->right, arr, --sz);
insert(&(*root)->left, arr, --sz);
}
}
```

First of all let me clarify the question: my understanding is that the tree generated by *postorder* traversal is given by the "i"-"l" array (or what exactly does the post-fix mean here?). If this understanding is correct, the following is my solution.

First of all it is easy to see that the last element of the array is the root. Then the difficulty in the recursive call is to separate the left subtree from the right subtree. To do so note that any tree has (number of "i") == (number of "l") - 1, therefore we can scan from the 2nd from the last element backwards and count the number of "i" and "l", until we have the condition (number of "i") == (number of "l") - 1 satisfied, and this will be the right subtree, and the rest is the left subtree.

All right if it is a post-order solution then your approach seems to be correct. I also thought about the post-fix thing but then i made a mistake by just considering it to be a normal array of non leaf nodes followed by leaf nodes

@vgeek

Thanks for the reply, but two questions for you:

1) Could the word "post-fix" possibly mean something else here? I really don't know... I looked it up and it seems to me it is only used when representing an algebraic expression, so I assume it is the "post-order" that should be used here.

2) If I am correct, why do I get two "-1"? LOL

Steps: (Let p and q be start and end position in postorder array)

1. Since the last element is root. we need to create a node postorder[r];

2. q=(p+r)/2;

3. Left subtree (postorder[1...q-1])

4 Right subtree(postorder[q+1 ... r])

The mistake I did was while constructing the tree , I had forgotten create the node at base case. Now I have rectified it . Attaching my code.

```
void construct_tree_postorder(int *postorder,int p,int r,struct node** tree)
{
int x=postorder[r];
if(r<p)
return;
if(r==p) // base case only root
{
(*tree)=create_a_node(postorder[r]);
return;
}
else
{
int q = (p+r-1)/2;
(*tree)=create_a_node(postorder[r]);
construct_tree_postorder(postorder,q+1,r-1,&((*tree)->right));
construct_tree_postorder(postorder,p,q,&((*tree)->left));
return;
}
}
```

6

4 8

3 5 7 9

ps={3547986}

nodetye={LLILLII}

Algo for creating binary tree

- rohit mathur November 05, 2013