Data Structures Part 5

How do you convert a tree into an array? 

          

The conversion is based on these rules If i > 1, i/2 is the parent If 2*i > n, then there is no left child, else 2*i is the left child. If (2*i + 1) > n, then there is no right child, else (2*i + 1) is the  right child. Converting a tree to an array is very easy Suppose we have a tree like this A B C D E F G The array representation would be a[1] a[2] a[3] a[4] a[5] a[6] a[7] A B C D E F G That is, for every node at position i in the array, its left child  will be stored at position (2*i) and right child at (2*i + 1). The root starts at position 1. A full N-ary tree has M non-leaf nodes, how many leaf nodes does it have?  Use Geometric progression. M + (N ^ (n-1)) = (1 - (N ^ n)) / (1 - N) Here (N ^ (n-1)) is the number of leaf-nodes. Solving for this leads to the answer Leaf nodes = M * (N - 1) + 1 Suppose you have a 3-ary tree A B C D E F G H I J K L M So, here M=4 and N=3. So using the formula above, Leaf nodes = M * (N - 1) + 1 = 4 * (3 - 1) + 1 = 9