Question

Hi I have the following problem. Given a Tree I want to be able to check the number of its nodes that have values higher than that of their root and nodes above them. i.e. if a node has a value of 11 it will should increase the counter as long as it is higher (or equal) than root and all the nodes above it (so all values up to root have to be lower or equal to 11). How to best achieve that?

thank you

Answer 1

Do a breadth first tree traversal. At the end of each level add the node values (for that level only) in a hash table, which is used to make your counter comparisons.

                 2
            /        \
           1            3
         /    \       /    \
      11       12    4      5

Playout:

hashTable = {}

1. Visit all nodes on Lvl. 1
2. val = 2. Greater than root and all(hashTable)? Yes. Incr. counter. Add all to hashTable. Goto next lvl.

hashTable = {2}

1. val = 1. Greater than root and all(hashTable)? No. Visit neighbor
2. val = 3. Greater than root and all(hashTable)? Yes. Incr. counter. Add all to hashTable. Goto next lvl.

hashTable = {2, 1, 3}

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count = 6 nodes greater or equal to all the nodes above them.