Question

1. A non-empty heap has n nodes. How many interior modes does it have?

2. A non-empty tree has n > 1 nodes. How many of them are interior nodes?

3. A non-empty heap has L leaves. How many nodes does it have?

Answer 1

1) It can vary, from 1 to (n-1).

• in case if there are only two elements in heap internal node will be only 1
• in case if there are n elements and they are like 1, 2, 3, 4, 5.. so on. Then heap will be similiar to a linear tree,  then number of internal node will be (n-1).  

2) Again it will vary and follow the same concept as part 1.

3) If a heap have L leaves then, it can have internal node between (L) to (n-1) as number of internal nodes. where n is total number of nodes in heap.