What is the maximum number of elements in a binary heap of height h?
Practice Questions
Q1
What is the maximum number of elements in a binary heap of height h?
2^h
2^(h+1) - 1
h + 1
h^2
Questions & Step-by-Step Solutions
What is the maximum number of elements in a binary heap of height h?
Step 1: Understand what a binary heap is. A binary heap is a complete binary tree, which means all levels are fully filled except possibly for the last level.
Step 2: Know what height (h) means. The height of a binary heap is the number of edges on the longest path from the root to a leaf.
Step 3: Recognize that a complete binary tree of height h has all levels filled with nodes except possibly the last level.
Step 4: Calculate the number of nodes at each level. The number of nodes at level 0 (the root) is 1, at level 1 is 2, at level 2 is 4, and so on. This follows the pattern 2^0, 2^1, 2^2, ..., 2^h.
Step 5: Add up the number of nodes from level 0 to level h. This gives you 1 + 2 + 4 + ... + 2^h.
Step 6: Use the formula for the sum of a geometric series. The sum of the series 1 + 2 + 4 + ... + 2^h is equal to 2^(h+1) - 1.
Step 7: Conclude that the maximum number of elements in a binary heap of height h is 2^(h+1) - 1.
