In a binary tree, how many edges are there if there are n nodes?

Practice Questions

Q1
In a binary tree, how many edges are there if there are n nodes?
  1. n-1
  2. n
  3. n+1
  4. 2n

Questions & Step-by-Step Solutions

In a binary tree, how many edges are there if there are n nodes?
  • Step 1: Understand what a binary tree is. A binary tree is a structure where each node can have at most two children.
  • Step 2: Know that a node is a point in the tree where data is stored.
  • Step 3: Realize that an edge is a connection between two nodes.
  • Step 4: In a binary tree, the first node (the root) does not have an edge connecting it to another node, but every other node does.
  • Step 5: If there are n nodes in the tree, then all nodes except the root (which is 1 node) must be connected by edges.
  • Step 6: Therefore, the number of edges is equal to the total number of nodes (n) minus 1 (the root node).
  • Step 7: Conclude that the formula for the number of edges in a binary tree is n - 1.
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