In a Red-Black Tree, what must be true about the path from any node to its desce

Practice Questions

Q1
In a Red-Black Tree, what must be true about the path from any node to its descendant leaves?
  1. All paths must have the same number of black nodes
  2. All paths must have the same number of red nodes
  3. All paths must alternate colors
  4. All paths must have at least one red node

Questions & Step-by-Step Solutions

In a Red-Black Tree, what must be true about the path from any node to its descendant leaves?
  • Step 1: Understand what a Red-Black Tree is. It is a type of binary search tree with specific properties to keep it balanced.
  • Step 2: Know that each node in a Red-Black Tree can be either red or black.
  • Step 3: Learn that there are rules for how red and black nodes can be arranged in the tree.
  • Step 4: Focus on the paths from any node to its leaves (the end points of the tree).
  • Step 5: Realize that for any node, as you move down to its leaves, you count the number of black nodes you encounter.
  • Step 6: The important rule is that every path from a node to its leaves must have the same count of black nodes.
  • Step 7: This rule helps maintain the balance of the tree, ensuring that no path is significantly longer than another.
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