Prove that redblack trees are balanced by induction method.pdf
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The document proves that red-black trees are balanced through mathematical induction. It demonstrates that on any path from the root to an external node, at least half of the nodes are black. This implication is then used to establish that the longest path is less than twice the length of the shortest path.
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Prove that redblack trees are balanced by induction method.pdf
- 1. Prove that red-black trees are balanced by induction method. Let T be a red-black tree (a) Prove that on any path from the root to an external node in T, at least half of the nodes are black by (b) Use (a) to show that the longest path from the root to an external node is less than twice as long as the shortest path from the root to an external node.