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Answers for “为什么每层的节点数是 2 的幂?”

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The number of nodes per level grows as a power of 2 because each recursive call splits into exactly two subcalls. Starting with 1 node at the root (level 1, 202^0), the second level has 2 nodes (212^1), the third has 4 nodes (222^2), and the fourth has 8 nodes (232^3).

Conditions: The recurrence relation is f(n)=f(n−1)+f(n−2)f(n) = f(n-1) + f(n-2), producing a binary tree.; Levels are numbered starting from 1.; The tree is counted as a full binary tree for theoretical estimation.