Properties of binary tree~

• It's not the second of an empty binary tree i layer , At most 2 ^i-1 Nodes （ i ≥1 ）

deduction ： There is a node in the first layer of a full binary tree , The root node , The second layer has two nodes , The third layer has four nodes , There are eight nodes on the fourth floor …
And so on , The first i layer , At most 2 ^i-1 Nodes

• At a height of h There are at most 2 ^h -1 Nodes （ h ≥1 ）

deduction ： Summation formula of equal ratio sequence ： First item x（1 - Gongbi ⁿ ）/（1 - Gongbi ）
And in the non empty binary tree , Gongbi = 2, First item = 1, and n Is the height of the binary tree （ Or depth ）
so： Total number of nodes = 1 x（1 - 2 ^h ）/（1 - 2）, After simplification ：2 ^h -1

• For any non empty binary tree , If the number of leaf nodes is n₀ , Degree is 2 The number of nodes of is n₂ , Then there are ：n₀ = n₂ + 1

deduction ： Suppose for a non empty binary tree , The number of leaf nodes is n₀, Degree is 1 The number of nodes of is n₁ , Degree is 2 The number of nodes of is n₂, be
Sum up points = n₀ + n₁ + n₂ , The total number of edges = n₁ + 2n₂
Each node corresponds to an edge , Except for the root node
so： Sum up points -1 = The total number of edges —> n₀ + n₁ + n₂ -1 = n₁ + 2n₂ —> n₀ = n₂ + 1