Binary tree, a high-frequency test site about digital computing

binary tree

1. The leaf node is equal to the number of branch nodes + 1, that ist0 =t₂ + 1

2. The i-th layer has at most 2^(i-1)one node

3. Height is n, contains at most 2ⁿ - 1nodes

4. The number of nodes is equal to the total degree plus one, namelyt = d + 1

Full binary tree:

1. has height n and contains 2ⁿ - 1 nodes
2. The sequence starts from 1, the left child of node i is 2i, the right child is 2i
   2i + 1, and the parent node isi/2

Complete binary tree:

top left fill up

1. The number of nodes is t
   t/2 rounded to a small integer, if
   i <= t/2is a branch node
   i >= t/2and is a leaf node

2. A complete binary tree of height n has at least 2^(n-1)one node and
   at most 2ⁿ - 1nodes

3. A complete binary tree has at most one node of degree 1,
   that is t₁ = 0, ort₁ = 1

    	若完全二叉树有偶数（2k）个节点，则必有
    	t0 = k, t₁ = 1, t₂ = k-1
    	若完全二叉树有奇数（2k-1）个节点，则必有
    	t0 = k, t₁ = 0, t₂ = k-1
   

4. Find the height of the complete binary tree n = ㏒₂(t+1), round up or
   round downn = ㏒₂t+1