<> one , Multiple choice questions
1. In the following statements about binary trees , The correct thing is ( ).
A. Degree is 2 The ordered tree of is a binary tree
B. contain n The height of a binary tree with nodes is Llog2n┘+ 1
C. In a complete binary tree , If a node has no left child , Then it must be a leaf node
D. In any non empty binary sort tree , Delete a node and insert it again , The resulting binary sort tree is the same as the original binary sort tree before deletion
2. In the following statement , The correct thing is ( ).
A. In a complete binary tree , Left brother of leaf node's parents ( If present ) It must not be a leaf node
B. Any binary tree , The number of leaf nodes is degree 2 Number of nodes minus 1, Namely n0=n2- 1
C. Complete binary tree is not suitable for sequential storage structure , Only full binary tree is suitable for sequential storage structure
D. In a binary tree with nodes numbered by complete binary tree sequence , Section i The number of the left child of nodes is 2i
3. have 10 In a binary tree with leaf nodes ( ) Individual degree is 2 Node of .
A.8
B.9
C.10
D.11
4. Set the height to h Only the degree is 0 The sum degree is 2 Node of , Then the number of nodes contained in such binary tree must be at least ().
A. h
B.2h- 1
C.2h+ 1
D.h+1
5. Suppose the number of nodes of a binary tree is 50, Then its minimum height is ( ).
A. 4
B.5
C.6
D.7
6. Let the binary tree have 2n Nodes , And m<n, Cannot exist ( ) Node of .
A. n Individual degree is 0
B. 2m Individual degree is 0
C.2m Individual degree is 1
D. 2m Individual degree is 2
7. One with 1025 Height of binary tree with nodes h by ( ).
A.11
B.10
C.11 ~ 1025
D.10~ 1024
8. Let only the degree of a binary tree be 0 and 2 Node of , The number of nodes is 15, Then the maximum depth of the binary tree
by ().
A.4
B.5
C.8
D.9
9. Height is h The complete binary tree of has at least ( ) Nodes .
A.2^h
B. 2^h+1
C.2^(h-1)
D.2^h- 1
10. The second order of a complete binary tree 6 layer ( Set root as No 1 layer ) have 8 Leaf nodes , Then the nodes of the complete binary tree
The minimum number is ().
A.39
B.52
C.111
D.119
11. The second order of a complete binary tree 6 layer ( Set root as No 1 layer ) have 8 Leaf nodes , Then the
The maximum number of nodes of a complete binary tree is ( ).
A.39
B.52
C. 111
D. 119
12. If the depth of a tree is 6 The second order of a complete binary tree of 6 Layer has 3 Leaf nodes , Then the binary tree has ( )
Leaf nodes .
A.17
B.18
C.19
D.20
13. On a binary tree 1001 Nodes , The number of leaf nodes is ( ).
A.250
B.500
C.254
D.501
14. If a complete binary tree has 768 Nodes , Then the number of nodes in the binary tree is ( ).
A.257
B.258
C.384
D.385
15. If a binary tree has 126 Nodes , On page 7 layer ( Root node at 1 layer ) At most () Nodes .
A.32
B.64
C. 63
D. No no 7 layer
16. One tree has 124 Complete binary tree with leaf nodes , At most ( ) Nodes .
A.247
B.248
C.249
D.250
analysis ： In a non empty binary tree , From degree to 0 and 2 Relationship between the number of nodes of n0=n2+1 knowable n2=123; Total points n=no+n1+n2=247+n1, Its maximum value is 248 (n
The value of is 1 or 0, When n=1 Maximum time nodes ). Another solution : 124< 2^7=
128, Old home 8 The floor is not full , front 7 Layer is a complete binary tree , From this, it can be inferred that 8 Layer may have 120 Leaf nodes , Section 7 Rightmost of layer 4 Are leaf nodes , Most considered cases , this 4 The leftmost of the leaf nodes can have 1 Left child ( Do not change the number of leaf nodes ), Therefore, the total number of nodes =2^7-1
+ 120+ 1= 248.
17. One tree has n Binary tree with nodes uses binary chain to store nodes , The number of empty fingers is ( ).
A. n
B.n+1
C.n-1
D.2n
18. In a complete binary tree , The sequence number of its root is 1, ( ) It can be judged that the serial number is p and q Two knots of
Whether the points are on the same layer .
A. Llog2p」=Llog2q」
B. log2P = log2q
C. Llog2p」+ 1 =Llog2q」
D. Llog2p」=Llog2q」+ 1
19. Suppose the node number of a trident tree is 50, Then its minimum height is ( ).
A.3
B.4
C.5
D.6
20. One tree is known to have 2011 Tree of nodes , The number of leaf nodes is 116, The number of nodes without right children in the binary tree corresponding to the tree is ( ).
A.115
B. 116
C.1895
D. 1896
* For a full binary tree , share n Nodes and m Leaf nodes , Height is h, be ( ).
A. n=h+ m
B.n+m=2h.
C. m=h- 1
D. n=2h- 1
22. Suppose a non empty complete binary tree T All leaf nodes of are on the same layer , And each non leaf
All nodes have 2 Child node . if T have k Leaf nodes , be T The total number of nodes is ( ).
A.2k-1
B.2k
C. k^2
D.2^k-1
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