算法导论（CLRS, 2nd） 个人答案 Ch6.1

6.1 - 1:

Define n to be the number of elements in a heap of height h, then:



6.1-2:



6.1-3:

For any of the sub-tree of one max-heap, it maintains the basic heap property, i.e., A[parent(i)] >= A[i]. and the root of one sub-tree is the ancestor of all its nodes, therefore, the root is the largest by recurrence relation.

6.1-4:

The smallest element would be at the leaf of the heap, since its parent is larger that that heap.

6.1-5:

It's not. Example of a heap which is also a sorted array: 1, 2,3, 4,5,6,7

While Example which a heap is not: 1, 2,3, 6,5,4,7

6.1-6:



6.1-7:

(Proof by Mathematical Induction, it's also possible done by reasoning):