6

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9

6.1

1

2

3

4

6.1 (con.t)(node)(edge)(ancestor)(descendant)(parent node)(children node)(sibling node)(terminal node)(leaf node)

6.1 (con.t)(degree)(level)(height)(depth)(forest)

6.2 (right subtree)(left subtree)ABAB

6.2 (con.t) 2/(left/right skewed tree)(a)(fully binary tree) (b)(complete binary tree) (c)

6.2 (con.t)

6.2 (con.t) i 2i-1i1()k2k-1k1n0n2 2 n0=n2+1Ex6.3

6.3 (c)

(c)(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)1234567891011121314151st level2nd level3rd level4th level

6.3 (con.t) (left link)(data)(right link)

6.4 (traversal)(inorder) (preorder) (postorder)

6.4 (con.t)(inorder) void inorder(Node type *tree){ if (tree != NULL){ inorder(tree->llink); printf("%d", tree->data); inorder(tree->rlink); }}

6.4 (con.t)(preorder) void preorder(Node type *tree){ if (tree != NULL){ printf("%d", tree->data); preorder(tree->llink); preorder(tree->rlink); } }

6.4 (con.t)(postorder)void postorder(Node type *tree){ if (tree != NULL){ postorder(tree->llink); postorder(tree->rlink); printf("%d", tree->data); } }

6.5 LINKn+1LINK(n)LINK(thread)LINK(head node)

6.5 (con.t) LINKLINK

6.5 (con.t)LBIT = 1LLINKLBIT = 0LLINKRBIT = 1RLINKRBIT = 0RLINK

6.5.1 (inorder successor)Node_type *insucc(Node_type *ptr){ Node_type *this_n; this_n = ptr->rlink; if (ptr->rbit == 1) while (this_n->lbit == 1) this_n = this_n->llink; return this_n;}

6.5.1 (con.t)void tinorder(Node_type *tree, Node_type *head){ tree = head; printf(%d, tree->data); for(;;){ tree = insuc(tree); if(tree == head) return; printf(%d,tree->data); } }

6.5.1 (con.t)(inorder predecessor)Node_type *pred(Node_type *ptr){ Node_type *this_n; this_n = ptr->llink; if(ptr->lbit == 1) while(this_n->rbit == 1) this_n = this_n->rlink; return this_n;}

6.5.2 void insert_right(Node_type *node_parent, Node_type *node){ Node_type *w; node->rchild = node_parent->rchild; node->rbit = node_parent->rbit; node->lchild = node_parent; node->lbit = 0; node_parent->rchild = node; node_parent->rbit = 1; if ( node->rbit == 1 ){ /*nodetree*/ w = insucc( node ); w->lchild = node; }} TS

6.5.2 (con.t)void insert_left(Node_type *node_parent, Node_type *node){ Node_type *w; node->lchild = node_parent->lchild; node->lbit = node_parent->lbit; node->rchild = node_parent; node->rbit = 0; node_parent->lchild = node; node_parent->lbit = 1; if ( node->lbit == 1 ){ /*node tree*/ w = inpred( node ); w->rchild = node; }} TS

6.5.3

6.5.3 (con.t)

prev1child = this1child;prev1bit = 0

6.5.3 (con.t) 4prev1child = this1child;prev1bit = 0

6.6 (binary search tree)(key value)

6.6.1 Ex

6.6.1 (con.t) 48

6.6.1 (con.t) 90

6.6.2 (Ex 50)

6.7 (Heap)()

6.7 (con.t) Heap Sort Heap()()

6.7 (con.t)

6.7 (con.t) n n/2 n/2()

6.7.1 Ex6-47

6.7.1 (con.t)Ex 50(Heap)

6.7.1 (con.t)

6.7.2 Ex

6.7.2 (con.t) 4010

6.7.3 Min-HeapHeapMax-heapMin-HeapMin-Max-HeapdeapMax-HeapMin-HeapMax-HeapEx

6.8 (Set)110S1={1, 3, 5, 7} S2={2, 4, 6} S3={8, 9,10}S1 S2 S3(disjoint set)S1 S2 S3S1 S2 S3

6.8.1

i p(i) i parent (p(i)-1parent)

i12345678 910p(i)3411343188

6.9 (forest)(1) (2) (3) 45Ex

6.9 (con.t)(1) (45)(2) (3) 45Ex(1)(1):

6.9 (con.t)(2)

(3)(3):(2):

6.9 (con.t)

6.9.2 Ex FDHGIBEAC ABDFGHIEC

6.9.2 (con.t)ACA

6.9.2 (con.t)BFDHGIEEB

6.9.2 (con.t)DFHGIFDHGID

6.9.2 (con.t)GHIHGIG