Binary Tree
Q2.
Consider the C function foo and the binary tree shown. typedef struct node { int val; struct node *left, *right; } node; int foo(node *p) { int retval; if (p == NULL) return 0; else { retval = p->val + foo(p->left) + foo(p->right); printf("%d ", retval); return retval; } } When foo is called with a pointer to the root node of the given binary tree, what will it print?Q3.
Consider a complete binary tree with 7 nodes. Let A denote the set of first 3 elements obtained by performing Breadth-First Search (BFS) starting from the root. Let B denote the set of first 3 elements obtained by performing Depth-First Search (DFS) starting from the root. The value of |A-B| is _____________Q4.
Let T be a full binary tree with 8 leaves. (A full binary tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) ___________ .Q5.
The postorder traversal of a binary tree is 8,9,6,7,4,5,2,3,1. The inorder traversal of the same tree is 8,6,9,4,7,2,5,1,3. The height of a tree is the length of the longest path from the root to any leaf. The height of the binary tree above is ______.Q6.
Which traversals of Tree-1 and Tree-2, respectively, will produce the same sequence?Q7.
If the post order traversal gives ab -cd * + then the label of the nodes 1,2,3.. will beQ8.
Consider the pseudocode given below. The function Dosomething () takes as argument a pointer to the root of an arbitrary tree represented by the leftMostChild-rightSibling representation. Each node of the tree is of type treeNode. typedef struct treeNode* treeptr; struct treeNode { treeptr leftMostChild, rightSibling; }; int DoSomething (treeptr tree) { int value=0; if (tree != NULL) { if (tree->leftMostChild == NULL) value = 1; else value = DoSomething(tree->leftMostChild); value = value + DoSomething(tree->rightSibling); } return(value); } When the pointer to the root of a tree is passed as the argument to DoSomething, the value returned by the function corresponds to theQ9.
In a binary tree with n nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree that have exactly one child?Q10.
A binary tree with n>1 nodes has n_{1}, n_{2} and n_{3} nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors. Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?