Suppose the values 10, −4, 15, 30, 20, 5, 60, 19 are inserted in that order into an initially empty binary search tree. Let \( T \) be the resulting binary search tree. The number of edges in the path from the node containing 19 to the root node of \( T \) is __________. (Answer in integer)
Suppose the values 10, −4, 15, 30, 20, 5, 60, 19 are inserted in that order into an initially empty binary search tree. Let \( T \) be the resulting binary search tree. The number of edges in the path from the node containing 19 to the root node of \( T \) is __________. (Answer in integer)
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Solution and Explanation
- 10 is the root.
- -4 goes to the left of 10.
- 15 goes to the right of 10.
- 30 goes to the right of 15.
- 20 goes to the left of 30.
- 5 goes to the right of -4.
- 60 goes to the right of 30.
- 19 goes to the left of 20.
\( 19 \to 20 \to 30 \to 15 \to 10 \) (4 edges). This path is traced by moving from node 19 up to the root, traversing through the parent nodes at each step until reaching 10.
Thus, the answer is 4 as there are 4 edges in this path.
Top Questions on Trees
Consider the following algorithm someAlgo that takes an undirected graph \( G \) as input.
someAlgo(G) Let \( v \) be any vertex in \( G \).
1. Run BFS on \( G \) starting at \( v \). Let \( u \) be a vertex in \( G \) at maximum distance from \( v \) as given by the BFS.
2. Run BFS on \( G \) again with \( u \) as the starting vertex. Let \( z \) be the vertex at maximum distance from \( u \) as given by the BFS. 3. Output the distance between \( u \) and \( z \) in \( G \).
The output of tt{someAlgo(T)} for the tree shown in the given figure is ____________ . (Answer in integer)
In a B+- tree where each node can hold at most four key values, a root to leaf path consists of the following nodes:
\( A = (49, 77, 83, -) \)
\( B = (7, 19, 33, 44) \)
\( C = (20^*, 22^*, 25^*, 26^*) \)
The *-marked keys signify that these are data entries in a leaf. Assume that a pointer between keys \( k_1 \) and \( k_2 \) points to a subtree containing keys in \([ k_1, k_2 )\), and that when a leaf is created, the smallest key in it is copied up into its parent. A record with key value 23 is inserted into the B+- tree. The smallest key value in the parent of the leaf that contains 25* is __________ . (Answer in integer)A meld operation on two instances of a data structure combines them into one single instance of the same data structure. Consider the following data structures:
P: Unsorted doubly linked list with pointers to the head node and tail node of the list.
Q: Min-heap implemented using an array.
R: Binary Search Tree.
Which ONE of the following options gives the worst-case time complexities for meld operation on instances of size \( n \) of these data structures?- Consider a binary tree \( T \) in which every node has either zero or two children. Let \( n%gt;0 \) be the number of nodes in \( T \). Which ONE of the following is the number of nodes in \( T \) that have exactly two children?
What is the output of the following C code?
void foo(int *p, int x) { *p = x; } void main() { int *z; int a = 20, b = 25; z = a; // Incorrect: Should be z = a; foo(z, b); printf("%d", a); }Issue: The statement
z = a;is invalid becauseais an integer, andzis a pointer.
Questions Asked in GATE CS exam
The unit interval \((0, 1)\) is divided at a point chosen uniformly distributed over \((0, 1)\) in \(\mathbb{R}\) into two disjoint subintervals. The expected length of the subinterval that contains 0.4 is ___________. (rounded off to two decimal places)
- GATE CS - 2025
- Calculus
A quadratic polynomial \( (x - \alpha)(x - \beta) \) over complex numbers is said to be square invariant if \[ (x - \alpha)(x - \beta) = (x - \alpha^2)(x - \beta^2). \] Suppose from the set of all square invariant quadratic polynomials we choose one at random. The probability that the roots of the chosen polynomial are equal is ___________. (rounded off to one decimal place)
- GATE CS - 2025
- Probability
Consider the following C program:
- GATE CS - 2025
- Programming in C
Consider the following C program:
The output of the above program is __________ . (Answer in integer)
- GATE CS - 2025
- Programming in C
An application executes \( 6.4 \times 10^8 \) number of instructions in 6.3 seconds. There are four types of instructions, the details of which are given in the table. The duration of a clock cycle in nanoseconds is ____________. (rounded off to one decimal place)
