Question:

Apply the master theorem on \(T(n) = 8T.(\frac{n}{2})+n^3\)

Updated On: Mar 16, 2024

O(n²)
O(n³)
\(O(n^3\,\,log_2n),\)
\(O(n\,\,\,log_2n),\)

Hide Solution

Verified By Collegedunia

The Correct Option is B

Solution and Explanation

The correct option is(B): O(n³)

Was this answer helpful?

Top Questions on Data Structures

Consider a hash table of size 10 with indices \( \{0, 1, \dots, 9\} \), with the hash function \[ h(x) = 3x \, (\text{mod} \, 10), \] where linear probing is used to handle collisions. The hash table is initially empty and then the following sequence of keys is inserted into the hash table: 1, 4, 5, 6, 14, 15. The indices where the keys 14 and 15 are stored are, respectively:
- GATE DA - 2025
- Computer Science
- Data Structures
View Solution

Consider the following pseudocode.

Create empty stack S
Set x = 0, flag = 0, sum = 0
Push x onto S
while (S is not empty){
    if (flag equals 0){
        Set x = x + 1
        Push x onto S
    }
    if (x equals 8):
        Set flag = 1
    if (flag equals 1){
        x = Pop(S)
        if (x is odd):
            Pop(S)
        Set sum = sum + x
    }
}
Output sum

The value of \( sum \) output by a program executing the above pseudocode is:

View Solution

Consider a directed graph \( G = (V,E) \), where \( V = \{0,1,2,\dots,100\} \) and
\[ E = \{(i,j) : 0 < j - i \leq 2, \text{ for all } i,j \in V \}. \] Suppose the adjacency list of each vertex is in decreasing order of vertex number, and depth-first search (DFS) is performed at vertex 0. The number of vertices that will be discovered after vertex 50 is:
- GATE DA - 2025
- Computer Science
- Data Structures
View Solution

Consider the following pseudocode.

Create empty stack S
Set x = 0, flag = 0, sum = 0
Push x onto S
while (S is not empty){
    if (flag equals 0){
        Set x = x + 1
        Push x onto S
    }
    if (x equals 8):
        Set flag = 1
    if (flag equals 1){
        x = Pop(S)
        if (x is odd):
            Pop(S)
        Set sum = sum + x
    }
}
Output sum

The value of \( sum \) output by a program executing the above pseudocode is:

View Solution

Consider a directed graph \( G = (V,E) \), where \( V = \{0,1,2,\dots,100\} \) and \[ E = \{(i,j) : 0<j - i \leq 2, \text{ for all } i,j \in V \}. \] Suppose the adjacency list of each vertex is in \textit{decreasing order of vertex number, and depth-first search (DFS) is performed at vertex 0. The number of vertices that will be discovered after vertex 50 is:}
- GATE DA - 2025
- Computer Science
- Data Structures
View Solution

View More Questions

Questions Asked in CUET PG exam

View More Questions