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Questions and Answers
Which algorithm has the worst time complexity for computing 1+2+...+n?
Which algorithm has the worst time complexity for computing 1+2+...+n?
- Algorithm C (correct)
- Algorithm B
- Algorithm A
- The time complexity is the same for all algorithms
In Algorithm B, what is the purpose of the inner loop (for j = n to i)?
In Algorithm B, what is the purpose of the inner loop (for j = n to i)?
- To subtract 1 from sum
- To perform division operations
- To add 1 to sum (correct)
- To multiply i by n and add it to sum
Which algorithm provides a closed-form expression for the sum of 1 to n?
Which algorithm provides a closed-form expression for the sum of 1 to n?
- Algorithm B
- Algorithm A
- None of the algorithms
- Algorithm C (correct)
What is the purpose of the loop in Algorithm A that runs from 1 to n?
What is the purpose of the loop in Algorithm A that runs from 1 to n?
Which algorithm requires the least number of total operations to compute 1+2+...+n?
Which algorithm requires the least number of total operations to compute 1+2+...+n?
If n is the input size, what is the complexity of Algorithm B in terms of T(n)?
If n is the input size, what is the complexity of Algorithm B in terms of T(n)?
What is the definition of f(n) = Ω(g(n))?
What is the definition of f(n) = Ω(g(n))?
In Example 2, what is the value of c and n0 used to prove that T(n) = 3n + 2 is an element of Ω(n)?
In Example 2, what is the value of c and n0 used to prove that T(n) = 3n + 2 is an element of Ω(n)?
What is the relationship between the Θ(g(n)) and O(g(n)) notations?
What is the relationship between the Θ(g(n)) and O(g(n)) notations?
In Example 4, what is the value of c and n0 used to prove that T(n) = 10n^2 + 4n + 2 is an element of O(n^2)?
In Example 4, what is the value of c and n0 used to prove that T(n) = 10n^2 + 4n + 2 is an element of O(n^2)?
What is the purpose of the Ω(g(n)) notation?
What is the purpose of the Ω(g(n)) notation?
In Example 3, what are the values of c1, c2, and n0 used to prove that T(n) = 3n + 2 is an element of Θ(n)?
In Example 3, what are the values of c1, c2, and n0 used to prove that T(n) = 3n + 2 is an element of Θ(n)?
How do we prove that $T(n) = \Omega(n^2)$?
How do we prove that $T(n) = \Omega(n^2)$?
For the function $T(n) = 10n^2 + 4n + 2$, what values of $c$ and $n_0$ can be used to prove $T(n) = \Omega(n^2)$?
For the function $T(n) = 10n^2 + 4n + 2$, what values of $c$ and $n_0$ can be used to prove $T(n) = \Omega(n^2)$?
What is the Big-Oh time complexity of multiplying two arrays of size $n$?
What is the Big-Oh time complexity of multiplying two arrays of size $n$?
What is the best case time complexity of a function $f(n)$, denoted as $\Omega(g(n))$?
What is the best case time complexity of a function $f(n)$, denoted as $\Omega(g(n))$?
For the function $f(n) = 3n^2 + 20$, what values of $c$ and $n_0$ can be used to prove $f(n) = O(n^2)$?
For the function $f(n) = 3n^2 + 20$, what values of $c$ and $n_0$ can be used to prove $f(n) = O(n^2)$?
What is the time complexity of the function $T(n) = 2n + 3$?
What is the time complexity of the function $T(n) = 2n + 3$?
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