17 Questions
In the context of algorithms analysis, what is the running time defined as?
The number of instructions executed before termination
Considering the induction steps for proof by induction, which step involves checking when k + 1 equals to (k + 1)?
The inductive step
How many memory locations are needed in the high-level example where x=y is executed?
2
In Example 1, if Sa is executed for i = 1 to n and then for j = 1 to n, how many times will Sa be executed?
$n^2$
In Example 2, considering the algorithm where Sa is executed while n > 1 and n=n/2, how many times will Sa be executed?
$\log n$
What does the order of growth in algorithm analysis primarily express?
The leading term of a formula that expresses function behavior towards infinity
What is the value of $\log_{10}2$?
3.3
If $n = 1,000,000$, what is the value of $100 * 10^6 * \log_{10}10^6$ in microseconds?
1.98 * $10^9$ µs
For what value of $n$ is $2^n > 100n^2$ for the first time?
16
If Algorithm B has a time complexity of $g(n) = 10^{12}$ µs, what is the ratio of $g(n)$ to $f(n)$ for $n = 1,000,000$?
5.05 * $10^3$
Based on the table, for what value of $n$ is $2^n \approx 100n^2$?
12
What is the value of $\log_2 128$?
7
What is the value of $\sum_{k=1}^{10} k$?
55
What is the value of $\sum_{i=1}^{8} (5i + 8i + 1)$?
896
Which of the following is a property of logarithms?
All of the above
What is the value of $1 + \sum_{k=1}^{49} k$?
6126
What is the value of $\sum_{i=1}^{10} (3i - 4)$?
115
This quiz covers the basics of logarithms, with examples and calculations involving log base 2. Topics include understanding logarithms, calculating log values, and applying logarithmic properties.
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