Algorithms Analysis and Design: Introduction to Logarithms
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Questions and Answers

In the context of algorithms analysis, what is the running time defined as?

  • The execution time of each individual instruction
  • The number of loops within the algorithm
  • The total memory space required for the algorithm
  • The number of instructions executed before termination (correct)
  • Considering the induction steps for proof by induction, which step involves checking when k + 1 equals to (k + 1)?

  • The summation step
  • The inductive step (correct)
  • The basis step
  • The hypothesis step
  • How many memory locations are needed in the high-level example where x=y is executed?

  • 2 (correct)
  • 1
  • 4
  • 3
  • 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?

    <p>$n^2$</p> Signup and view all the answers

    In Example 2, considering the algorithm where Sa is executed while n > 1 and n=n/2, how many times will Sa be executed?

    <p>$\log n$</p> Signup and view all the answers

    What does the order of growth in algorithm analysis primarily express?

    <p>The leading term of a formula that expresses function behavior towards infinity</p> Signup and view all the answers

    What is the value of $\log_{10}2$?

    <p>3.3</p> Signup and view all the answers

    If $n = 1,000,000$, what is the value of $100 * 10^6 * \log_{10}10^6$ in microseconds?

    <p>1.98 * $10^9$ µs</p> Signup and view all the answers

    For what value of $n$ is $2^n > 100n^2$ for the first time?

    <p>16</p> Signup and view all the answers

    If Algorithm B has a time complexity of $g(n) = 10^{12}$ µs, what is the ratio of $g(n)$ to $f(n)$ for $n = 1,000,000$?

    <p>5.05 * $10^3$</p> Signup and view all the answers

    Based on the table, for what value of $n$ is $2^n \approx 100n^2$?

    <p>12</p> Signup and view all the answers

    What is the value of $\log_2 128$?

    <p>7</p> Signup and view all the answers

    What is the value of $\sum_{k=1}^{10} k$?

    <p>55</p> Signup and view all the answers

    What is the value of $\sum_{i=1}^{8} (5i + 8i + 1)$?

    <p>896</p> Signup and view all the answers

    Which of the following is a property of logarithms?

    <p>All of the above</p> Signup and view all the answers

    What is the value of $1 + \sum_{k=1}^{49} k$?

    <p>6126</p> Signup and view all the answers

    What is the value of $\sum_{i=1}^{10} (3i - 4)$?

    <p>115</p> Signup and view all the answers

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