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Element pl-big-o-input: Input of asymptotic expressions

An example with constant complexity.

Submit $O(1)$.

$O($ $)$

$\Theta($ $)$

$\Omega($ $)$

$o($ $)$

$\omega($ $)$

An example with logarithmic complexity. Uses $m$ as the input variable.

Submit $O(\log m)$. We've set placeholder="expression in terms of m" to change the placeholder text.

$O($ $)$

$\Theta($ $)$

$\Omega($ $)$

$o($ $)$

$\omega($ $)$

An example with linear complexity.

Submit $O(n)$. Here, we've set display="block" to widen the input box. The attribute initial-value pre-fills the input with a starting expression when the question first renders.

$O($ $)$

$\Theta($ $)$

$\Omega($ $)$

$o($ $)$

$\omega($ $)$

An example with nearly linear complexity.

Submit $O(n \log^2 n)$. Here, we've set size="5" to shrink the input box and placeholder="" to hide the placeholder text.

$O($ $)$

$\Theta($ $)$

$\Omega($ $)$

$o($ $)$

$\omega($ $)$

An example with polynomial complexity.

Submit $O(n^2)$. Here we've set show-help-text="false" to hide the help popup.

$O($ $)$

$\Theta($ $)$

$\Omega($ $)$

$o($ $)$

$\omega($ $)$

An example with exponential complexity.

Submit $O(2^n)$. We set allow-blank="true" to allow blank inputs.

$O($ $)$

$\Theta($ $)$

$\Omega($ $)$

$o($ $)$

$\omega($ $)$

An example with only one expected answer.

Submit nothing (by leaving the inputs blank) except for the $\Omega(2^n)$. We set allow-blank="true" and blank-value="" to support blank answers without a placeholder value.

$O($ $)$

$\Theta($ $)$

$\Omega($ $)$

$o($ $)$

$\omega($ $)$

An example with factorial complexity.

Submit $O(n!)$. We set show-score="false" to hide the score badge.

$O($ $)$

$\Theta($ $)$

$\Omega($ $)$

$o($ $)$

$\omega($ $)$

Correct answer

An example with constant complexity.

$O(1)$

$\Theta(1)$

$\Omega(1)$

$o(1)$

$\omega(1)$

An example with logarithmic complexity. Uses $m$ as the input variable.

$O(\log{\left(m \right)})$

$\Theta(\log{\left(m \right)})$

$\Omega(\log{\left(m \right)})$

$o(\log{\left(m \right)})$

$\omega(\log{\left(m \right)})$

An example with linear complexity.

$O(n)$

$\Theta(n)$

$\Omega(n)$

$o(n)$

$\omega(n)$

An example with nearly linear complexity.

$O(n \log{\left(n \right)}^{2})$

$\Theta(n \log{\left(n \right)}^{2})$

$\Omega(n \log{\left(n \right)}^{2})$

$o(n \log{\left(n \right)}^{2})$

$\omega(n \log{\left(n \right)}^{2})$

An example with polynomial complexity.

$O(n^{2})$

$\Theta(n^{2})$

$\Omega(n^{2})$

$o(n^{2})$

$\omega(n^{2})$

An example with exponential complexity.

$O(2^{n})$

$\Theta(2^{n})$

$\Omega(2^{n})$

$o(2^{n})$

$\omega(2^{n})$

An example with only one expected answer.

$O(\mathtt{\text{}})$

$\Theta(\mathtt{\text{}})$

$\Omega(2^{n})$

$o(\mathtt{\text{}})$

$\omega(\mathtt{\text{}})$

An example with factorial complexity.

$O(n!)$

$\Theta(n!)$

$\Omega(n!)$

$o(n!)$

$\omega(n!)$

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Question

QID:

element/bigOInput

Title:

Element pl-big-o-input: Input of asymptotic expressions

Variant

Started at:

2026-08-04 23:38:39 (CDT)

Duration:

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{
  "m1": "1",
  "m2": "log(m)",
  "m3": "n",
  "m4": "n * (log(n)**2)",
  "m5": "n**2",
  "m6": "2**n",
  "m7": "n!",
  "q1": "1",
  "q2": "log(m)",
  "q3": "n",
  "q4": "n * (log(n)**2)",
  "q5": "n**2",
  "q6": "2**n",
  "q7": "n!",
  "r1": "1",
  "r2": "log(m)",
  "r3": "n",
  "r4": "n * (log(n)**2)",
  "r5": "n**2",
  "r6": "2**n",
  "r7": "n!",
  "s1": "1",
  "s2": "log(m)",
  "s3": "n",
  "s4": "n * (log(n)**2)",
  "s5": "n**2",
  "s6": "2**n",
  "s7": "n!",
  "t1": "1",
  "t2": "log(m)",
  "t3": "n",
  "t4": "n * (log(n)**2)",
  "t5": "n**2",
  "t6": "2**n",
  "t7": "n!",
  "m6_b": "",
  "q6_b": "",
  "r6_b": "",
  "s6_b": "",
  "t6_b": "2**n"
}

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