Initial commit.

Author: eldridgejm

.github/workflows/deploy-website.yaml

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+name: deploy website
+on:
+  push:
+    branches:
+      - main
+
+jobs:
+  deploy-website:
+    runs-on: ubuntu-latest
+    steps:
+        - uses: actions/checkout@v2
+
+        - uses: cachix/install-nix-action@v27
+          with:
+            github_access_token: ${{ secrets.GITHUB_TOKEN }}
+
+        - run: nix develop --command make
+
+        - name: Deploy
+          uses: peaceiris/actions-gh-pages@v4
+          with:
+            github_token: ${{ secrets.GITHUB_TOKEN }}
+            publish_dir: ./_build

.gitignore

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+_build
+.DS_Store

Makefile

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+.PHONY: html
+html:
+	practicebank build problems _build --template template.html
+	cp style.css _build/style.css

flake.lock

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+{
+  inputs.nixpkgs.url = github:NixOS/nixpkgs/nixos-23.05;
+
+  inputs.practicebank.url = github:eldridgejm/practicebank/0.1.5;
+  inputs.practicebank.inputs.nixpkgs.follows = "nixpkgs";
+
+  outputs = {
+    self,
+    nixpkgs,
+    practicebank,
+  }: let
+    supportedSystems = ["x86_64-linux" "x86_64-darwin" "aarch64-darwin"];
+    forAllSystems = f: nixpkgs.lib.genAttrs supportedSystems (system: f system);
+  in {
+    devShell = forAllSystems (
+      system: let
+        pkgs = nixpkgs.legacyPackages.${system};
+      in
+        pkgs.mkShell {
+          buildInputs = [
+            # python environment
+            (
+              pkgs.python3.withPackages (p: [
+                practicebank.defaultPackage.${system}
+              ])
+            )
+          ];
+        }
+    );
+  };
+}

flake.nix

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+def foo(n):
+    i = 0
+    while i < n**2:
+        i = i + 2
+        j = 0
+        while j < n:
+            for k in range(n):
+                print(i + j + k)
+            j = j + 10

problems/001/code.py

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+%% source: 2022-fa-redemption_midterm_01
+%% tags: [time complexity]
+\begin{prob}
+    What is the time complexity of the following function in terms of $n$?
+    State your answer using asymptotic notation (e.g., $\Theta(n)$).
+
+    \inputminted{python}{./code.py}
+
+    \begin{soln}
+        $\Theta(n^4)$
+    \end{soln}
+
+\end{prob}

problems/001/problem.tex

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+def foo(n):
+    for i in range(n**2):
+
+        for j in range(i):
+            print(i+j)
+
+        for k in range(n):
+            print(i+k)
+
+        for x in range(n - i):
+            print(x)

problems/002/code.py

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+%% source: 2022-fa-redemption_midterm_01
+%% tags: [time complexity]
+\begin{prob}
+    What is the time complexity of the following function in terms of $n$?
+
+    \inputminted{python}{./code.py}
+
+    \begin{soln}
+        $\Theta(n^4)$
+    \end{soln}
+
+\end{prob}

problems/002/problem.tex

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+from math import sqrt, log, ceil
+
+def foo(n):
+    for i in range(ceil(n**3 - 10*n + sqrt(n))):
+        for j in range(ceil(log(n**2))):
+            print(i, j)

problems/003/code.py

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+%% source: 2022-fa-redemption_midterm_01
+%% tags: [time complexity]
+\begin{prob}
+    What is the time complexity of the following function in terms of $n$?
+
+    \inputminted{python}{./code.py}
+
+    \begin{soln}
+        $\Theta(n^3 \log n)$
+    \end{soln}
+
+\end{prob}

problems/003/problem.tex

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+def foo(arr):
+    """`arr` is a list containing n numbers."""
+    for x in arr:
+        if x > max(arr) / 2:
+            print('large!')
+        elif x < min(arr) * 2:
+            print('small!')
+        else:
+            print('neither!')

problems/004/code.py

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+%% source: 2022-fa-redemption_midterm_01
+%% tags: [time complexity]
+\begin{prob}
+    What is the time complexity of the following function in terms of $n$?
+
+    \inputminted{python}{./code.py}
+
+    \begin{soln}
+        $\Theta(n^2)$
+    \end{soln}
+
+\end{prob}

problems/004/problem.tex

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+def foo(arr):
+    """`arr` is a list containing n numbers."""
+    previous = None
+    n = len(arr)
+    for x in arr:
+        if x == previous:
+            for i in range(n**2):
+                print('Equal!')
+            return
+        previous = x

problems/005/code.py

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+%% source: 2022-fa-redemption_midterm_01
+%% tags: [best and worst case]
+\begin{prob}
+    What is the \textbf{best case} time complexity of the following function in
+    terms of $n$?
+
+    \inputminted{python}{./code.py}
+
+    \begin{soln}
+        $\Theta(n)$
+    \end{soln}
+
+\end{prob}

problems/005/problem.tex

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+%% source: 2022-fa-redemption_midterm_01
+%% tags: [best and worst case]
+\begin{prob}
+    What is the \textbf{worst case} time complexity of the function in the previous problem?
+
+    \begin{soln}
+        $\Theta(n^2)$
+    \end{soln}
+
+\end{prob}

problems/006/problem.tex

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+%% source: 2022-fa-redemption_midterm_01
+%% tags: [theoretical lower bounds]
+\begin{prob}
+    Suppose you are given a (possibly unsorted) array containing $n$ elements.
+    Each element is either zero or one. You are tasked with determining if
+    the majority (at least half) of the array's elements are one.
+
+    What is the \textbf{tight} theoretical lower bound for the worst case time
+    complexity of this problem?
+
+    \begin{soln}
+        $\Theta(n)$
+    \end{soln}
+
+\end{prob}

problems/007/problem.tex

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+%% source: 2022-fa-redemption_midterm_01
+%% tags: [theoretical lower bounds, sorted structure]
+\begin{prob}
+
+    Consider the same problem as above, except now you may assume that the array
+    is \textbf{sorted}. What is the \textbf{tight} theoretical lower bound for the worst
+    case time complexity of any algorithm which solves this problem?
+
+    \begin{soln}
+        $\Theta(1)$
+    \end{soln}
+
+\end{prob}

problems/008/problem.tex

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+import random
+
+def foo(n):
+    # draw a random number uniformly from 0, 1, 2, ..., 99
+    # in constant time
+    x = random.randrange(100)
+    for i in range(x):
+        for j in range(n):
+            print("Here!")

problems/009/code.py

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+%% source: 2022-fa-redemption_midterm_01
+%% tags: [expected time]
+\begin{prob}
+    What is the \textbf{expected} time complexity of the function below?
+
+    \inputminted{python}{./code.py}
+
+    \begin{soln}
+        $\Theta(n)$
+    \end{soln}
+
+\end{prob}

problems/009/problem.tex

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+import random
+
+def foo(n):
+    # draw a number uniformly at random from 0, 1, 2, ..., n-1
+    # in constant time
+    x = random.randrange(n)
+    if x < 100:
+        for j in range(n**2):
+            print(j)

problems/010/code.py

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+%% source: 2022-fa-redemption_midterm_01
+%% tags: [expected time]
+\begin{prob}
+    What is the \textbf{expected} time complexity of the function below?
+
+    \inputminted{python}{./code.py}
+
+    \begin{soln}
+        $\Theta(n)$
+    \end{soln}
+
+\end{prob}

problems/010/problem.tex

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+def foo(arr, stop=None):
+    if stop is None:
+        stop = len(arr) - 1
+
+    if stop < 0:
+        return 1
+
+    last = arr[stop]
+    return last * foo(arr, stop - 1)

problems/011/code.py

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+%% source: 2022-fa-redemption_midterm_01
+%% tags: [recurrence relations]
+\begin{prob}
+    State (but do not solve) the recurrence describing the run time of the following code,
+    assuming that the input, \mintinline{python}{arr}, is a list of size $n$.
+
+    \inputminted{python}{./code.py}
+
+    \begin{soln}
+        $T(n) = T(n-1) + \Theta(1)$
+    \end{soln}
+
+\end{prob}