Add details on insertion sort.

notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json

@@ -75,8 +75,8 @@
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     "journal/2024-02-02.md": "e2acbe75752d9c39875553223e34fb0d",
     "bash/prompts.md": "64bd3cd3c2feb9edb68ad8dc5ba65a35",
-    "algorithms/sorting/index.md": "9aedfae96c9bb86fcba6afd2800538ae",
-    "algorithms/sorting/insertion-sort.md": "0bdccffe868d40986aa7d0d49da918f3",
+    "algorithms/sorting/index.md": "cd189e1a2cf32b5656b16aaf9f488874",
+    "algorithms/sorting/insertion-sort.md": "c78c9983f87cdc4198f82803d418967f",
     "algorithms/index.md": "1583c07edea4736db27c38fe2b6c4c31"
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notes/algorithms/sorting/index.md

@@ -11,6 +11,21 @@ tags:
 
 Let $n \geq 0$ and $S = \langle a_1, a_2, \ldots, a_n \rangle$ be a sequence. The **sorting problem** refers to permuting **keys** $a_1, a_2, \ldots, a_n$ into a new sequence $\langle a_1', a_2', \ldots, a_n' \rangle$ such that $a_1' \leq a_2' \leq \cdots \leq a_n'$.
 
+%%ANKI
+Basic
+What makes a sorting algorithm stable?
+Back: "Equal" values are ordered the same in the output as they are in the input.
+Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+<!--ID: 1706925787139-->
+END%%
+
+%%ANKI
+Basic
+What is an in place sorting algorithm?
+Back: One in which only a constant number of input values are ever stored outside the array.
+Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+<!--ID: 1706925787146-->
+END%%
 ## Structural Comparison
 
 The #Elixir documentation makes a point that there exist two types of comparisons between data types.[^structural] The first is **structural** in which comparisons are made on the underlying data structures used to describe the data types. The second is **semantic** which focuses on making the comparison with respect to what the data types represent.

notes/algorithms/sorting/insertion-sort.md

@@ -9,24 +9,85 @@ tags:
 
 ## Overview
 
-| Property      | Value      |
-| ------------- | ---------- |
-| Best Case     ||
-| Worst Case    ||
-| Average Case  ||
-| Memory        ||
-| In place      ||
-| Stable        ||
+| Property   | Value    |
+| ---------- | -------- |
+| Best Case  | $O(n)$   |
+| Worst Case | $O(n^2)$ |
+| Avg. Case  | $O(n^2)$ |
+| Memory     | $O(1)$   |
+| In place   | Yes      |
+| Stable     | Yes      |
 
-Insertion sort works by advancing an index `i` through an array `A[1..n]` such that `A[1..i]` is put into sorted order. Consider precondition `Q` and postcondition `R`:
+Insertion sort works by advancing an index `i` through an array `A[1..n]` such that `A[1..i]` is kept in sorted order.
 
-* `Q`: `i = 1`
-* `R`: `i = n` and `A[1..n]` is in sorted order
+%%ANKI
+Basic
+What is insertion sort's best case runtime?
+Back: $O(n)$
+Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+<!--ID: 1706925879541-->
+END%%
 
-Next establish loop invariant `P` and bounds function `t`:
+%%ANKI
+Basic
+What input value does insertion sort perform best on?
+Back: An already sorted array.
+Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+<!--ID: 1706925921544-->
+END%%
 
-* `P`: `1 \leq i \leq n` and `A[1..i]` is in sorted order
-* `t`: the number of inversions of `A[1..i]`
+%%ANKI
+Basic
+What is insertion sort's worst case runtime?
+Back: $O(n^2)$
+Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+<!--ID: 1706926586947-->
+END%%
+
+%%ANKI
+Basic
+What input value does insertion sort perform worst on?
+Back: An array in reverse-sorted order.
+Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+<!--ID: 1706926586951-->
+END%%
+
+%%ANKI
+Basic
+Is insertion sort in place?
+Back: Yes
+Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+<!--ID: 1706926586955-->
+END%%
+
+%%ANKI
+Basic
+Is insertion sort stable?
+Back: Yes
+Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+<!--ID: 1706926586959-->
+END%%
+
+```c
+void insertion_sort(const int n, int A[static n]) {
+  for (int i = 1; i < n; ++i) {
+	int key = A[i];
+	int j = i - 1;
+	for (; j >= 0 && A[j] > key; --j) {
+	  A[j + 1] = A[j];
+	}
+	A[j + 1] = key;
+  }
+}
+```
+
+%%ANKI
+Basic
+What loop invariant is maintained in insertion sort?
+Back: `A[1..i]` is in sorted order.
+Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+<!--ID: 1706927594718-->
+END%%
 
 ## Analogy
 
@@ -34,6 +95,22 @@ Suppose you have a shuffled deck of playing cards face-down on a table. Start by
 
 If you repeat this process for every card in the deck, your left hand will eventually contain the entire deck in sorted order.
 
+%%ANKI
+Basic
+What analogy does Cormen et al. use to explain insertion sort?
+Back: Sorting a shuffled deck of playing cards.
+Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+<!--ID: 1706927594729-->
+END%%
+
+%%ANKI
+Basic
+What invariant does the left hand maintain in Cormen et al.'s insertion sort analogy?
+Back: It contains all drawn cards in sorted order.
+Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+<!--ID: 1706927594732-->
+END%%
+
 ## References
 
-* Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).
+* Thomas H. Cormen et al., _Introduction to Algorithms_, 3rd ed (Cambridge, Mass: MIT Press, 2009).