Improving notes on linear search algorithm.

Author: Clément

source/code/projects/LinearSearch/LinearSearch/Program.cs

@@ -0,0 +1,41 @@
+using System;
+
+class Program
+{
+    public static void Main()
+    {
+        // Example value
+        int[] arrayExample = { 1, 8, -12, 9, 10, 1, 30, 1, 32, 3 };
+
+        bool foundTarget = false;
+        int target = 8;
+
+        for (int i = 0; i < arrayExample.Length; i++)
+        {
+            if (arrayExample[i] == target) foundTarget = true;
+        }
+        Console.WriteLine(target + " is in the array: " + foundTarget + ".");
+
+
+        // We can optimize this algorithm
+        // by exiting when the target is found.
+
+        bool foundYet = false;
+        target = 30;
+        int index = 0;
+
+        do
+        {
+            if (arrayExample[index] == target) foundYet = true;
+            index++;
+        }
+        while (index < arrayExample.Length && !foundYet);
+        Console.WriteLine(target + " is in the array: " + foundYet +
+        "\nNumber of elements inspected: " + (index) + ".");
+
+        // This would display:
+        // 30 is in the array: True
+        // Number of elements inspected: 7.
+    }
+}
+

source/docs/programming_and_computer_usage/complexity.md

@@ -159,10 +159,23 @@ The reason why worst case is generally preferred is because:
 
 ### Linear search algorithm
 
-The [linear search algorithm](https://princomp.github.io/lectures/data/search#finding-a-particular-value) look for a particular value in an array. The version that exit exit prematurely the loop when the target value is found has the following complexity:
+The [linear search algorithm](https://princomp.github.io/lectures/data/search#finding-a-particular-value) look for a particular value in an array by inspecting the values one after the other:
+
+```{download="./code/projects/LinearSearch.zip"}
+!include`snippetStart="// Example value",snippetEnd="// We can optimize this algorithm"` code/projects/LinearSearch/LinearSearch/Program.cs
+```
+
+
+It can be slightly tuned, to exit as soon as the target value is found:
+
+```{download="./code/projects/LinearSearch.zip"}
+!include`snippetStart="// by exiting when the target is found.",snippetEnd="// This would display:"` code/projects/LinearSearch/LinearSearch/Program.cs
+```
+
+The version that exit exit prematurely the loop when the target value is found has the following complexity (in terms of "number of steps"):
 
 - The **best case** is if the target is the very first value, in this case, the time complexity is $O(c)$.
-- The **worst case** is if the target is the very last value, in this case the time complexity is $O(n)$ where $n$ is the size of the array.
+- The **worst case** is if the target is the very last value (or is not in the array), in this case the time complexity is $O(n)$ where $n$ is the size of the array.
 - The **average case** is $O(n)$.
 
 Note that the space usage of this algorithm is $O(c)$, it requires only one variable if we do not copy the array.

source/lectures/data/search.md

@@ -36,37 +36,16 @@ The simplest way to perform such a search is to
 #. Set the Boolean variable to `false`,
 #. Inspect the values in `arrayExample` one by one, comparing them to `target`, and setting the Boolean variable to `true` if they are identical.
 
-```
-int[] arrayExample = { 1, 8, -12, 9, 10, 1, 30, 1, 32, 3 };
 
-bool foundTarget = false;
-int target = 8;
-
-for (int i = 0; i < arrayExample.Length; i++)
-{
-    if (arrayExample[i] == target) foundTarget = true;
-}
-Console.WriteLine(target + " is in the array: " + foundTarget + ".");
+```{download="./code/projects/LinearSearch.zip"}
+!include`snippetStart="// Example value",snippetEnd="// We can optimize this algorithm"` code/projects/LinearSearch/LinearSearch/Program.cs
 ```
 
 Note that in the particular example above, we could have stopped exploring the array after the second index, since the target value was found.
 A slightly different logic would allow to exit prematurely the loop when the `target` value is found:
 
-```
-int[] arrayExample = { 1, 8, -12, 9, 10, 1, 30, 1, 32, 3 };
-
-bool foundYet = false;
-int target = 30;
-int index = 0;
-
-do
-{
-    if (arrayExample[index] == target) foundYet = true;
-    index++;
-}
-while (index < arrayExample.Length && !foundYet);
-Console.WriteLine(target + " is in the array: " + foundYet + 
-"\nNumber of elements inspected: " + (index) +".");
+```{download="./code/projects/LinearSearch.zip"}
+!include`snippetStart="// by exiting when the target is found.",snippetEnd="// This would display:"` code/projects/LinearSearch/LinearSearch/Program.cs
 ```
 
 This code would display: