Refactor Binary Search (#722)

* ref: refactor binary search
- Simplyfy implementation logic
- Add docstring
- Rewrite tests using macro

* ref: eliminate nested match statements

* ref(tests): add suggested tests

---------

Co-authored-by: Piotr Idzik <[email protected]>

Author: sozelfist

src/searching/binary_search.rs

@@ -1,106 +1,153 @@
+//! This module provides an implementation of a binary search algorithm that
+//! works for both ascending and descending ordered arrays. The binary search
+//! function returns the index of the target element if it is found, or `None`
+//! if the target is not present in the array.
+
 use std::cmp::Ordering;
 
+/// Performs a binary search for a specified item within a sorted array.
+///
+/// This function can handle both ascending and descending ordered arrays. It
+/// takes a reference to the item to search for and a slice of the array. If
+/// the item is found, it returns the index of the item within the array. If
+/// the item is not found, it returns `None`.
+///
+/// # Parameters
+///
+/// - `item`: A reference to the item to search for.
+/// - `arr`: A slice of the sorted array in which to search.
+///
+/// # Returns
+///
+/// An `Option<usize>` which is:
+/// - `Some(index)` if the item is found at the given index.
+/// - `None` if the item is not found in the array.
 pub fn binary_search<T: Ord>(item: &T, arr: &[T]) -> Option<usize> {
-    let mut is_asc = true;
-    if arr.len() > 1 {
-        is_asc = arr[0] < arr[arr.len() - 1];
-    }
+    let is_asc = is_asc_arr(arr);
+
     let mut left = 0;
     let mut right = arr.len();
 
     while left < right {
-        let mid = left + (right - left) / 2;
-
-        if is_asc {
-            match item.cmp(&arr[mid]) {
-                Ordering::Less => right = mid,
-                Ordering::Equal => return Some(mid),
-                Ordering::Greater => left = mid + 1,
-            }
-        } else {
-            match item.cmp(&arr[mid]) {
-                Ordering::Less => left = mid + 1,
-                Ordering::Equal => return Some(mid),
-                Ordering::Greater => right = mid,
-            }
+        if match_compare(item, arr, &mut left, &mut right, is_asc) {
+            return Some(left);
         }
     }
+
     None
 }
 
-#[cfg(test)]
-mod tests {
-    use super::*;
-
-    #[test]
-    fn empty() {
-        let index = binary_search(&"a", &[]);
-        assert_eq!(index, None);
-    }
-
-    #[test]
-    fn one_item() {
-        let index = binary_search(&"a", &["a"]);
-        assert_eq!(index, Some(0));
-    }
-
-    #[test]
-    fn search_strings_asc() {
-        let index = binary_search(&"a", &["a", "b", "c", "d", "google", "zoo"]);
-        assert_eq!(index, Some(0));
-
-        let index = binary_search(&"google", &["a", "b", "c", "d", "google", "zoo"]);
-        assert_eq!(index, Some(4));
-    }
-
-    #[test]
-    fn search_strings_desc() {
-        let index = binary_search(&"a", &["zoo", "google", "d", "c", "b", "a"]);
-        assert_eq!(index, Some(5));
-
-        let index = binary_search(&"zoo", &["zoo", "google", "d", "c", "b", "a"]);
-        assert_eq!(index, Some(0));
-
-        let index = binary_search(&"google", &["zoo", "google", "d", "c", "b", "a"]);
-        assert_eq!(index, Some(1));
-    }
-
-    #[test]
-    fn search_ints_asc() {
-        let index = binary_search(&4, &[1, 2, 3, 4]);
-        assert_eq!(index, Some(3));
-
-        let index = binary_search(&3, &[1, 2, 3, 4]);
-        assert_eq!(index, Some(2));
-
-        let index = binary_search(&2, &[1, 2, 3, 4]);
-        assert_eq!(index, Some(1));
-
-        let index = binary_search(&1, &[1, 2, 3, 4]);
-        assert_eq!(index, Some(0));
+/// Compares the item with the middle element of the current search range and
+/// updates the search bounds accordingly. This function handles both ascending
+/// and descending ordered arrays. It calculates the middle index of the
+/// current search range and compares the item with the element at
+/// this index. It then updates the search bounds (`left` and `right`) based on
+/// the result of this comparison. If the item is found, it updates `left` to
+/// the index of the found item and returns `true`.
+///
+/// # Parameters
+///
+/// - `item`: A reference to the item to search for.
+/// - `arr`: A slice of the array in which to search.
+/// - `left`: A mutable reference to the left bound of the search range.
+/// - `right`: A mutable reference to the right bound of the search range.
+/// - `is_asc`: A boolean indicating whether the array is sorted in ascending order.
+///
+/// # Returns
+///
+/// A `bool` indicating whether the item was found.
+fn match_compare<T: Ord>(
+    item: &T,
+    arr: &[T],
+    left: &mut usize,
+    right: &mut usize,
+    is_asc: bool,
+) -> bool {
+    let mid = *left + (*right - *left) / 2;
+    let cmp_result = item.cmp(&arr[mid]);
+
+    match (is_asc, cmp_result) {
+        (true, Ordering::Less) | (false, Ordering::Greater) => {
+            *right = mid;
+        }
+        (true, Ordering::Greater) | (false, Ordering::Less) => {
+            *left = mid + 1;
+        }
+        (_, Ordering::Equal) => {
+            *left = mid;
+            return true;
+        }
     }
 
-    #[test]
-    fn search_ints_desc() {
-        let index = binary_search(&4, &[4, 3, 2, 1]);
-        assert_eq!(index, Some(0));
+    false
+}
 
-        let index = binary_search(&3, &[4, 3, 2, 1]);
-        assert_eq!(index, Some(1));
+/// Determines if the given array is sorted in ascending order.
+///
+/// This helper function checks if the first element of the array is less than the
+/// last element, indicating an ascending order. It returns `false` if the array
+/// has fewer than two elements.
+///
+/// # Parameters
+///
+/// - `arr`: A slice of the array to check.
+///
+/// # Returns
+///
+/// A `bool` indicating whether the array is sorted in ascending order.
+fn is_asc_arr<T: Ord>(arr: &[T]) -> bool {
+    arr.len() > 1 && arr[0] < arr[arr.len() - 1]
+}
 
-        let index = binary_search(&2, &[4, 3, 2, 1]);
-        assert_eq!(index, Some(2));
+#[cfg(test)]
+mod tests {
+    use super::*;
 
-        let index = binary_search(&1, &[4, 3, 2, 1]);
-        assert_eq!(index, Some(3));
+    macro_rules! test_cases {
+        ($($name:ident: $test_case:expr,)*) => {
+            $(
+                #[test]
+                fn $name() {
+                    let (item, arr, expected) = $test_case;
+                    assert_eq!(binary_search(&item, arr), expected);
+                }
+            )*
+        };
     }
 
-    #[test]
-    fn not_found() {
-        let index = binary_search(&5, &[1, 2, 3, 4]);
-        assert_eq!(index, None);
-
-        let index = binary_search(&5, &[4, 3, 2, 1]);
-        assert_eq!(index, None);
+    test_cases! {
+        empty: ("a", &[] as &[&str], None),
+        one_item_found: ("a", &["a"], Some(0)),
+        one_item_not_found: ("b", &["a"], None),
+        search_strings_asc_start: ("a", &["a", "b", "c", "d", "google", "zoo"], Some(0)),
+        search_strings_asc_middle: ("google", &["a", "b", "c", "d", "google", "zoo"], Some(4)),
+        search_strings_asc_last: ("zoo", &["a", "b", "c", "d", "google", "zoo"], Some(5)),
+        search_strings_asc_not_found: ("x", &["a", "b", "c", "d", "google", "zoo"], None),
+        search_strings_desc_start: ("zoo", &["zoo", "google", "d", "c", "b", "a"], Some(0)),
+        search_strings_desc_middle: ("google", &["zoo", "google", "d", "c", "b", "a"], Some(1)),
+        search_strings_desc_last: ("a", &["zoo", "google", "d", "c", "b", "a"], Some(5)),
+        search_strings_desc_not_found: ("x", &["zoo", "google", "d", "c", "b", "a"], None),
+        search_ints_asc_start: (1, &[1, 2, 3, 4], Some(0)),
+        search_ints_asc_middle: (3, &[1, 2, 3, 4], Some(2)),
+        search_ints_asc_end: (4, &[1, 2, 3, 4], Some(3)),
+        search_ints_asc_not_found: (5, &[1, 2, 3, 4], None),
+        search_ints_desc_start: (4, &[4, 3, 2, 1], Some(0)),
+        search_ints_desc_middle: (3, &[4, 3, 2, 1], Some(1)),
+        search_ints_desc_end: (1, &[4, 3, 2, 1], Some(3)),
+        search_ints_desc_not_found: (5, &[4, 3, 2, 1], None),
+        with_gaps_0: (0, &[1, 3, 8, 11], None),
+        with_gaps_1: (1, &[1, 3, 8, 11], Some(0)),
+        with_gaps_2: (2, &[1, 3, 8, 11], None),
+        with_gaps_3: (3, &[1, 3, 8, 11], Some(1)),
+        with_gaps_4: (4, &[1, 3, 8, 10], None),
+        with_gaps_5: (5, &[1, 3, 8, 10], None),
+        with_gaps_6: (6, &[1, 3, 8, 10], None),
+        with_gaps_7: (7, &[1, 3, 8, 11], None),
+        with_gaps_8: (8, &[1, 3, 8, 11], Some(2)),
+        with_gaps_9: (9, &[1, 3, 8, 11], None),
+        with_gaps_10: (10, &[1, 3, 8, 11], None),
+        with_gaps_11: (11, &[1, 3, 8, 11], Some(3)),
+        with_gaps_12: (12, &[1, 3, 8, 11], None),
+        with_gaps_13: (13, &[1, 3, 8, 11], None),
     }
 }