Add binary search implementation to find largest integer index

This commit introduces the `get_index` function, which uses binary search to identify the index of the largest integer in an array. It includes updates to the `ArrayReader` class and adds several unit tests to validate edge cases and standard scenarios. This ensures robustness and correctness of the implementation.

Author: nicholasadamou

Binary Search/Standard Search/find_the_index_of_the_larger_integer.py

@@ -19,7 +19,35 @@
 
 
 def get_index(reader: "ArrayReader") -> int:
-    pass
+    # Get the length of the array from the reader
+    n = reader.length()
+
+    # Initialize the left and right pointers for binary search
+    left, right = 0, n - 1
+
+    # Perform binary search to find the index
+    while left < right:
+        # Calculate the middle index
+        mid = (left + right) // 2
+
+        # Determine if the current subarray has an even number of elements
+        if (right - left + 1) % 2 == 0:
+            # Compare the two halves of the subarray
+            compare = reader.compareSub(left, mid, mid + 1, right)
+        else:
+            # Compare the two halves including the middle element in both halves
+            compare = reader.compareSub(left, mid, mid, right)
+
+        # If the left half is smaller, the element is in the right half
+        if compare < 0:
+            left = mid + 1
+            continue
+
+        # If the left half is larger or equal, the element is in the left half
+        right = mid
+
+    # Return the index of the element
+    return left
 
 
 class ArrayReader:
@@ -35,10 +63,10 @@ def compareSub(self, l: int, r: int, x: int, y: int) -> int:
         """
         Compares the sum of arr[l..r] with the sum of arr[x..y].
 
-        :param l: Start index of the first range
-        :param r: End index of the first range
-        :param x: Start index of the second range
-        :param y: End index of the second range
+        :param l: The start index of the first range
+        :param r: The end index of the first range
+        :param x: The start index of the second range
+        :param y: The end index of the second range
         :return:
             - 1 if sum(arr[l..r]) > sum(arr[x..y])
             - 0 if sum(arr[l..r]) == sum(arr[x..y])
@@ -61,3 +89,66 @@ def length(self) -> int:
         :return: Length of the array
         """
         return len(self.array)
+
+
+class TestGetIndex(unittest.TestCase):
+    def test_single_element(self):
+        array = [10]
+        reader = ArrayReader(array)
+        self.assertEqual(get_index(reader), 0)
+
+    def test_two_elements_first_large(self):
+        array = [20, 10]
+        reader = ArrayReader(array)
+        self.assertEqual(get_index(reader), 0)
+
+    def test_two_elements_second_large(self):
+        array = [10, 20]
+        reader = ArrayReader(array)
+        self.assertEqual(get_index(reader), 1)
+
+    def test_large_array_uniform_with_one_large(self):
+        array = [
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            46,
+            57,
+            46,
+            46,
+            46,
+            46,
+        ]
+        reader = ArrayReader(array)
+        self.assertEqual(get_index(reader), 20)
+
+    def test_large_array_middle_large(self):
+        array = [1, 1, 50, 1, 1]
+        reader = ArrayReader(array)
+        self.assertEqual(get_index(reader), 2)
+
+    def test_large_array_end_large(self):
+        array = [1, 1, 1, 1, 50]
+        reader = ArrayReader(array)
+        self.assertEqual(get_index(reader), 4)
+
+    def test_large_array_start_large(self):
+        array = [50, 1, 1, 1, 1]
+        reader = ArrayReader(array)
+        self.assertEqual(get_index(reader), 0)