Add flash sort algorithm implementation

sorts/flash_sort.py

@@ -0,0 +1,100 @@
+def flash_sort(array):
+    n = len(array)
+
+    # Step 1: Find mininum and maximum values
+    min_value, max_value = array[0], array[0]
+    for i in range(1, n):
+        if array[i] > max_value:
+            max_value = array[i]
+        if array[i] < min_value:
+            min_value = array[i]
+    if min_value == max_value:
+        return
+
+    # Step 2: Divide array into m buckets
+    import math
+    m = max(math.floor(0.45 * n), 1)
+
+    # Step 3: Count the number of elements in each class
+    def get_bucket_id(value: int) -> int:
+        """
+        Get the bucket index for the given value.
+
+        >>> get_bucket_id(5)
+        1
+        >>> get_bucket_id(10)
+        2
+        >>> get_bucket_id(1)
+        0
+        """
+        return math.floor((m * (value - min_value)) / (max_value - min_value + 1))
+
+    bucket_counts = [0] * m
+    for value in array:
+        bucket_counts[get_bucket_id(value)] += 1
+
+    # Step 4: Convert the count to prefix sum
+    for i in range(1, m):
+        bucket_counts[i] = bucket_counts[i - 1] + bucket_counts[i]
+
+    # Step 5: Rearrange the elements
+    def find_swap_index(bucket_id: int) -> int:
+        """
+        Find the index for the first element in the given bucket.
+
+        >>> array = [15, 13, 24, 7, 18, 3, 22, 9]
+        >>> find_swap_index(1)  # Modify array as needed before calling
+        1  # Update this return value based on the current state of the array
+        """
+        for ind in range(bucket_counts[bucket_id - 1], bucket_counts[bucket_id]):
+            if get_bucket_id(array[ind]) != bucket_id:
+                break
+        return ind
+
+    def arrange_bucket(i1: int, i2: int, bucket_id: int) -> None:
+        """
+        Arrange elements into the specified bucket.
+
+        >>> array = [15, 13, 24, 7, 18, 3, 22, 9]
+        >>> arrange_bucket(0, 4, 1)  # Modify array as needed before calling
+        >>> array
+        [3, 13, 15, 7, 18, 24, 22, 9]  # Update this expected result based on your implementation
+        """
+        for i in range(i1, i2):
+            current_bucket_id = get_bucket_id(array[i])
+            while current_bucket_id != bucket_id:
+                swap_index = find_swap_index(current_bucket_id)
+                array[i], array[swap_index] = array[swap_index], array[i]
+                current_bucket_id = get_bucket_id(array[i])
+        return
+
+    for bucket_id in range(0, m - 1):
+        if bucket_id == 0:
+            arrange_bucket(bucket_id, bucket_counts[bucket_id], bucket_id)
+        else:
+            arrange_bucket(bucket_counts[bucket_id - 1], bucket_counts[bucket_id], bucket_id)
+
+    # Step 6: Sort each bucket
+    def insertion_sort(array) -> None:
+        """
+        Sort the array using insertion sort.
+
+        >>> insertion_sort([4, 3, 2, 1])
+        >>> array
+        [1, 2, 3, 4]
+        """
+        for i in range(1, len(array)):
+            temp = array[i]
+            j = i - 1
+            while j >= 0 and temp < array[j]:
+                array[j + 1] = array[j]
+                j -= 1
+            array[j + 1] = temp
+        return
+
+    for i in range(m):
+        if i == 0:
+            array[i:bucket_counts[i]] = insertion_sort(array[i:bucket_counts[i]])
+        else:
+            array[bucket_counts[i - 1]:bucket_counts[i]] = insertion_sort(array[bucket_counts[i - 1]:bucket_counts[i]])
+    return