Merge pull request #2 from esramish/problem-257-optimization

Added optimized solution for #257

Solutions/257.py

@@ -6,7 +6,8 @@
 [3, 7, 5, 6, 9], you should return (1, 3).
 """
 
-
+from time import perf_counter
+from random import randint
 from typing import List, Tuple
 
 
@@ -26,15 +27,70 @@ def get_sort_range(arr: List[int]) -> Tuple[int, int]:
     return start, end
 
 
+def get_sort_range_optimized(arr: List[int]) -> Tuple[int, int]:
+    # Find rightmost possible index of left bound
+    left = 0
+    while left < len(arr) - 1 and arr[left] < arr[left + 1]:
+        left += 1
+
+    # Check if sorted
+    if left == len(arr) - 1:
+        return -1, -1
+
+    # Find leftmost possible index of right bound
+    right = len(arr) - 1
+    while right > 0 and arr[right] > arr[right - 1]:
+        right -= 1
+
+    # Find the minimum and the maximum of the current window
+    i = left + 1
+    min_val = max_val = arr[left]
+    while i <= right:
+        if arr[i] < min_val:
+            min_val = arr[i]
+        if arr[i] > max_val:
+            max_val = arr[i]
+        i += 1
+
+    # Expand the window leftwards to include all elements greater than the min,
+    # so that everything remaining to the left is less than the smallest element to the right
+    while left > 0 and arr[left - 1] > min_val:
+        left -= 1
+
+    # Expand the window rightwards to include all elements less than the max,
+    # so that everything remaining to the right is greater than the largest element to the left
+    while right < len(arr) - 1 and arr[right + 1] < max_val:
+        right += 1
+
+    return left, right
+
+
+def print_both(arr: List[int]) -> None:
+    for f in [get_sort_range, get_sort_range_optimized]:
+        start = perf_counter()
+        result = f(arr)
+        end = perf_counter()
+        print(f"{result} ({end - start:.3} sec)")
+
+
 if __name__ == "__main__":
-    print(get_sort_range([3, 5, 6, 7, 9]))
-    print(get_sort_range([3, 7, 5, 6, 9]))
-    print(get_sort_range([5, 4, 3, 2, 1]))
+    print_both([3, 5, 6, 7, 9])
+    print_both([3, 7, 5, 6, 9])
+    print_both([5, 4, 3, 2, 1])
+    print_both([0, 1, 3, 4, 2, 7, 5, 6, 8, 9])
+    print_both(
+        [0] + list([randint(1, 10**7 - 1) for _ in range(10**7 - 1)]) + [10**7]
+    )  # Expecting (1, 9999999)
 
 
 """
 SPECS:
 
+get_sort_range:
 TIME COMPLEXITY: O(n x log(n))
 SPACE COMPLEXITY: O(n)
+
+get_sort_range_optimized:
+TIME COMPLEXITY: O(n)
+SPACE COMPLEXITY: O(1) (auxiliary)
 """