diff --git a/data_structures/stacks/next_greater_element.py b/data_structures/stacks/next_greater_element.py index 7d76d1f47..216850b4b 100644 --- a/data_structures/stacks/next_greater_element.py +++ b/data_structures/stacks/next_greater_element.py @@ -6,9 +6,20 @@ expect = [-5, 0, 5, 5.1, 11, 13, 21, -1, 4, -1, -10, -5, -1, 0, -1] def next_greatest_element_slow(arr: list[float]) -> list[float]: """ - Get the Next Greatest Element (NGE) for all elements in a list. - Maximum element present after the current one which is also greater than the - current one. + Get the Next Greatest Element (NGE) for each element in the array + by checking all subsequent elements to find the next greater one. + + This is a brute-force implementation, and it has a time complexity + of O(n^2), where n is the size of the array. + + Args: + arr: List of numbers for which the NGE is calculated. + + Returns: + List containing the next greatest elements. If no + greater element is found, -1 is placed in the result. + + Example: >>> next_greatest_element_slow(arr) == expect True """ @@ -28,9 +39,21 @@ def next_greatest_element_slow(arr: list[float]) -> list[float]: def next_greatest_element_fast(arr: list[float]) -> list[float]: """ - Like next_greatest_element_slow() but changes the loops to use - enumerate() instead of range(len()) for the outer loop and - for in a slice of arr for the inner loop. + Find the Next Greatest Element (NGE) for each element in the array + using a more readable approach. This implementation utilizes + enumerate() for the outer loop and slicing for the inner loop. + + While this improves readability over next_greatest_element_slow(), + it still has a time complexity of O(n^2). + + Args: + arr: List of numbers for which the NGE is calculated. + + Returns: + List containing the next greatest elements. If no + greater element is found, -1 is placed in the result. + + Example: >>> next_greatest_element_fast(arr) == expect True """ @@ -47,14 +70,23 @@ def next_greatest_element_fast(arr: list[float]) -> list[float]: def next_greatest_element(arr: list[float]) -> list[float]: """ - Get the Next Greatest Element (NGE) for all elements in a list. - Maximum element present after the current one which is also greater than the - current one. + Efficient solution to find the Next Greatest Element (NGE) for all elements + using a stack. The time complexity is reduced to O(n), making it suitable + for larger arrays. - A naive way to solve this is to take two loops and check for the next bigger - number but that will make the time complexity as O(n^2). The better way to solve - this would be to use a stack to keep track of maximum number giving a linear time - solution. + The stack keeps track of elements for which the next greater element hasn't + been found yet. By iterating through the array in reverse (from the last + element to the first), the stack is used to efficiently determine the next + greatest element for each element. + + Args: + arr: List of numbers for which the NGE is calculated. + + Returns: + List containing the next greatest elements. If no + greater element is found, -1 is placed in the result. + + Example: >>> next_greatest_element(arr) == expect True """