from __future__ import annotations arr = [-10, -5, 0, 5, 5.1, 11, 13, 21, 3, 4, -21, -10, -5, -1, 0] 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 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 """ result = [] arr_size = len(arr) for i in range(arr_size): next_element: float = -1 for j in range(i + 1, arr_size): if arr[i] < arr[j]: next_element = arr[j] break result.append(next_element) return result def next_greatest_element_fast(arr: list[float]) -> list[float]: """ 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 """ result = [] for i, outer in enumerate(arr): next_item: float = -1 for inner in arr[i + 1 :]: if outer < inner: next_item = inner break result.append(next_item) return result def next_greatest_element(arr: list[float]) -> list[float]: """ 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. 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 """ arr_size = len(arr) stack: list[float] = [] result: list[float] = [-1] * arr_size for index in reversed(range(arr_size)): if stack: while stack[-1] <= arr[index]: stack.pop() if not stack: break if stack: result[index] = stack[-1] stack.append(arr[index]) return result if __name__ == "__main__": from doctest import testmod from timeit import timeit testmod() print(next_greatest_element_slow(arr)) print(next_greatest_element_fast(arr)) print(next_greatest_element(arr)) setup = ( "from __main__ import arr, next_greatest_element_slow, " "next_greatest_element_fast, next_greatest_element" ) print( "next_greatest_element_slow():", timeit("next_greatest_element_slow(arr)", setup=setup), ) print( "next_greatest_element_fast():", timeit("next_greatest_element_fast(arr)", setup=setup), ) print( " next_greatest_element():", timeit("next_greatest_element(arr)", setup=setup), )