refer to: https://www.algoexpert.io/questions/Array%20Of%20Products
Problem Statement
Sample input
Analysis
approach 1: brute force, two full loops to iterate the array, for each current index, calculate the product except the current index value
code. time complexity: O(N^2). space complexity: O(N)
def arrayOfProducts(array): # Write your code here. product = [1 for i in range(len(array))] for i in range(len(array)): res = 1 for j in range(len(array)): if i != j: res *= array[j] product[i] = res return product
approach 2: calculate the leftProducts and the rightProducts seperately, then multiple the right and left element of the current index
code. time complexity: O(N). space complexity: O(N)
def arrayOfProducts(array): # Write your code here. left = [1 for i in range(len(array))] right = [1 for i in range(len(array))] res = [1 for i in range(len(array))] leftProduct = 1 rightProduct = 1 for i in range(len(array)): left[i] = leftProduct leftProduct *= array[i] for i in reversed(range(len(array))): right[i] = rightProduct rightProduct *= array[i] for i in range(len(array)): res[i] = right[i] * left[i] return res
approach 3: avoid store the extra leftProducts and rightProducts, only update the products array
code. time complexity: O(N). space complexity: O(N)
def arrayOfProducts(array): # Write your code here. product = [1 for i in range(len(array))] leftProduct = 1 rightProduct = 1 for i in range(len(array)): product[i] = leftProduct leftProduct *= array[i] for i in reversed(range(len(array))): product[i] *= rightProduct rightProduct *= array[i] return product