Time Complexity Reduction | Factorization
The Magic of Finding Factors Faster By The Code Shed Have you ever wanted to find all the factors of a number but dreaded the idea of iterating through every possible value? Today, we’ll explore an efficient trick rooted in mathematics and see how Python makes it even easier. The Secret: Square Root Simplifies Everything Factors of a number come in pairs . For example, if n = 36 n = 36 , the factor pairs are: ( 1 , 36 ) , ( 2 , 18 ) , ( 3 , 12 ) , ( 4 , 9 ) , ( 6 , 6 ) (1, 36), (2, 18), (3, 12), (4, 9), (6, 6) Notice something? The smaller factor in each pair is always less than or equal to n \sqrt{n} . This means you only need to check divisors up to n \sqrt{n} . For every factor i i you find, the corresponding factor n / i n/i is automatically included. Why It’s Efficient Instead of iterating from 1 1 to n n , you only loop up to n \sqrt{n} , significantly reducing the number of operations. Python Implementation Let’s put this theory into action with Python. Belo...