The goal here is to calculate the sum of squares of the first n natural numbers. The sum of squares is the result of adding up the squares of each number from 1 to n. For example, if n = 5, the sum of squares would be 1² + 2² + 3²+ 4²+5²=55. Let's explore different methods to compute this sum efficiently.

Using mathematical formula

This method uses mathematical formula to directly compute the sum of squares of the first n natural numbers. It is the most efficient and fastest approach since it avoids any iteration and performs the calculation in constant time.

n = 5
res = n * (n + 1) * (2 * n + 1) // 6
print(res)

55

Explanation: For n = 5, the expression becomes 5 * 6 * 11 // 6, which equals 330 // 6, giving the final result 55. The // operator performs integer division, ensuring the result is returned as a whole number without any decimal part.

Using generator expression

Generator expression inside the built-in sum() function to calculate the square of each number and sum them. It’s simple and memory-efficient because it doesn't store all the values in memory (unlike a list comprehension).

n = 5
res = sum(x * x for x in range(1, n + 1))
print(res) 

55

Explanation: Generator function generates the square of each number x in the range from 1 to n. For n = 5, it calculates 1² + 2² + 3² + 4² + 5², resulting in 55.

Using reduce

reduce() function from Python’s functools module applies a lambda function cumulatively to the items of the sequence, reducing them to a single value here, summing up the squares of numbers.

from functools import reduce

n = 5
res = reduce(lambda x, y: x + y * y, range(1, n + 1), 0)
print(res)

55

Explanation: reduce() applies the lambda x + y * y to the numbers from 1 to n, starting with 0. For n = 5, it calculates 0 + 1² + 2² + 3² + 4² + 5², resulting in 55. In each step, y is squared and added to the accumulated total x, effectively summing the squares.

Using for loop

This is the most traditional and beginner-friendly method. It uses a simple for loop to iterate from 1 to n, calculating the square of each number and adding it to the total.

n = 5
total = 0

for i in range(1, n + 1):
    total += i * i
print(total)

55

Explanation: For loop iterates over each number from 1 to n and for each number i, it calculates i * i and adds it to the running total. For n = 5, the loop calculates 1² + 2² + 3² + 4² + 5², resulting in 55.

Related Articles

• Generator expression
• reduce()
• for loop