Algorithm to Compute Squares of 1st N Natural Numbers Without Using Multiplication

TL;DR

This paper introduces an optimized algorithm to compute squares of the first N natural numbers using only addition, avoiding multiplication, which can be faster on certain processors.

Contribution

The paper presents a novel algorithm that computes squares without multiplication, improving efficiency on processors where addition is faster than multiplication.

Findings

Algorithm reduces computation time compared to traditional methods.

Can be used to efficiently compute sum of squares.

Demonstrates optimization in processor-specific operations.

Abstract

Processors may find some elementary operations to be faster than the others. Although an operation may be conceptually as simple as some other operation, the processing speeds of the two can vary. A clever programmer will always try to choose the faster instructions for the job. This paper presents an algorithm to display squares of 1st N natural numbers without using multiplication (* operator). Instead, the same work can be done using addition (+ operator). The results can also be used to compute the sum of those squares. If we compare the normal method of computing the squares of 1st N natural numbers with this method, we can conclude that the algorithm discussed in the paper is more optimized in terms of time complexity.