[SOLVED] 02393 Assignment 2-Basics

Assignment 2

In the following exercises, you will have to compute a function with an input parameter that you should read from cin. The result is to be provided on cout.

Gaussian Sum. Write a program that computes the sum 1 + 2 + . . . + n for a given positive integer n. For example, for n = 100, the result is 5050.

Another sum. Write a program that computes the sum of all even integers between 0 and n. For instance, for n = 6, the result is 0 + 2 + 4 + 6 = 12.

Prime Factorization. Write a program that computes the prime factorization of a given posi- tive integer. For instance, the factorization of 60 is 2 ∗ 2 ∗ 3 ∗ 5.

Hints:

• In C++, the modulus function % gives the remainder of integer division, i.e., x is divisible

  by y if and only if x%y == 0.

• Given the number n to factorize, iterate through all the numbers i = 2, 3, 4, 5, . . . and check whether i divides n. If so, print out “i ∗ ” and continue to check the factorization of n/i. Stop when n cannot be further factorised.

  In order to check with CodeJudge, please ensure that (i) the factors are printed in ascending order, (ii) between two factors print a space, an asterisk (∗), and another space, (iii) and at the end there is a newline (see example above).

  Approximating π. Compute an approximation of π using Leibniz’ formula: π 􏰄∞ (−1)i 1 1 1 1 1

  4 =

  To that end write a function with header double pi(int n) that computes the first n terms of the infinite summation (and then multiplies by 4). For instance for n = 1 we get the bad approximation 4, and with increasing n, the approximation gets better.

i=0

2i + 1 = 1 − 3 + 5 − 7 + 9 − 11 + . . .