a game to transform letters read from a file to a prime number. Do and enjoy it!
The goal of this is to construct a C++ program that will read all letters from a specified file and transform them to a prime number.
The tasks you have to perform are:
(A) Read letters in sequence from a specified file, which contains 1 sentence. Transform each letter to the corresponding ASCII value.
For example, if the file contains What? then
W corresponds to 87
h corresponds to 104
a corresponds to 97
t corresponds to 116
(B) Calculate and output r1=the sum of all obtained integers (e.g. r1=87+104+97+116=404)
(C) Calculate and output r2=the length of Syracuse sequence seeded by r1.
Let n be a positive integer and f(n) be the transformation that sends n to n/2 if n is even and sends n to 3n+1 if n is odd. Starting with a positive value u called the seed, the sequence of integers iteratively generated by f and u is called a Syracuse sequence.
For example, starting with the seed u = 1, the subsequent terms of the sequence are 4, 2, and 1. The length of the sequence (excluding the seed) is therefore 3.
For u = 4, the next terms are 2 and 1. The length is 2.
For u = 404, the next terms are 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, and 1. The length is 27.
It is conjectured (this means that we do not have a proof of this fact, only strong evidences) that for any positive seed the sequence will always reach to 1. In fact, computations show that for any seed u less than or equal to 3*2^53, the corresponding sequence always reaches 1. The general case is unknown.
(D) Calculate and output r3=the largest prime factor of r2.
A prime factor of n is a factor of n which is a prime number. A prime number is any integer greater than 1 and only divisible by itself and 1 (e.g. 2, 3, 5, 7, 11, 13, 17 etc). For example, 3 is the largest prime factor of 27 and 7 is the largest prime factor of 49.
Here are some example
Example 1
Enter the name of the input file: in1.txt
963
49
7
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