The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, … By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form …
A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before. For example, 44 → 32 → 13 → 10 → 1 → 1 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 …
This program generates 25 polynomials of increasing degree randomly using a Mersenne twister, solves them via Horner’s rule and records runtime. /////////////////////////////////////////////////////////////////////////////// #include <iostream> #include <vector> #include <random> #include <iomanip> #include <chrono> /////////////////////////////////////////////////////////////////////////////// std::vector<int> randIntGen(int count); float randRealGen(void); void polyPrint(float x, std::vector<int> polyVals); void hornersRuleTime(float x, int n, std::vector<int> polyVals); …
/////////////////////////////////////////////////////////////////////////////// // This program takes a RSA encrypted message in a text file, // by given parameters, and decrypts it. After which it outputs to console. /////////////////////////////////////////////////////////////////////////////// #include <iostream> #include <fstream> #include <sstream> #include <vector> #include <math.h> /////////////////////////////////////////////////////////////////////////////// void fileRead(std::ifstream &inFile, std::vector &fileBuff); void decrypt(std::vector<int> cipherText, std::vector<char> &plaintText, int pq, …
This program takes an input WAM, and applies Kruskal’s and Prim’s algorithms to it. /////////////////////////////////////////////////////////////////////////////// #include <iostream> #include <vector> #include <sstream> /////////////////////////////////////////////////////////////////////////////// struct Edge { int vertOne, vertTwo, weight; Edge(int one, int two, int passedWeight) { this->vertOne = one; this->vertTwo = two; this->weight = passedWeight; } }; class Vertex { …
Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420. We shall call a positive integer …
An irrational decimal fraction is created by concatenating the positive integers: 0.123456789101112131415161718192021… It can be seen that the 12th digit of the fractional part is 1. If dn represents the nth digit of the fractional part, find the value of the following expression. d1 × d10 × d100 × d1000 …
Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits: 1634 = 14 + 64 + 34 + 44 8208 = 84 + 24 + 04 + 84 9474 = 94 + 44 + 74 + 44 As 1 = 14 is not a sum it is not included. The sum …
This program generates the intersection, union, relative composition, cross product, and power set, of given input (which generates the sets the operations are performed on. ///////////////////////////////////////////////////////////////////////////////// #include <iostream> #include <vector> #include <algorithm> #include <iterator> #include <sstream> //////////////////////////////////////////////////////////////////////////////// std::vector<std::string> createSet(void); // creates set from user input std::vector<std::string> getIntersection(std::vector<std::string> set_A, std::vector<std::string> set_B); …
//////////////////////////////////////////////////////////////////////////////// #include <iostream> #include <math> //////////////////////////////////////////////////////////////////////////////// void numberQuery(unsigned long long &a, unsigned long long &n, unsigned long long &m); unsigned long long powertworesidual(unsigned long long a, unsigned long long n, unsigned long long m); unsigned long long nonpowertworesidual(unsigned long long a, unsigned long long n, unsigned long long m); //////////////////////////////////////////////////////////////////////////////// …