Let Tn satisfy the recurrence Tn aTnb fn where fn is a pol

Let T(n) satisfy the recurrence T(n) = aT(n/b) + f(n), where f(n) is a polynomial satisfying deg(f) > log_b (a). Prove that ease (3) of the Master Theorem applies, and in particular that the regularity condition necessarily holds.

Solution

#include #include #include #include #include using namespace std; // Determines if the string is a number bool isNumeric(string pszInput); int main () { // Hold the line in the file string line; // Open the file ifstream myfile (\"example.txt\"); if (myfile.is_open()) { // While the file is good while (myfile.good() ) { // Get the current line in the file getline (myfile, line); // Verify that the line is an integer if (isNumeric(line)) { // Convert \'line\' to an integer and calculate if (atoi(line.c_str())%2 == 0) { cout << \"Even\ \"; } else { cout << \"Odd\ \"; } } } myfile.close(); } else { cout << \"Unable to open file\ \"; } // Exit return 0;