This is study resource 6 for the 24-week cohort during the summer of 2019. There are 5 questions in it.
Do not just copy and paste the answers, you must understand the content in order to do well in the NYU Bridge To Tandon program. Good luck!.
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Question #1
The Fibonacci numbers sequence, Fn, is defined as follows: F1 is 1, F2 is 1, and Fn = Fn-1 + Fn-2 for n = 3, 4, 5, … In other words, each number is the sum of the previous two numbers. The first 10 numbers in Fibonacci sequence are: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 Note: Background of Fibonacci sequence: https://en.wikipedia.org/wiki/Fibonacci_number
1. Write a function int fib(int n) that returns the n-th element of the Fibonacci
sequence.
2. Write a program that prompts the user to enter a positive integer num, and then
prints the numโs elements in the Fibonacci sequence.
Your program should interact with the user exactly as it shows in the following
example:
Please enter a positive integer: 7 13
#include <iostream>
using namespace std;
int fib(int n);
int main() {
int numEntered, fibonacciElement;
cout << "Please enter a positive integer: ";
cin >> numEntered;
fibonacciElement = fib(numEntered);
cout << fibonacciElement;
return 0;
}
int fib(int n){
if ( n == 0 ){
return 0;
}
if (n < 3){
return 1;
}
//Since position F1 = F2 = 1, then prevVal1 & 2 are default to 1
int positionVal1 = 1, positionVal2 = 1, currentValue = 0;
for(int position = 3; position <= n; position++){
currentValue = positionVal1 + positionVal2;
positionVal1 = positionVal2;
positionVal2 = currentValue;
}
return currentValue;
}
Question #2
Write a program that, prints a โpine treeโ consisting of triangles of increasing sizes, filled with a character (eg. โ*โ or โ+โ or โ$โ etc). Your program should interact with the user to read the number of triangles in the tree and the character filling the tree.
Your implementation should include the following functions:
a. void printShiftedTriangle(int n, int m, char symbol)
It prints an n-line triangle, filled with symbol characters, shifted m spaces from the left margin.
b. void printPineTree(int n, char symbol)
It prints a sequence of n triangles of increasing sizes (the smallest triangle is a 2-line triangle), which forms the shape of a pine tree. The triangles are filled with the symbol character.
#include <iostream>
using namespace std;
void printShiftedTriangle (int n, int m, char symbol);
void printPineTree (int n, char symbol);
int main() {
int numberOfLines, numberOfSpaces, numberOfTriangles;
char characterToPrint;
cout << "Enter the number of lines for the triangle (positive integer): ";
cin >> numberOfLines;
cout << "Enter the number of spaces to the left: ";
cin >> numberOfSpaces;
cout << "Enter the character to use (e.g. *, +, $): ";
cin >> characterToPrint;
cout << endl;
printShiftedTriangle(numberOfLines,numberOfSpaces,characterToPrint);
cout << endl;
cout << endl;
cout << "Enter the number of triangles: ";
cin >> numberOfTriangles;
cout << "Enter the character to use (e.g. *, +, $): ";
cin >> characterToPrint;
printPineTree(numberOfTriangles,characterToPrint);
return 0;
}
void printShiftedTriangle (int n, int m, char symbol){
//n = total # of rows
//m = total # of left spaces
for(int row = 1; row <= n; row++){
for(int colSpaces = 1; colSpaces <= (n-row) + m; colSpaces++){
cout << " ";
}
for(int colStars = 1; colStars <= (2*row) - 1; colStars++){
cout << symbol;
}
cout <<endl;
}
}
void printPineTree (int n, char symbol){
for(int i = 1; i <= n; i++){
printShiftedTriangle(i+1,n-i,symbol);
}
}
Question #3
The number e is an important mathematical constant that is the base of the natural logarithm. e also arises in the study of compound interest, and in many other applications.
Background of e: https://en.wikipedia.org/wiki/E_(mathematical_constant) e can be calculated as the sum of the infinite series:
The value of e is approximately equal to 2.71828. We can get an approximate value of e, by calculating only a partial sum of the infinite sum above (the more addends we add, the better approximation we get).
Implement the function: double eApprox(int n)
This function is given a positive integer n, and returns an approximation of e, calculated by the sum of the first (n+1) addends of the infinite sum above.
To test your function use the following main:
Notes:
1. Pay attention to the running time of eApprox. An efficient implementation would run in ฮ(๐).
2. Since the values of the factorials will grow to be very large, use a variable of type double to store them.
#include <iostream>
using namespace std;
double eApprox( int n );
int main() {
cout.precision(30);
for(int n=1; n <= 15; n++){
cout << "n = " << n << "\t" << eApprox(n) << endl;
}
return 0;
}
double eApprox( int n ){
double result = 1.0;
double currentFactorial = 1.0;
for(int i = 1; i <= n; i++){
currentFactorial *= i;
result += (1/currentFactorial);
}
return result;
}
Question #4
a. Implement a function: void printDivisors(int num)
This function is given a positive integer num, and prints all of numโs divisors in ascending order, separated by a space.
For Example, if we call printDivisors(100), the expected output is:
1 2 4 5 10 20 25 50 100
Implementation requirement: Pay attention to the running time of your function. An efficient implementation would run in ฮ โ๐๐ข๐4.
b. Use the function above when implementing a program that reads from the user a positive integer (โฅ2), and prints all itโs divisors.
Your program should interact with the user exactly as it shows in the following example:
Please enter a positive integer >= 2: 100 1 2 4 5 10 20 25 50 100
#include <iostream>
#include <cmath>
using namespace std;
void printDivisors(int num);
int main() {
int numberEntered;
cout << "Please enter a positive integer >= 2: ";
cin >> numberEntered;
if(numberEntered > 1){
printDivisors(numberEntered);
}else{
cout << "Invalid input, please try again!";
}
cout << endl;
return 0;
}
void printDivisors(int num){
for(int i=1; i <= sqrt(num); i++){
if(num % i == 0){
cout << i << " ";
}
}
for(int i=sqrt(num); i >= 1; i--){
if(num % i == 0){
if(num / i != i){
cout << num / i << " ";
}
}
}
}
Question #5
Use the definition of ฮ in order to show the following:
a. 5n3 + 2n2 + 3n = ฮ(๐3)
b. โ7n2+ 2n โ 8 = ฮ(๐)
No answer available. If you have the answer for these 2 questions, share it with everyone in the comment section below. Thanks!
very useful do u have exam samples and/or exam questions.
very useful do u have exam samples
Hi Mellisa, send me an email. I may be able to help. Good luck.
can you send an email of exam samples, thank you.3158944@gmail.com
I want some test samples too, please. 3158944@gmail.com
Kindly tell me the email address so I can receive your message. Thanks!
Hi, may i also give my email for the resources?
Hi Tahsina,
You can now find these resources by visiting – https://csbridgehelp.com/resources/exam-resources/exam-resource/
Good luck.
vconatct@gmail.com
Hi, could you send exam question or practice exam to me if any ? My email is liujinglg@gmail.com. Thanks!
hello are the week 5 questions related to algoritham and data structures.
Hi, xstudent:
My name is Max and I was admitted to the Bridge to Tandon Program for the Spring 2021 session. I have a quick question here: will the exam questions look similar to the questions in the study material? If so, how many questions will be there in a single exam? Thanks for answering my questions and have a wonderful week!
Sincerely,
Max
Hi Max, congratulations on your acceptance to the program. Some of the questions are similar to the homework, but I would recommend practicing as much as possible since this is a tough program. I have added some exam resources to the site. I hope this can help you out. Good Luck! Exam Resources โ NYU Bridge To Tandon Program