Question

In: Computer Science

Using C++ use dynamic programming to list first 30 Fibonacci numbers. Fibonacci sequence is famous problem...

Using C++ use dynamic programming to list first 30 Fibonacci numbers.

Fibonacci sequence is famous problem solved with recursion. However, this can also be done more efficiently using dynamic programming. Create a program that uses dynamic programming techniques to list the first 30 Fibonacci numbers.

Solutions

Expert Solution

Program:

#include <iostream>
using namespace std;

int main ()
{
   int n = 30;
   int f[n], i;

   f[0] = 0;
   f[1] = 1;

   for(i = 2; i < n; i++)
   {
       f[i] = f[i - 1] + f[i - 2];
   }
  
   cout <<"\nThe First 30 fibonacci numbers: " << endl;
  
   for(i = 0; i < n; i++)
   {
       cout << f[i] << endl;
   }
   cout << endl << endl;
  
   return 0;
}


Screenshot: ( for reference )

Output:

-----------------
Note: If you have any doubts please comment.

It will be great help If you like.


Related Solutions

Using Python: The Fibonacci sequence is a famous series of numbers with the following rules: The...
Using Python: The Fibonacci sequence is a famous series of numbers with the following rules: The first number in the sequence is 0 - The second number in the sequence is 1 - The other numbers in the sequence are composed by adding up the two previous numbers in the sequence. We therefore have the following sequence: 1 st number: 0 2nd number: 1 3 rd number: 0 + 1 = 1 4 th number: 1+1 =2 5 th number:...
The Fibonacci Sequence is a series of integers. The first two numbers in the sequence are...
The Fibonacci Sequence is a series of integers. The first two numbers in the sequence are both 1; after that, each number is the sum of the preceding two numbers. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... For example, 1+1=2, 1+2=3, 2+3=5, 3+5=8, etc. The nth Fibonacci number is the nth number in this sequence, so for example fibonacci(1)=1, fibonacci(2)=1, fibonacci(3)=2, fibonacci(4)=3, etc. Do not use zero-based counting; fibonacci(4)is 3, not 5. Your assignment...
(a) The Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence,...
(a) The Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and are characterised by the fact that every number after the first two is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 114, … etc. By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two. We define Fib(0)=0,...
A Fibonacci sequence, is a sequence of numbers with the property that each number is the...
A Fibonacci sequence, is a sequence of numbers with the property that each number is the sum of the two preceding Fibonacci numbers, starting from 0 and 1. Fibonacci number are usually denoted by Fn, where Fn is the nth Fibonacci number. Thus Fn = 0, and Fn = 1, and Fn = Fn-1 + Fn-2, n ≥ 2. Here are the first few Fibonacci numbers: F0=0 (by definition) F1=1 (by definition) F2 = F1 + F0 = 1 +...
Google the first 50 numbers of the Fibonacci sequence (starting with 1) to answer the following...
Google the first 50 numbers of the Fibonacci sequence (starting with 1) to answer the following questions:          (a) Test to see if the leading digits conform to Benford’s law. Do this both graphically and analytically.          (b) Using the first 10 odd numbers in the sequence as sample 1 and the first 10 even numbers in the sequence as sample 2, use Wilcoxon’s Rank-Sum to test the claim that the numbers come from different populations.          (c) Repeat (b)...
In this assignment, you will calculate and print a list of Fibonacci Numbers . Fibonacci numbers...
In this assignment, you will calculate and print a list of Fibonacci Numbers . Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones: The sequence Fn of Fibonacci numbers is defined by the recurrence relation:  which says any Nth Fibonacci number is the sum of the (N-1) and (N-2)th Fibonacci numbers. Instructions Your task will be...
. (a) Write a C++ program to find Fibonacci numbers. (For the definition of Fibonacci numbers...
. (a) Write a C++ program to find Fibonacci numbers. (For the definition of Fibonacci numbers and the recursive formula please refer to problem 5 of Chapter 2 at page 81 in the text-book.) The program asks the user to input an integer and outputs the corresponding Fibonacci number. For example, if the user inputs 4, the program outputs the fifth Fibonacci number, which is 3. Introduce two local variables in the recursion function (suppose we call it fib(n)), one...
Consider the Fibonacci sequence 1,1,2,3,5,8,13,21,34,55,89,…. . The first two numbers are 1 and 1. When you...
Consider the Fibonacci sequence 1,1,2,3,5,8,13,21,34,55,89,…. . The first two numbers are 1 and 1. When you add these numbers you get 2 = 1+1, which becomes the third number in the sequence. When you add the second and third numbers, you get 3 = 1+2, which becomes the fourth number in the sequence. When you add the third and fourth numbers, you get 5 = 2+3, which becomes the fifth number in the sequence; and so on to generate the...
Please use C++ 1. A Sequence of numbers and a sum is given as input. List...
Please use C++ 1. A Sequence of numbers and a sum is given as input. List all combinations of numbers that can add upto the given Sum. User input:- Enter numbers: -   1, 3,7,9,11 Enter a sum :- 20 Output: 11+9 = 20 1+3+7+9 = 20 2. Print absolute prime numbers between a given range:- Enter Range - 2,99 For eg Prime numbers are:- Prime numbers ==> 2,3,5,7,11,13,17,19,23 Absolute Prime numbers ==> 2,3,5,7,11,23 3. Write an encoder and decoder program,...
The Fibonacci sequence is an infinite sequence of numbers that have important consequences for theoretical mathematics...
The Fibonacci sequence is an infinite sequence of numbers that have important consequences for theoretical mathematics and applications to arrangement of flower petals, population growth of rabbits, and genetics. For each natural number n ≥ 1, the nth Fibonacci number fn is defined inductively by f1 = 1, f2 = 2, and fn+2 = fn+1 + fn (a) Compute the first 8 Fibonacci numbers f1, · · · , f8. (b) Show that for all natural numbers n, if α...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT