2. Code a top-down recursive solution for the classic Fibonacci Sequence (starting from 0) using dynamic programming with heap memory for storage. fibonacci top-down solution (memoization) 0(n) time complexity Recursive Function step 1: if n < 2 return the data at position n step 2: else, if a solution for n has not been stored in a[n] recurse fibo(n-1) + fibo (n-2) and store the answer into a[n] step 3: return the data at position n in the array */ int fibonacci(int n, long long *a){ if(n == 0){ return 0; } if(n == 1){ return 1; } else(n=!-1) return fibonacci(n-1) + fibonacci(n-2); } int main (){ // step 1: create a dynamic array of 50 integers. // step 2: populate the first two indicies of the array with 0 and 1 // step 3: populate the rest of the array with the value -1 // step 4: call the fibonacci sequence for various values of n int *a = new int[50]{0, 1}; cout <« endl; cout << "fib(0): " << fibonacci(0) < endl; cout << "fib(6): " << fibonacci(6) << endl; " < fibonacci(8) << endl; <« fibonacci(15) << endl; cout << "fib(20): " << fibonacci(20) << endl; cout << "fib(37): " << fibonacci(37) << endl; cout << "fib(8): cout << "fib(15): cout <« endl; delete [] a; return 0; }

2. Code a top-down recursive solution for the classic Fibonacci Sequence (starting from 0) using dynamic programming with heap memory for storage. fibonacci top-down solution (memoization) 0(n) time complexity Recursive Function step 1: if n < 2 return the data at position n step 2: else, if a solution for n has not been stored in a[n] recurse fibo(n-1) + fibo (n-2) and store the answer into a[n] step 3: return the data at position n in the array / int fibonacci(int n, long long a){ if(n == 0){ return 0; } if(n == 1){ return 1; } else(n=!-1) return fibonacci(n-1) + fibonacci(n-2); } int main (){ // step 1: create a dynamic array of 50 integers. // step 2: populate the first two indicies of the array with 0 and 1 // step 3: populate the rest of the array with the value -1 // step 4: call the fibonacci sequence for various values of n int *a = new int[50]{0, 1}; cout <« endl; cout << "fib(0): " << fibonacci(0) < endl; cout << "fib(6): " << fibonacci(6) << endl; " < fibonacci(8) << endl; <« fibonacci(15) << endl; cout << "fib(20): " << fibonacci(20) << endl; cout << "fib(37): " << fibonacci(37) << endl; cout << "fib(8): cout << "fib(15): cout <« endl; delete [] a; return 0; }

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 20SA

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