DISCRETE MATH A function receives a positive integer m as the input and returns

Question

DISCRETE MATH

A function receives a positive integer m as the input and returns the value Compute (n) = sigma_j = 1^n(j + 2)j^2. Fill in the blanks for recursive algorithm to compute the sum given above. The value returned should be a mathematical expression that uses variables y and/or n and only uses addition or multiplication operations. There should be no summation notation in your responses. Compute Sum (n) If (_____)Return (_____)//Base case y: = Compute Sum (_____)//Recursive Call Return(_____) End The function below receives two inputs: a and n, where a is a real number and n is a non-negative integer. The algorithm returns a times n. Product (a, n) If(n = 0) Return (0) y: Product(a, n -1) Return (a + y) End Let NUMADD(a, n) be the number of addition operations performed by the algorithm Product on inputs a and n. What is NUMADD(a, 0)? Express NUMADD (a, k + 1) is a function of NUMADD (a, k).

Explanation / Answer

8)

computeSum(n)

     if (n==1) return 3;   //(1+2)*1*1 // (j+2)*j*j

     y = computeSum(n-1)

     return (y+((n+2)*n*n))

end

9)

a) zero

explanation : zero times a is a, no need to perform any addition

b)

NumADD(a,k+1) = NumADD(a,k)+1

explanation:

NumADD(a,n) returns the number of addition operations required by algorithm Product

in Product algorithm, n times a, means, a added to itself n times... so.. 'n' addition operations needed

hence NumADD(a,n) returns 'n'..

NumADD(a,k+1) should return    k+1 (addition operations)

NumADD(a,k) should return k

so..

NumADD(a,k+1) = NumADD(a,k)+1

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.