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Consider the two functions below which both compute the value of f(n). The function f1 was
replaced with f2 because integer multiplications () were found to take 4 times longer than integer
additions (+).
int f1(n : integer)
if (n == 1) then return(1)
else return(2 f1(n 1));
int f2(n : integer)
if (n == 1) then return(1)
else return(f2(n 1) + f2(n 1));
i. Give a recurrence relation for f1, which satisfies the number of multiplications (*) executed as
a function of n.
ii. Solve the recurrence relation from Part i.
iii. Give a recurrence relation for f2, which satisfies the number of additions (+) executed as a
function of n.
iv. Solve the recurrence relation from Part iii. v. Both functions compute the same function f.
Was it a good idea to replace f1 with f2?

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Consider the two functions below which both compute the value of f(n.pdf

  • 1. Consider the two functions below which both compute the value of f(n). The function f1 was replaced with f2 because integer multiplications () were found to take 4 times longer than integer additions (+). int f1(n : integer) if (n == 1) then return(1) else return(2 f1(n 1)); int f2(n : integer) if (n == 1) then return(1) else return(f2(n 1) + f2(n 1)); i. Give a recurrence relation for f1, which satisfies the number of multiplications (*) executed as a function of n. ii. Solve the recurrence relation from Part i. iii. Give a recurrence relation for f2, which satisfies the number of additions (+) executed as a function of n. iv. Solve the recurrence relation from Part iii. v. Both functions compute the same function f. Was it a good idea to replace f1 with f2?