Lecture 7 Notes

What is the run me ie how many iteraons for a given

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Unformatted text preview: t;best" quotient à༎ smallest error myPi = pBest/qBest; Lecture 8 4 Ques,on Time This is an example of a “nested loop” for every q M p’s are checked. What is the run ,me? (i.e. how many itera,ons for a given M?) A) M B) 2M C) M^2 D) M^M Improvements •  Inner loop floor(qπ) < qπ < ceil(qπ) => floor(qπ)/q < π < ceil(qπ)/q => need only check p- = floor(qπ), p+ = ceil(qπ) This also gives bound J༄ p- /q < π < p+/q 1 2/13/14 % Better BetterEg3_1! ! pBest = 1; % Best numerator! qBest = 1; % Best denominator ! err_pq = abs(pBest/qBest - pi); % Error qBest/pBest! ! % Check out all possible denominators...! for q = 1:M! % For this q, find the best numerator p! for p = floor(q*pi):ceil(q*pi)! % Check to see if we have a better quotient! if abs(pi - p/q) < err_pq! ! ! ! err_pq= abs(pi - p/q);! pBest= p;! qBest= q;! end! end!...
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