a. Find gcd(31415, 14142) by applying Euclid’s algorithm. b. Estimate how many times faster it will...
a. Find gcd(31415, 14142) by applying Euclid’s algorithm.
b. Estimate how many times faster it will be to find gcd(31415, 14142) by Euclid’s algorithm compared with the algorithm based on checking consecutive integers from min{m, n}down to gcd(m, n).
Homework Answers
ANS:- The bormula for compute gredest common dVIS a) ged (min) = gcd (nim mad n) "The ged (31415, 14142) by applying Euclid's algorthm 18 ged ( 31415, 14.1 42) = ged(14,142, 3,131) ged (3,131,1,618) -gedciG18.1513) ged ( 1,513, 105) ged (105, 43) ged (43119) - ged (19,5) ged c5,4) ged (411) %3D = 1. b) The no of comparison's on given mput with the algai thm checking consutive integers and Eucltas algorthm based on The no ot ciu Bions using Eudid's algorithm = 10 brom part caj The consueutive integen checesing algorithm 81 2 divislong fan iterations. The no-of terations = 14,142 and 14,142 2= number of divisions<=24 14
ANS:- The bormula for compute gredest common dVIS a) ged (min) = gcd (nim mad n) "The ged (31415, 14142) by applying Euclid's algorthm 18 ged ( 31415, 14.1 42) = ged(14,142, 3,131) ged (3,131,1,618) -gedciG18.1513) ged ( 1,513, 105) ged (105, 43) ged (43119) - ged (19,5) ged c5,4) ged (411) %3D = 1. b) The no of comparison's on given mput with the algai thm checking consutive integers and Eucltas algorthm based on The no ot ciu Bions using Eudid's algorithm = 10 brom part caj The consueutive integen checesing algorithm 81 2 divislong fan iterations. The no-of terations = 14,142 and 14,142 2= number of divisions<=24 14
18 faster by least Eucl'all's algorithm 8 at 14,142/10= 140o times. At mosf 2*14,142 2800 timos . 10
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a. Find gcd(31415, 14142) by applying Euclid’s algorithm.
b. Estimate how many times faster it will...
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2,3,4,5,6 please 2. Use the Euclidean algorithm to find the following: a gcd(100, 101) b. ged(2482,...
2,3,4,5,6 please
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1. Design an algorithm to find all the non-common elements in two sorted lists of numbers. What is the maximum number of comparisons your algorithm makes if the lengths of the two given lists are m and n, ?respectively 2. Estimate how many times faster it will be to find ged(98765, 56789) by Euclid's algorithm compared with the algorithm based on checking consecutive integers from min{m, n} down to gcd(m, n). 3. For each of the following functions, indicate how...
a Find the greatest common divisor (gcd) of 322 and 196 by using the Euclidean Algorithm. gcd- By working back in the Euclidean Algorithm, express the gcd in the form 322m196n where m and n are integers b) c) Decide which of the following equations have integer solutions. (i) 322z +196y 42 ii) 322z +196y-57
PROBLEM 1 For each of the following pairs of integers, use the Euclidean Algorithm to find ged(a,b), and to write gcd(a,b) as a linear combination of a and b, i.e. find integers m and n such that gcd(a,b) = am + bn. (a) a = 36, b = 60. (b) a = 12628, b = 21361. (c) a = 901, b = -935. (d) a = 72, b = 714. (e) a = -36, b = -60.
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2,3,4,5,6 please
2. Use the Euclidean algorithm to find the following: a gcd(100, 101) b. ged(2482, 7633) 3. Prove that if a = bq+r, then ged(a, b) = ged(b,r). such that sa tb ged(a,b) for the following pairs 4. Use Bézout's theorem to find 8 and a. 33, 44 b. 101, 203 c. 10001, 13422 5. Prove by induction that if p is prime and plaja... An, then pla, for at least one Q. (Hint: use n = 2 as...
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