Construct a trace table to trace the action of the algorithm below for the input variables given. a := 5,862, b := 1,240, r := 1,240 while (b + 0) r:=a mod b a:=b b:=r end while gcd :=a iteration 1 3 4 5 6 a 5,862 1,240 r 1,240 gcd gcd(5,862, 1,240) =

For the list [44, 18, 74, 61, 42, 31], how will the array elements look like after second pass (after i-2 but before i=3) of the Insertion sort algorithm? def insertionSort(a): for i in range(1,len(a)): currentvalue = a[i] position = i while position>0 and a[position-1]>currentvalue: a[position]=a[position-1] position = position-1 a[position]=currentvalue return a [18, 44, 74, 61, 42, 31] [18, 44, 61, 74, 42, 31] [18, 42, 44, 61, 74, 31] [18, 31, 42, 44, 61, 74]

Learning Target N2 (Core): I can perform back-substitution in the Euclidean Algorithm to write the the greatest common divisor of a and b as in Bézout's Lemma, gcd(a, b) =as + bt, noting the + between the terms with a, b, s, te Z Use the Euclidean Algorithm with back-substitution to find the gcd (a, b) and then write ged(a, b) = as+bt, noting the between the terms with a, b, s, t € Z. 1. a 36, b= 15. The answer is 3 = 36 (-2) +15 (5), now show the work. 2. a = 567, b = 1234. The answer is 1= 567 (37) +1234(-17), now show the work. I

1. a. Find ged(31415, 14142) by applying Euclid's algorithm. b. Estimate how many times faster it will be to find ged(31415, 14142) by Euclid's algorithm compared with the algorithm based on checking con- secutive integers from min{m, n} down to gcd(m, n).