Algorithm 5 : Complete Base Change Input : a base B = [~1,132 ..... ~k] and a strong generating set S of a group G; a sequence B' = [[3' 1, 13'2 ..... 13'k'] to form an initial segment of the new base; Output : a base B for G that is an extension (or initial segment) of B' and a strong generating set S relative to B;
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Input : a base B = [~1,132 ..... ~k] and a strong generating set S of a group G;
a sequence B' = [[3' 1, 13'2 ..... 13'k'] to form an initial segment of the new base;
Output : a base B for G that is an extension (or initial segment) of B' and
a strong generating set S relative to B;
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- Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. Bag union and intersection are defined in terms of #. bag-union: List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-union. bag-intersection : List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-intersection. Allowed functions. Your code must use only the following functions:1. define, let2. lambda3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. +, -, /, * Racket code only please. Thank you!Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. sum : List × List -> List This function should take as arguments two lists representing bags and should return the list representing the list resulting from simply appending the input lists together. Racket code only please. No loops Allowed: 1. define, let2. lambda, curry3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. map, append-map, andmap, ormap, filter, apply7. +, -, /, * Thank you!Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. Bag union and intersection are defined in terms of #. bag-union: List × List -> List This function should take as arguments two lists representing bags and should return the list representing their bag-union. bag-intersection : List × List -> List This function should take as arguments two lists representing bags and should return the list representing their bag-intersection. Allowed functions. Your code must use only the following functions:1. define, let2. lambda, curry3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. map, append-map, andmap, ormap, filter, apply7. +, -,…
- Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. Bag union and intersection are defined in terms of #. bag-union: List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-union. bag-intersection : List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-intersection. Allowed functions. Your code must use only the following functions:1. define, let2. lambda3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. +, -, /, * No loops or use of hash Racket code only please.…Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. sum : List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing the list resulting from simply appending the input lists together. Racket code only please. No loops Allowed: 1. define, let2. lambda3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond7. +, -, /, * Thank you!HW 3: Given the regular expression ((a/b)(abb)): • Construct an equivalent NFA using Thompson's construction. • Convert this NFA to a DFA using the subset construction method.
- Question 1 The power set P((A x B) u (B x A)) has the same number of elements as the power set P((A x B) u (A x B)) if and only if: O Ae or B e or A B O Bo or A-B O Ao or Beo ABDefine a function named get_sorted_in_parallel (tuples1, tuples 2) which takes two tuples of integers as parameters. The tuples have the same length and their elements are related, i.e. the element at each index of the second parameter tuple corresponds to the element at the same index in the first parameter tuple, e.g. the element at index 1 in the first tuple corresponds to the element at index 1 in the second tuple. The function sorts the first parameter tuple, keeping the elements of the second parameter tuple in the order corresponding to the sorted first parameter tuple. The function returns a tuple made up of the sorted first parameter tuple and the new corresponding second tuple. For example, the following code fragment: tuple1 = (4, 1, 3) tuple2 (9, 8, 6) tuple3, tuple4 = get_sorted_in_parallel (tuplel, tuple2) print (tuplel, "-", tuple2) print (tuple3, "-", tuple4) prints: (4, 1, 3) - (9, 8, 6) (1, 3, 4) (8, 6, 9) 4 and 9 are connected, 1 and 8 are connected, 3 and 6 are…A deque DQUE is to be implemented using a circular one-dimensional array of size N. Execute procedures to:i) insert and delete elements from DQUE at either end;ii) implement DQUE as an output restricted deque;iii) implement DQUE as an input restricted deque;iv) for the procedures, what are the conditions used for testing whether DQUE is full (DQUE_FULL) and empty (DQUE_EMPTY)?
- Given an array of integers and a positive integer k, determine the number of (i, j) pairs where i < j and ar[i] + ar[j] is divisible by k. Example ar [1, 2, 3, 4, 5, 6] k=5 Three pairs meet the criteria: [1, 4], [2, 3], and [4, 6]. Function Description Complete the divisibleSumPairs function in the editor below. divisibleSumPairs has the following parameter(s): • int n: the length of array ar ⚫int ar[n]: an array of integers . int k: the integer divisor Returns -int: the number of pairs Input Format The first line contains 2 space-separated integers, 11 and k. The second line contains space-separated integers, each a value of arr[i]. Constraints • 2 ≤ n ≤ 100 • 1<k<100 • 1 ≤ ar[i] ≤ 100 Sample Input More STDIN 63 1 3 2 6 12 Function n6, k3 ar [1, 3, 2, 6, 1, 2] Sample Output 5 Explanation Here are the 5 valid pairs when k = 3: (0,2) ar[0] + ar[2]=1+2=3 (0,5) ar[0] + ar[5]=1+2=3 • (1,3) ar[1]+ar [3]=3+6=9 (2, 4) ar[2] + ar[4] = 2+1=3 • (4,5)→ ar[4] + ar[5]=1+ 2=3 with…Algorithm 1 : Miniature SearchInput : a group G;a base [111,112 ..... 1]k] for G and a strong generating set;an integer j between 1 and k- 1;Output : a set T of coset representatives of G (j+2) in ~(j+l) ;What are the requirements for determining if a linked list T is empty if T is one of the following: (i) a simple singly linked list, (ii) a headed singly linked list, (iii) a simple circularly linked list, or (iv) a headed circularly linked list?
