Write Algorithm for Interchange Base Points Input : a group G; a base [131,132 ..... 13k] for G and a strong generating set; an integer j between 1 and k-l; Output : a base B = [131,132 ..... 13j-1, 13L.+1, 13j, 13j+2, 13j+3 ..... 13k] for G; a strong generating set relative to B;
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Input : a group G; a base [131,132 ..... 13k] for G and a strong generating set; an integer j between 1 and k-l;
Output : a base B = [131,132 ..... 13j-1, 13L.+1, 13j, 13j+2, 13j+3 ..... 13k] for G; a strong generating set relative to B;
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- Algorithm to Interchange Base PointsInput : a group G;a base [131,132 ..... 13k] for G and a strong generating set;an integer j between 1 and k-l;Output : a base B = [131,132 ..... 13j-1, 13L.+1, 13j, 13j+2, 13j+3 ..... 13k] for G;a strong generating set relative to B;Write Algorithm for Interchange Base PointsInput : a group G;a base [131,132 ..... 13k] for G and a strong generating set;an integer j between 1 and k-l;Output : a base B = [131,132 ..... 13j-1, 13L.+1, 13j, 13j+2, 13j+3 ..... 13k] for G;a strong generating set relative to B;procedure interchange( var B : sequence of points;vat S : set of elements;j : 1..k-1 );(* Given a base B = [131,132 ..... 13~] and a strong generating set S of G,return the base obtained by interchanging 13j and 13j+1,and return a strong generating set relative to the new base. *)The Virtual Weight (VW) of an integer number (which consists of more than 1 digit) is the sumof the individual digits that are composing the number. For example, consider the followingtwo numbers; 5638 and 1145, then the VW of each is calculated as following:VW(5638) = 5+6+3+8 = 22VW(1145) = 1+1+4+5 = 11Then, the VW can be classified as L (mean Low) or H (means High) using a specific cut-offvalue. For example, if the cut-off value is 15, then the VW of the number 5638 is H (High),and the VW of the number 1145 is L because 22 > 15 and 11 ≤ 15 respectivelyWrite a C++ program that: reads a positive integer n (where 5≤n≤20) from the user. If the user enters invalidnumber, then the program should continue prompting until he/she enters a valid numberwithin the specified range. Then, the program should generate n random numbers using the built-in rand()function. Every time a random number is generated, the program will classify that number as Lor H using the above method. Use a…
- Interchange Base Points AlgorithmAn integer j between 1 and k-l, a group G, a base [131,132,..... 13k] for G, and a strong generating set are all inputs.Output: a powerful generating set for G with base B = [131,132..... 13j-1, 13L.+1, 13j, 13j+2, 13j+3..... 13k];The parity function is a very simple hash function producing a one-bit digest, which is 0 if the number of bits in the message is even and 1 if it is odd. Consider a communication system that uses 7 bits out of every byte to transmit data, and reserves the 8th bit (the one on the right) to transmit the parity of the other seven bits, for purposes of error checking. Below is the binary representation of some bytes that were transmitted using this system. For each one, tell whether there is a reason to suspect an error in transmission, giving the reason for your answer. 10110011 11101111 10101100 00110011Given a set of n positive integers, C = {c1,c2, ..., cn} and a positive integer K, is there a subset of C whose elements sum to K? A dynamic program for solving this problem uses a 2-dimensional Boolean table T, with n rows and k + 1 columns. T[i,j] 1≤ i ≤ n, 0 ≤ j ≤ K, is TRUE if and only if there is a subset of C = {c1,c2, ..., ci} whose elements sum to j. Which of the following is valid for 2 ≤ i ≤ n, ci ≤ j ≤ K? a) T[i, j] = ( T[i − 1, j] or T[i, j − ci]) b) T[i, j] = ( T[i − 1, j] and T[i, j − ci ]) c) T[i, j] = ( T[i − 1, j] or T[i − 1, j − ci ]) d) T[i, j] = ( T[i − 1, j] and T[i − 1, j − cj ]) In the above problem, which entry of the table T, if TRUE, implies that there is a subset whose elements sum to K? a) T[1, K + 1] b) T[n, K] c) T[n, 0] d) T[n, K + 1]
- Given a set of n positive integers, C = {c1,c2, ..., cn} and a positive integer K, is there a subset of C whose elements sum to K? A dynamic program for solving this problem uses a 2-dimensional Boolean table T, with n rows and k + 1 columns. T[i,j] 1≤ i ≤ n, 0 ≤ j ≤ K, is TRUE if and only if there is a subset of C = {c1,c2, ..., ci} whose elements sum to j. Which of the following is valid for 2 ≤ i ≤ n, ci ≤ j ≤ K? a) ?[?, ?] = ( ?[? − 1, ?] ?? ?[?, ? − ?? ]) b) ?[?, ?] = ( ?[? − 1, ?] ??? ?[?, ? − ?? ]) c) ?[?, ?] = ( ?[? − 1, ?] ?? ?[? − 1, ? − ?? ]) d) ?[?, ?] = ( ?[? − 1, ?] ??? ?[? − 1, ? − ?? ]) In the above problem, which entry of the table T, if TRUE, implies that there is a subset whose elements sum to K? a) ?[1, ? + 1] b) ?[?, ?] c) ?[?, 0] d) ?[?, ? + 1]Let A = {1, 2, 5} and B = {3, 4, 5} be sets. What is the cardinality of the power set p(p((A U B)-B)) [Input numeric value only] Answer: ?Algorithm 5 : Complete Base ChangeInput : 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' anda strong generating set S relative to B;
- Problem Alice was given a number line containing every positive integer, x, where 1<=x<=n. She was also given m line segments, each having a left endpoint, l (1<=l<=n), a right endpoint, r (1<=r<=n), and an integer weight, w. Her task is to cover all numbers on the given number line using a subset of the line segments, such that the maximum weight among all the line segments in the chosen subset is minimal. In other words, let S=(l1,r1,w1),(l2,r2,w2),....,(lk,rk,wk), represent a set of k line segments chosen by Alice, max(w1,w2,...,wk) should be minimized. All numbers 1,2,....n should be covered by at least one of k the chosen line segments. It is okay for the chosen line segments to overlap. You program should output the minimized maximum weight in the chosen subset that covers all the numbers on the number line, or -1 if it is not possible to cover the number line. Input format The first line of the input contains an integer, n - denoting the range of numbers…Let s = σ1. . . σk be a binary string of length k > 0. We say that a binary string w = w1 . . . wn contains s as a subsequence if there are k indices 1 ≤ i1 < i2, . . . < ik ≤ n such that wik = sr for every 1 ≤ r ≤ k. For example, if s = 11 then 10001, 1010 and 110 contain s as a subsequence whereas 000 and 1000 do not. Prove that the language of all binary strings containing a fixed binary string s of length k as a subsequence is a regular language.Choose the correct answer from the number of the set S={x | x is the square of an integer x<100} is:a) {0,2,4,5,958,49,56,99,12}b) {0,1,4,9,16,25,36,49,64,81}c) {0,1,4,9,16,25,36,49,64,121}