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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Write
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 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) ;def mystery (1st); for idx in range(1, len(1st)); tmp = 1st[idx) idx2 = idx while 1dx2 > 9 and 1st[idx2-11 tmp: 1st[idx2] 1st[10/2 - 11 1dx2 = 1dx2 - 1 1st[idx2] = tmp print(1st) a. If we call this function as follows: mystery(lt) where ist 15, 2, 8, 11, what is printed out t clear about what is printed out, don't make me try to figure it out). b. What does this function do? c. What is the complexity of this function? Oni Ora, On³ Ologinil, Onioginil? Explain your reasoningQuestion 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 AB
- For Letter -> A | B Digit -> 0 | 1 Id -> letter (letter | digit)* Generate NFA and transfer it to DFA.Plot the following function for -5 ≤ x ≤ 5: y = 1 1+x² The x-values can be generated with x = np.linspace (-5, 5, n), where n refers to the number of x-values generated (you pick a n-value).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…
- 6 7 8 9 10 ======= 11 12 13 14 15 16 17 18 19 20 21 22 XO la b 1 m Periodicity U 50 33 97 D XI E F G H I J L M N Use linear congruential generator approach to find Xi, what is the periodicity? Rename cells C4, C5, C6 and C7 as X0, a, b and m, respectively. RUDIMENTS OF RANDOM NUMBER GENERATION (1 OF 2) LINEAR CONGRUENTIAL GENERATORS (BYLEHMER 1951 A sequence of integers defined by the following recursive formula X = (ax +b) MOD m, 1 = 0, 1.... which means divide (ax, + b) by m, let X... be the remainder of this division a multiplier b increment m the modulus x0 seed or initial point 0 PGiven two arrays X and Y of positive integers, find the number of pairs such that xy > yx (raised to power of) where x is an element from X and y is an element from Y. Example 1: Input: M = 3, X[] = [2 1 6] N = 2, Y[] = [1 5]Output: 3Explanation: The pairs which follow xy > yx are as such: 21 > 12, 25 > 52 and 61 > 16 .Example 2: Input: M = 4, X[] = [2 3 4 5]N = 3, Y[] = [1 2 3]Output: 5Explanation: The pairs for the given input are 21 > 12 , 31 > 13 , 32 > 23 , 41 > 14 , 51 > 15 . Your Task:This is a function problem. You only need to complete the function countPairs() that takes X, Y, M, N as parameters and returns the total number of pairs. Expected Time Complexity: O((N + M)log(N)).Expected Auxiliary Space: O(1). Constraints:1 ≤ M, N ≤ 1051 ≤ X[i], Y[i] ≤ 103Exercise Generate a log-log plot of your period T vs. dynamic mass ma. This is the same plot that you drew on the log-log graphing paper from your materials pack. Perform these steps: 1. Define lists or numpy arrays that contain your experimental data. For example, md = [0.10, 0,15, 0.20] defines a list of dynamic masses 0.1, 0.15 and 0.20 kg, and T = [0.75, 0.83, 0.91] defines a list of periods (in seconds). 2. Generate a log-log plot of T vs. ma that shows your data as points (not lines!) using plt.loglog() with the 'o' option. The dynamic mass should be on the horizontal (x) axis. 3. Add grid lines for both the "major" and "minor" ticks, and both axes. Look up the documentation of plt.grid() to see how this is done. Remember that you can get the documentation for any command by running it in a cell of its own and appending a question mark, e.g. plt.grid?. 4. The axis tick labels will likely show up in scientific notation (e.g. 6 × 10−²). For our values (mostly in the 0.1...1 kg…Java Only Solution: Let's consider a rectangular R table containing N rows and M columns. Rows are numbered 1 to N from top to bottom. Columns are calculated from 1 to M from left to right. Each element of R is a non-negative number. R is pronounced steadily if the total number of elements in the ith line is not less and then the total number of elements in the i-line (1) th for each i lapho is 2 Kanye N and the total element in the Nth line is less than or equal to M. Your job is to find the number of fixed tables of different sizes N x M modulo 1 000 000 000 000 Using the Java Programming language. Input: 1 11 Output: 2SEE MORE QUESTIONS