In Fibonacci's model, rabbits live forever. The following modification of Definition 3.1 accounts fo if n ≤ 0 if n = 1 or n = 2 G(n) = G(n-1) + G(n-2) (a) Compute G(n) for n = 1, 2, ..., 12. G(1) G(2) G(3) G(4) G(5) G(6) G(7) G(8) G(9) G(10) G(11) G(12) = = = = = G(n-8) if n > 2. (b) In this modified model, how long do rabbits live? months
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- Correct answer will be upvoted else downvoted. Computer science. Allow us to signify by d(n) the amount of all divisors of the number n, for example d(n)=∑k|nk. For instance, d(1)=1, d(4)=1+2+4=7, d(6)=1+2+3+6=12. For a given number c, track down the base n to such an extent that d(n)=c. Input The principal line contains one integer t (1≤t≤104). Then, at that point, t experiments follow. Each experiment is characterized by one integer c (1≤c≤107). Output For each experiment, output: "- 1" in case there is no such n that d(n)=c; n, in any case.Modeling the spread of a virus like COVID-19 using recursion. Let N = total population (assumed constant, disregarding deaths, births, immigration, and emigration). S n = number who are susceptible to the disease at time n (n is in weeks). I n = number who are infected (and contagious) at time n. R n = number who are recovered (and not contagiuous) at time n. The total population is divided between these three groups: N = S n + I n + R n There are several hidden assumptions here that may or may not apply to COVID-19, such as a recovered person is assumed to not be able to get the disease a second time, at least within the time window being examined. On week 0 (the start), you assume a certain small number of people have the infection (just to get things going). Everyone else is initially susceptible, and no one is recovered. There are two constants of interest: Let period = time period that it takes for an infected person to recover (recover meaning they become not infectious to…Correct answer will be upvoted else downvoted. Computer science. stage is a succession of n integers from 1 to n, in which every one of the numbers happen precisely once. For instance, [1], [3,5,2,1,4], [1,3,2] are stages, and [2,3,2], [4,3,1], [0] are not. Polycarp was given four integers n, l, r (1≤l≤r≤n) and s (1≤s≤n(n+1)2) and requested to find a stage p of numbers from 1 to n that fulfills the accompanying condition: s=pl+pl+1+… +pr. For instance, for n=5, l=3, r=5, and s=8, the accompanying stages are reasonable (not all choices are recorded): p=[3,4,5,2,1]; p=[5,2,4,3,1]; p=[5,2,1,3,4]. However, for instance, there is no change reasonable for the condition above for n=4, l=1, r=1, and s=5. Help Polycarp, for the given n, l, r, and s, find a stage of numbers from 1 to n that fits the condition above. In case there are a few appropriate changes, print any of them. Input The primary line contains a solitary integer t (1≤t≤500). Then, at that point,…
- In chess, a walk for a particular piece is a sequence of legal moves for that piece, starting from a square of your choice, that visits every square of the board. A tour is a walk that visits every square only once. (See Figure 5.13.) 5.13 Prove by induction that there exists a knight’s walk of an n-by-n chessboard for any n ≥ 4. (It turns out that knight’s tours exist for all even n ≥ 6, but you don’t need to prove this fact.)For relatively small values of n, algorithms with larger orders can be more efficient than algorithms with smaller orders. Use a graphing calculator or computer to answer this question. For what values of n is an algorithm that requires n operations more efficient than an algorithm that requires [50 log2(n)] operations? (Assume n is an integer such that n > 1.) n?READ AND SOLVE VERY CAREFULLY WITH PYTHONthanks in advance Given a jungle matrix N*M:jungle = [[1, 0, 0, 0],[1, 1, 0, 1],[0, 1, 0, 0],[1, 1, 1, 1,]]Where 0 means the block is dead end and 1 means the block can be used in the path from source to destination. Task: (Use Python)Starting at position (0, 0), the goal is to reach position (N-1, M-1).Your program needs to build and output the solution matrix, a 4*4 matrix with 1’s in positions used to get from the starting position (0,0) to the ending position (N-1, M-1) with the following constraints:- You can only move one space at a time.- You can only move in two directions: forward and down.- You can only pass thru spaces on the jungle matrix marked ‘1’If you cannot reach the ending position, print a message that you’re trapped in the jungle Algorithm:If destination is reached print the solution matrixElse Mark current cell in the solution matrix Move forward horizontally and recursively check if this leads to…
- Exercise on Big-Oh Analysis. Answer True or False whether a function with growth rate is a member of the set of algorithms that grow with a certain complexity. Draw also the graph. n3/2 = O (n2); if n = 500 4n2+5n+2 = Ω (n2); if n = 150 2n3+8n2+6n+7 = ω (2n); if n = 500 (n+1)(n-1)/ 3 = o (logn); if n = 200 5n + 3 = O (nlogn); if n = 1000 int[] arr = {2,4,6,8,10,12,14,16}; for(int i= 0; i<arr.length; i++){ System.out.println(arr[i]); } = o (n) 7. for(int row= 1; row<=5; row++){ for(int col=1; col<=3; col++){ System.out.print(“*”); } System.out.println(); } = Ω (n2) 8. 2n = ω (n); if n = 20 9. 6n2+2n+5 = O (n!); if n = 50 10. 2n + 10 = ϴ (nlogn); if n = 200Suppose a Genetic Algorithm uses chromosomes of the form x=abcdef with a fixed length of six genes.Each gene can be any digit between 0 and 9 . Let the fitness of individual x be calculated as : f(x) =(a+b)-(c+d)-(e+f) And let the initial population consist of four individuals x1, ... ,x4 with the following chromosomes : x1 = 3 5 3 2 6 5, x2 = 9 8 0 1 2 2, x3 = 1 2 2 1 2 3, x4 = 7 9 2 3 1 1 1. 1.Evaluate the fitness of each individual, showing all your workings, and arrange them in order with the fittest first and the least fit last. 2. calculate the average fitness. 3. Perform the following crossover operations:a- Cross the fittest two individuals using one point crossover at the middle point.b- Cross the second and third fittest individuals using a two point crossover (points b and e). Suppose the new population consists of the four offspring individuals received by the crossover operations in the above question. Evaluate the fitness of the new population, showing all your…2. Prove from the definition that 2n2 + 100n log n + 1000 = O(n2) 3. For what values of n is 50 n lg n greater than 0.5 n2? Why do we say that 0.5 n2 is asymptotically larger, if 50 n lg n is larger for many values? (Hint: you may need to graph the functions or play around with your calculator.)
- The travel time function of an algorithm has the form: f(n) = 3n^2+4n+8.a. Determine the values of c and n0, so that big-oh O(n^2) satisfies the rule f(n) <= cg(n); n≥n0,b. Show (picture) the graphs of f(n) and g(n).Given is a strictly increasing function, f(x). Strictly increasing meaning: f(x)< f(x+1). (Refer to the example graph of functions for a visualization.) Now, define an algorithm that finds the smallest positive integer, n, at which the function, f(n), becomes positive. The things left to do is to: Describe the algorithm you came up with and make it O(log n).Running Time Analysis: Give the tightest possible upper bound for the worst case running time for each of the following in terms of N. You MUST choose your answer from the following (not given in any particular order), each of which could be reused (could be the answer for more than one of a) – f)): O(N2), O(N3 log N), O(N log N), O(N), O(N2 log N), O(N5), O(2N), O(N3), O(log N), O(1), O(N4), O(NN), O(N6)