Design an algorithm to find the kth number such that the only prime factors are 3, 5, and 7. Note that 3, 5, and 7 do not have to be factors, but it should not have any other prime factors. For example, the first several multiples would be (in order) 1, 3, 5, 7, 9, 15, 21.
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- Computer Science Use the non-restoring division algorithm to compute the division of a dividend X = 14 = (1110) and a divisor D = 6 = (0110).Nuts and bolts You are given a collection of n bolts of different widths and n corresponding nuts. You are allowed to try a nut and bolt together, from which you can determine whether the nut is larger than the bolt, smaller than the bolt, or matches the bolt exactly. However, there is no way to compare two nuts together or two bolts together. The problem is to match each bolt to its nut. Design an algorithm for this problem with average-case efficiency in (n log n).Let n be a positive integer and let MaxCrossing(n) be a function that returns the maximum number of line crossings that you can create by drawing n straight lines. Write down a recursive formula for MaxCrossing(n) and analyze the time complexity of the corresponding recursive algorithm. You must write a formal recursive formula including the base case and general recursive step. Note: if n=1, there is 0 crossing, if n = 2, there is 1 crossing, if n = 3, there are 3 crossings (not only 2) if n = 4, there are 6 crossings (not only 3) if n = 5, there are 10 crossings, etc.
- The first time you run algorithm A on a dataset of n elements; it is faster than algorithm B. The second time you run algorithm A on a dataset of n elements; it is slower than algorithm B. Explain how this is possible. Give an example for algorithm A and algorithm B.You are asked to sort n English words alphabetically. What is the best achievable complexity? (Note: we are talking about actual English words that can be found in a Marriam-Webster dictionary.) Describe the algorithm that achieves the best complexity.Let n be a positive integer and let MaxCrossing(n) be a function that returns the maximum number of line crossings that you can create by drawing n straight lines. Write down a recursive formula for MaxCrossing(n) and analyze the time complexity of the corresponding recursive algorithm. You must write a formal recursive formula including the base case and general recursive step.
- Overview One of the oldest methods for computing the square root e of a number is the Babylonian Method e. The Babylonian Method uses an iterative algorithm to make successively more accurate estimates of a number's square root. The algorithm stops iterating when the estimate shows no further sign of improvement, or when the estimate is within some acceptable margin of error. The acceptable margin of error is often called an epsilon. Assuming that you need to solve for the square root of x, the algorithm works as follows. 1. Choose an epsilon value that determines how close your solution should be to the actual square root value before you decide it is "good enough." Because this assignment asks you to solve for the square root to three decimal places, we can safely set the epsilon value to 0.0001 (four decimal places). This guarantees that our solution will be accurate to the precision we need to display to the screen. 2. Choose an initial estimate e for the square root of x. An easy…You have an array of 10,000 subject scores for a high-school exam and you want to find the scores that are ranked from 4900 to 5100 that is the 201 most middle-ranked scores. Precisely describe two alternative algorithmic ap proaches to doing this - one of which is, in terms of time complexity, more efficient than the other.Euclid’s algorithm (or the Euclidean algorithm) is an algorithm that computes thegreatest common divisor, denoted by gcd, of two integers. Below are the original versions ofEuclid’s algorithm that uses repeated subtraction and another one that uses the remainder.int gcd_sub(int a, int b){ if (!a) return b; while (b) if (a > b) a = a – b; else b = b – a; return a;}int gcd_rem(int a, int b){ int t; while (b) { t = b; b = a % b; a = t; } return a;}1. Trace each of the above algorithm using specific values for a and b.2. Compare both algorithms.
- Weighted Intervals Problem EXAMPLE:Suppose we have the following weighted intervals. start finish weight 11 14 4 10 13 5 9 11 5 11 14 3 8 9 2 To solve the problem, we start out by sorting the intervals by finish time. This gives us the following. start finish weight 8 9 2 9 11 5 10 13 5 11 14 4 11 14 3 Next we calculate the p-values. P(j) = k where interval k is the last interval prior to interval j in the list below which does not conflict with interval j, or P(j) = 0 if all intervals prior to interval j conflict with it. # start finish weight P 1 8 9 2 0 2 9 11 5 1 3 10 13 5 1 4 11 14 3 2 5 11 14 4 2 Finally, we use the formula OPT(j) = max{OPT(j-1), weight(j)+ OPT(P(j))} to fill in the OPT value for each j. (The…The following algorithm construct a sequence of positive whole numbers, which demonstrates the famous Collatz's conjecture: starting from any positive whole number, the sequence will eventually go down to 1. By tracing the algorithm, how many times does the algorithm perform Step 3.2.1. if the input is set to ?For the following problem please write an algorithm in plain English .i.e give details as to how you will solve the problem.A deck of 52 playing cards (as used for playing bridge) has to be sorted. At the end of the attempt, the sorted deck of cards should be on the table with the backside up.The order within a suite is Ace - King - Queen - Jack- 10 -9 - 8 - 7- 6- 5- 4- 3- 2. The very first card in the sorted deck is the Ace of Clubs, the next ones are the King of Clubs, the Queen of Clubs, the Jack of Clubs, the 10 of Clubs ... down to the 2 of Clubs. The next card is Ace of Spades, followed by the King of Spades etc. The hearts and diamonds cards follow in the same order.The deck of cards must be well-shuffled immediately prior to the challenge.Please write the algorithm in steps like you write a recipe for a dish.If any steps need to be repeated try to use a loop.Please try to not use any programming language.(IT's one question just with a lot of instructions to be understood well)