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- The Famous Gauss You must know about Gauss, the famous mathematician. Back in late 1700’s, he was at elementary school. Gauss was asked to find the sum of the numbers from 1 to 100. The question was assigned as “busy work” by the teacher. He amazed his teacher with how quickly he found the sum of the integers from 1 to 100 to be 5050. Gauss recognized he had fifty pairs of numbers when he added the first and last number in the series, the second and second-last number in the series, and so on. For example:(1 + 100), (2 + 99), (3 + 98), ..., (50 + 51). Each pair has a sum of 101 and there are 50 pairs. History repeats itself. Jojo’s teacher assign a “busy work” to the students. The teacher believes that there will be no shortcut to finish this task in a minute. The teacher gives N integers A1, A2, ..., AN to the students. The teacher also gives Q questions. Each question contains two integers L and R asking the sum of all Ai where L <= Ai <= R. As a good friend of Jojo, help Jojo…arrow_forwardDevelop pseudocode for the problem of reading in an arbitrary number of DNA (deoxyribonucleic acid) bases, one at a time, and print out the complementary base sequence in the same order as the DNA bases were input. There are four DNA bases: A (adenine), C (cytosine), G (guanine), T (thymine). You should verify that a correct base is input each time and print out an error message if it is incorrect. Assume that “!” is used as the input symbol to indicate that no more DNA bases will be entered (i.e., it is the end of the DNA base sequence). The following table shows the complementary base for each DNA base: DNA Base Complementary Base A T C G G C T A As an example, if the input is “ATGGTCA”, then the output should be “TACCAGT”.arrow_forwardDesign and implement a recursive program to determine and print the Nth line of Pascal’s Triangle, as shown below. Each interior value is the sum of the two values above it. (Hint: Use an array to store the values on each line.) 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 11 8 28 56 70 56 28 8 1arrow_forward
- What are the advantages and disadvantages of iterative algorithms compared to recursive algorithms, and in what scenarios would you prefer to use one over the other?arrow_forwardCompare the number of operations and time taken to compute Fibonacci numbers recursively versus that needed to compute them iterativelyarrow_forwardRECURSIVE PYTHON The Fibonacci sequence begins with 0 and then 1 follows. All subsequent values are the sum of the previous two, for example: 0, 1, 1, 2, 3, 5, 8, 13. Complete the fibonacci() function, which takes in an index, n, and returns the nth value in the sequence. Any negative index values should return -1. Ex: If the input is: 7 the output is: fibonacci(7) is 13 Note: Use recursion and DO NOT use any loops. # TODO: Write recursive fibonacci() functiondef fibonacci(): if __name__ == "__main__": start_num = int(input()) print('fibonacci({}) is {}'.format(start_num, fibonacci(start_num)))arrow_forward
- Demonstrate as many algorithmic paradigms as possibleto write a program that raises the number X to the power n (Xn).arrow_forward2) A computer science student designed two candidate algorithms for a problem while working on his part-time job The time complexity of these two algorithms are T1(n) = 3 n log n and T2(n) = nº/5 . a) Which algorithm is better? Why? b) If we run both algorithms at the same time with an input size of 105, which algorithm produces results faster than the other one? Why?arrow_forwardImplement c# program to compare the times it takes to compute a Fibonacci number using both the recursive version and the iterative version.arrow_forward
- Recursion can be direct or indirect. It is direct when a function calls itself and it is indirect recursion when a function calls another function that then calls the first function. To illustrate solving a problem using recursion, consider the Fibonacci series: - 1,1,2,3,5,8,13,21,34...The way to solve this problem is to examine the series carefully. The first two numbers are 1. Each subsequent number is the sum of the previous two numbers. Thus, the seventh number is the sum of the sixth and fifth numbers. More generally, the nth number is the sum of n - 2 and n - 1, as long as n > 2.Recursive functions need a stop condition. Something must happen to cause the program to stop recursing, or it will never end. In the Fibonacci series, n < 3 is a stop condition. The algorithm to use is this: 1. Ask the user for a position in the series.2. Call the fib () function with that position, passing in the value the user entered.3. The fib () function examines the argument (n). If n < 3…arrow_forwardComputer Science Perform the given polynomial arithmetic in GF (23) modulo the given polynomial e.g. (x3 + x2 + 1): For example: 011 + 011 or 111 * 111 etc.arrow_forwardAn arithmetic sequence a starts 84,77,... Define a recursively Define a for the n th termarrow_forward
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