Give a recursive algorithm for the sequential search and explain its running time.
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A: Please refer to the following step for the complete solution of the problem above.
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Q: Question: Let t(x) be the number of primes that are <x. Show that T(x) is primitive recursive.
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A: Answer: I have given answered in the handwritten format in brief explanation.
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A: SUMMARY: -Hence, we got the result
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- The Tower of Hanoi is a puzzle where n disks of different sizes arestacked in ascending order on one rod and there are two other rods with nodisks on them. The objective is to move all disks from the first rod to thethird, such that:- only one disk is moved at a time- a larger disk can never be placed on top of a smaller oneWrite a recursive function that outputs the sequence of steps needed tosolve the puzzle with n disks.Write a test program in C++ that allows the user to input number of disks andthen uses your function to output the steps needed to solve the puzzle.Hint: If you could move up n−1 of the disks from the first post to thethird post using the second post as a spare, the last disk could be moved fromthe first post to the second post. Then by using the same technique you canmove the n−1 disks from the third post to the second post, using the firstdisk as a spare. There! You have the puzzle solved. You only have to decidewhat the nonrecursive case is, what the recursive…using recursion python Consider the English alphabet consisting of 26 lowercase letters: a, b, c, · · ·, x, y, z. • To this order, letters appear earlier are defined smaller. For example, the letter a is smaller than the letter b, and z is the largest letter since it appears last in the alphabet. • The least letter of an English word is the smallest letter that appears in that word. For example, the least letter of “Saturday” is “a”, and the least letter of “hello” is “e”. You are asked to write a program consisting of a function and a main interface as follows. (a) function recur_least_letters(l): Goal: collects all the least letters of words in list l (one least letter for each word) and returns the string of the obtained least letters in the order that the corresponding words appear in list l. • Input: a list l of English words • Output: string of all the least letters of words appearing in list l • Example: input: l = [‘today’, ‘is’, ‘saturday’] → output: “aia” Recursion is…Write a recursive function recursiveMinimum that takes an integer array, a starting subscript, and an ending subscript as arguments, and returns the smallest element of the array. The function should stop processing and return when the starting sub- script equals the ending subscript. c++
- Write a C program that uses a recursive function to find the maximum value in an array of integers using pointers. The program should take user input for the size of the array and the elements of the array, and then use pointers to recursively find the maximum value.Consider the following recursive function to compute factorialint fact (int n) {if (n <= 1)return 1;elsereturn n * fact(n-1);}int main() {cout << fact(5) << endl;return 0;} Show the stack of activation records each time the function fact is called (either directly or recursively). Each activation record needs to be identified by the name of the function and the parameter value, but there is no need to elaborate the specific content of each activation record.Question#1: Let P and Q be integers and suppose F (P, Q) is recursively defined by: F(int P, int Q) if (P == 0) return Q else return F(P- 1, P + Q) Find and Trace F(8,1)
- 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…Write and test a recursive function max to find the largest number in a list.The max is the larger of the first item and the max of all the other items.A palindrome is a sentence that contains the same sequence of letters reading it either forwards or backwards. A classic example is '1\.ble was I, ereI saw Elba." Write a recursive function that detects whether a string is apalindrome. The basic idea is to check that the first and last letters of thestring are the same letter; if they are, then the entire string is a palindromeif everything between those letters is a palindrome.There are a couple of special cases to check for. If either the first orlast character of the string is not a letter, you can check to see if the restof the string is a palindrome with that character removed. Also, when youcompare letters, make sure that you do it in a case-insensitive way.Use your function in a program that prompts a user for a phrase andthen tells whether or not it is a palindrome. Here's another classic fortesting: '1\. man, a plan, a canal, Panama!"
- In order to accomplish the task of terminating recursion, you must first describe three distinct types of recursion, a high-level description of each kind, and a specific technique that fits into each category.For function decToBinary, write the missing parts of the recursion case. This function should return a string that stores the binary equivalent for int variable num. Example: The binary equivalent of 13 may be found by repeatedly dividing 13 by 2. So, 13 in base 2 is represented by the string "1101". Examples: decToBinary(13) -> "1101" public String decToBinary (int num) { if (num < 2) return Integer.toString(num); else return <<Missing recursive call>> + <<Missing calculation>>;}implement QuickSort of ints that sorts the numbers in the non-decreasing order and in c language Implement the rearrange function used for QuickSort using the O(n) time algorithm with two pointers. The function gets as input an array, and index of the pivot. The function rearranges the array, and returns the index of the pivot after the rearrangement. please write form as: int rearrange(int* A, int n, int pivot_index); 2, Implement the QuickSort algorithm. For n<=2 the algorithm just sorts the (small) array (smaller number first). - For n>=3 the algorithm uses the rearrange function with the pivot chosen to be the median of A[0], A[n/2], A[n-1]. write as form: void quick_sort(int* A, int n);