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- Remove the left recursion from the productions: S ->A a |b A ->A c |S d | €Q4. Recursion Find how many possible combinations that a number can be decomposed into the multiple of integers (smaller than the number itself) by a recursion function.Suppose we have a positive number Y as input, and it need to be decomposed into the multiple of several integers, Yi, where each Yi, is smaller than Y(e.g., Y=Y1∗Y2∗ Y3∗...∗Yn). In addition, these decomposed integers can only be arranged in an ascending order (Y1Remove left recursions only from:S -> Sa | SBa | aS | bA -> aa | bAB -> ba | b |
- Remove indirect recursion A---->aA | Ab | Bab | C | d B---->AC | Ad | C C----> Ad | dQuestion 10 Code the following in Java using Recursion1. Write a recursive function named RecursiveSum that, given a positive number n (n> 0), returns the sum of the numbers from 1 to n. Also, show the process of finding the result using a recursion tree.
- ce from the user t using recursion.Task 4: The first problem that you solve recursively is to implement enoughGate() to check if the dogMaze has at least two gates (one for the entrance and one for the exit). This problem must be solved recursively, however there is no limitation on what type of recursion (i.e., direct or indirect recursion) you use . As a reminder, a direct recursion refers to the function that calls itself to solve the given problem. However, by indirect recursion, more than one function involves in solving the problem. It is possible that a non-recursive function solves a small part of the problem and then calls the recursive function to finish the job. /** * This method returns true if the number of * gates in dogMaze >= 2. * @return it returns true, if enough gate exists (at least 2), otherwise false. */ publicboolean enoughGate (){ // insert your code here. Change the return value to fit your purpose. return true; }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>>;}
- PLZ help with the following: In Java Write a program using recursion to display all valid (i.e. properly open and closed) combinations of n-pairs of parentheses.The following recursion occurs when there are more than two calls for each non-base case: : c)Multiple recursion d)Two Step Recursion a)Linear recursion b)Binary recursionQuestion#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)