Recursive program to print formula for GCD of n integers
Given a function gcd(a, b) to find GCD (Greatest Common Divisor) of two number. It is also known that GCD of three elements can be found by gcd(a, gcd(b, c)), similarly for four element it can find the GCD by gcd(a, gcd(b, gcd(c, d))). Given a positive integer n. The task is to print the formula to find the GCD of n integer using given gcd() function.
Input : n = 3 Output : gcd(int, gcd(int, int)) Input : n = 5 Output : gcd(int, gcd(int, gcd(int, gcd(int, int))))
Approach: The idea is to use recursion to print the single line command. Now, to write a recursive function, say recursiveFun(n), the required string is composed of gcd(int, + recursiveFun(n – 1) + ). This means that the recursiveFun(n) should return a string that contains a call to itself and in order to evaluate that value, the recursive function will begin again for n – 1. This will, in turn, return another string with a call to n – 1 and so until n == 1 and the recursive function instead returns the string “int”.
Below is implementation of the above approach:
gcd(int, gcd(int, gcd(int, gcd(int, int))))
Time Complexity: O(N), where N is the given number.
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