Give a recursive algorithm that takes as input two non-negative integers x and y and returns the sum of x and y. The only arithmetic operations your algorithm can perform are Increment(x) which returns x 1 and Decrement(x) which returns x-1. Your algorithm should have no loops.

The recursive program which calls itself in a function is used to return the value of y for a given x, y value in the program. The code written in python 3 goes thus :

def calc_sum (x,y) :

#initializes a function named calc_sum which takes in two arguments

if x ==0 :

#checks of the value of x is equal to 0

return y

#it returns y if x == 0

else :

#otherwise

x = x - 1

# decrease the value of x by 1

y = y + 1

#increase the value of y by 1

return calc_sum(x,y)

# calls the function recursively until x ==0

A sample run of the program is given below

print(calc_sum(4, 5 ))

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Following are the code to this question:

Cal_sum(x,y)//defining a recursive method Cal_sum that takes two variable as a parameter

{

if(x==0)// defining If that checks x equal to 0

return y; //return y value

x- 1;//decreasing x value  

y+1;//increasing y value

return Cal_sum(x,y)// calling method recursively

}

Explanation:

In the above-given code, a recursive method "Cal_sum" is declared, that accepts two-variable "x and y" in its parameter, and use if block to checks x is equal to 0 and return the value y variable, and, in the next step, it decreases the value of " x" by "1" and increment the value of y by "1", and call the method "Cal_sum" recursively.