Write a recursive function that takes a start index, array of integers, and a target sum. Your goal is to find whether a subset of the array of integers adds up to the target sum. The start index is initially 0. A target sum of 0 is true for any array.

Here is the recursive function:

public static boolean subsetSum(int start, int[] nums, int target) { //method definition

   if (start >= nums.length) //base case

   return (target == 0);

  if(subsetSum(start + 1, nums, target - nums[start]) || subsetSum(start + 1, nums, target)) //recursive case

 return true;  

 return false; }

Explanation:

Here is the complete program to test the working of the above method:

public class Main { //class name

public static void main(String[] args) { //start of main method

 int[] nums = {2, 4, 8}; //creates and initializes array

System.out.println(subsetSum(0,nums,10)); } //calls method by passing start index i.e. 0, nums array and 10 is target sum

public static boolean subsetSum(int start, int[] nums, int target) { //method that takes start index, integer array and target sum as parameters

       if (start >= nums.length) //if start index is greater than or equals to length of the array (base case)

               return (target == 0); //returns target == 0

      if(subsetSum(start + 1, nums, target - nums[start]) || subsetSum(start + 1, nums, target)) //recursive case to find whether a subset of the array of integers adds up to the target sum

                return true; //returns true if the above condition is true

 return false; } } //returns false if above condition is false

I will explain the program with the help of an example:

Lets say the num array has elements: 2,4 and 8. The method subsetSum works as follows:

Here start = 0

nums[] = {2,4,8}

target = 10

if (start >= nums.length) becomes:

if (0>= 3) this statement is false so the program moves to the recursive part:

if(subsetSum(start + 1, nums, target - nums[start]) || subsetSum(start + 1, nums, target))  this becomes:

if(subsetSum(0+ 1, {2,4,8}, 10 - nums[0]) || subsetSum(0+ 1, {2,4,8}, 10))

if(subsetSum(1, {2,4,8}, 10 - 2) || subsetSum(1, {2,4,8}, 10))

if(subsetSum(1, {2,4,8}, 8) || subsetSum(1, {2,4,8}, 10))

Now this method calls itself recursively to  find whether a subset of the array nums adds up to 10.

The above recursive condition evaluates to true so the function returns true. The screenshot of program and its output is attached.

the answer is e ; )(: