Question

Subset Sum-2 Write an algorithm (in comments) and specify the big O, and a C program to solve the problern below. Read the input for the set elements, the value of K from the user. Assume the size of the set is not bigger than 20. Subset Sum-3 Write an algorithm (in comments) and specify from the user. Assume the size of the set is not bigger than 20 1. Given a finite set of integers, is there a subset the big O, and a C program to solve the problem below. Read the input for the set elements, the value of K s there a non-empty subset with the sum of the elements being greater than K J and less than Ku ? Write an algorithm (in comments) and specify the big O, and a C program to solve the problem below. Read the input for the set elements, the value of K, from the user. Assume the size of the set is not bigger than 20. 1. Given a finite set of positive integers, is there a non-empty subset with the sum of the elements being equal to K2 MacBook Air

Answer 1

as per HomeworkLib rules i cannot answer more than one question so please post again for the rest.

• The problem is to tell whether there is a subset in a set in which the sum of all elements is less than given 'K'
• we have to return true or false as answer as to whether such a set exists or not

• What is important to note here that size of a subset of a set can be as small as a single element. eg:-{1,2,3,4,5} the subset of this set can be {1},{2},{3},{4},{5},{1,2},{1,3}... etc
• so to test whether a subset exists whose sum of elements is less than 'K' we just need to find out if there is a single element in the parent set whose value is less than K.
• eg: suppose a set {1,2,3}, here K=2, subsets of set - {1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}, now subset {1} is the only subset in which sum of all elements is less than K(2), bu the important point is that the subset {1} contains only a single element.
• Hence In order to find out whether any subset of a set exists whose sum is less than K, we just need to check whether there is any single element in the parent set whose value is less than K, if there is then return TRUE otherwise return FALSE

ALGORITHM

// Take a set of elements as input

// Take K as input

// Iterate from first to last element of the set

// if while iterating any element in the set is found whose value is less than K, end loop and return TRUE from the function

// if the iteration ends and no element in the set is found whose value is less than K return FALSE

C CODE

#include <stdio.h>

// function which checks whether any element exists in the set which is less than K
// function takes three parameters
// arr- array of elements
// n- size of array
// K- value for comparison
int check(int *arr,int n,int K)
{
   // iterate through the array
   for(int i=0;i<n;i++)
   {
       // if any element exist which is less than K return true
       if(arr[i]<K)
           return 1;
   }
  
   // no element exist which is less than K so return false
   return 0;
}

int main(void) {

   // number of elements in the set
   int n;
   scanf("%d",&n);
  
   // array of numbers
   int arr[n];
  
   // input of set elements
   for (int i=0;i<n;i++)
       scanf("%d",&arr[i]);

   // value for comparison 'K'
int K;
   scanf("%d",&K);
  
   // call check() function and see whether it return true or false
   if(check(arr,n,K))
       printf("Yes there exists a subset of the given set whose sum of elements is less than K");
   else
       printf("No such subset exists");
  
   return 0;
}

OUTPUT:

5 //(number of elements)

1 2 3 4 5 //elements of set

2 //K

Yes there exists a subset of the given set whose sum of elements is less than K

BIG-O

The Big-O of above algorithm is O(n), where 'n' is number of elements in the set

In worst-case the algorithm will have to iterate from first element of the set to last element of the set to find out whether there exists any element whose value is less than K