Table of Contents

## What is the sum of the subset problem?

The SUBSET-SUM problem involves determining whether or not a subset from a list of integers can sum to a target value. For example, consider the list of nums = [1, 2, 3, 4] . If the target = 7 , there are two subsets that achieve this sum: {3, 4} and {1, 2, 4} . If target = 11 , there are no solutions.

## How do you prove subset sum is NP-complete?

To establish that Subset Sum is NP-complete we will prove that it is at least as hard asSAT. Theorem 1. SAT ≤ Subset Sum. ajBj, and we set the base B as B = 2 maxj kj, which will make sure that additions among our numbers will never cause a carry.

**What is a subset sum problem * 1 point?**

Explanation: in subset sum problem check for the presence of a subset that has sum of elements equal to a given number.

**Why is subset sum not polynomial?**

A problem is strongly NP-Complete when it remains NP-Complete even when all the numeric values are polynomial in the input length. SUBSET-SUM isn’t (it’s called weakly NP-Complete). The kind of running time that is polynomial in the numeric values in the input is known as pseudo-polynomial.

### Is subset sum a problem in NP?

The number of additions is at most n-1. So the addition and comparision can be done in polynomial time. Hence, SUBSET-SUM is in NP.

### Why is subset sum problem NP-hard?

An instance of the subset sum problem is a set S = {a1, …, aN} and an integer K. Since an NP-complete problem is a problem which is both in NP and NP-hard, the proof for the statement that a problem is NP-Complete consists of two parts: The problem itself is in NP class.

**Why is Subset sum problem NP-hard?**

**Is subset sum NP hard?**

SSP can also be regarded as an optimization problem: find a subset whose sum is at most T, and subject to that, as close as possible to T. It is NP-hard, but there are several algorithms that can solve it reasonably quickly in practice.

#### Which of the following is not true about subset sum problem?

Which of the following is not true about subset sum problem? Explanation: Recursive solution of subset sum problem is slower than dynamic problem solution in terms of time complexity. Dynamic programming solution has a time complexity of O(n*sum).

#### What is Subset sum problem discuss the possible solution strategies using backtracking?

Subset sum problem is to find subset of elements that are selected from a given set whose sum adds up to a given number K. We are considering the set contains non-negative values. It is assumed that the input set is unique (no duplicates are presented).

**What is Subset sum problem in backtracking?**

**How do you solve the subset sum problem?**

The Subset-Sum Problem is to find a subset’s’ of the given set S = (S 1 S 2 S 3 …S n) where the elements of the set S are n positive integers in such a manner that s’∈S and sum of the elements of subset’s’ is equal to some positive integer ‘X.’ The Subset-Sum Problem can be solved by using the backtracking approach.

## Is there a subset whose sum is zero?

In computer science, the subset sum problem is an important problem in complexity theory and cryptography. The problem is this: given a set (or multiset) of integers, is there a non-empty subset whose sum is zero? For example, given the set {−7, −3, −2, 5, 8}, the answer is yes because the subset {−3, −2, 5} sums to zero.

## What is an approximate version of the subset sum?

An approximate version of the subset sum would be: given a set of N numbers x 1, x 2., x N and a number s, output yes, if there is a subset that sums up to s; no, if there is no subset summing up to a number between (1 − c)s and s for some small c > 0;

**Is there a non-empty subset such that the sum is m integer?**

The question arises that is there a non-empty subset such that the sum of the subset is given as M integer?. For example, the set is given as [5, 2, 1, 3, 9], and the sum of the subset is 9; the answer is YES as the sum of the subset [5, 3, 1] is equal to 9.