## Subset sum problem

Given a set of numbers, check whether it can be partitioned into two subsets such that the sum of elements in both subsets is same or not. Input: The first line contains an integer ' T ' denoting the total number of test cases. Each test case constitutes of two lines. First line contains ' N ', representing the number of elements in the set and the second line contains the elements of the set.

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You will get quick replies from GFG Moderators there. Please choose 'ReadOnlyMode' if you needn't to 'Edit' the problem e. Please note that Custom Input s should be mentioned in the same order format as stated in the problem description.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I'm having a problem with counting which is continuation of this question. I am not really a math person so it's really hard for me to figure out this subset sum problem which was suggested as resolution. Type Transaction Number Price 8 Buy I'm adding numbers to ArrayList likewhen it is TransferIn or Buy etc and then i remove them doing it likewhen it's TransferOut, Sell.

My solution works for that without a problem. Edit: Since some of you were so astonished and blinded by my polish variable names i translated all of them to english for simplicity and visiblity. Hopefully this will help me to get some help How you should do this depends on a number important things: how many numbers will you have and how big will they be? How often do you need to make these queries? I'll present two solutions. I suggest you use the second, as I suspect it's better for what you need and it's a lot easier to understand.

You would update this accordingly in the if condition above. It's also slow for even one run as long as your numbers can be very big and you can have a lot of them. In fact, "a lot" is misleading. It's a good solution to know, but not really useful in practice, or at least not in your case I think. You should do some error checking perhaps, and maybe store the last sum in the class so as not to allow the possibility of calling GetLastResult with a different sum than the sum Find was last called with.

Anyway, this is the idea.

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Now, this is easier. Keep two lists: usedNums and unusedNums. Also keep a variable usedSum that, at any point in time, contains the sum of all the numbers in the usedNums list. Whenever you need to insert a number into your set, also add it to one of the two lists doesn't matter which, but do it randomly so there's a relatively even distribution.

Update usedSum accordingly.

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Whenever you need to remove a number from your set, find out which of the two lists it's in. You can do this with a linear seach as long as you don't have a lot this time a lot means over 10maybe even on a fast computer and assuming you don't do this operation often and in fast succession. Anyway, the linear search can be optimized if you need it to be.We are considering the set contains non-negative values.

It is assumed that the input set is unique no duplicates are presented. One way to find subsets that sum to K is to consider all possible subsets. A power set contains all those subsets generated from a given set. The size of such a power set is 2 N. Backtracking can be used to make a systematic consideration of the elements to be selected.

## Dynamic Programming – Subset Sum Problem

Tree diagrams can be used to design backtracking algorithms. In the above tree, a node represents function call and a branch represents candidate element. The root node contains 4 children. The branches at each level represent tuple element to be considered. For example the left most child of root generates all those subsets that include w[1].

Similarly the second child of root generates all those subsets that includes w[2] and excludes w[1]. The tree should trigger a clue to implement the backtracking algorithm try yourself.

### Subset Sum

It prints all those subsets whose sum add up to given number. We need to explore the nodes along the breadth and depth of the tree. Generating nodes along breadth is controlled by loop and nodes along the depth are generated using recursion post order traversal. Pseudo code given below. Following is C implementation of subset sum using variable size tuple vector.

Note that the following program explores all possibilities similar to exhaustive search. It is to demonstrate how backtracking can be used. See next code to verify, how we can optimize the backtracking solution. The power of backtracking appears when we combine explicit and implicit constraints, and we stop generating nodes when these checks fail.

We can improve the above algorithm by strengthening the constraint checks and presorting the data. By sorting the initial array, we need not to consider rest of the array, once the sum so far is greater than target number. We can backtrack and check other possibilities. Similarly, assume the array is presorted and we found one subset.

Given below is optimized implementation it prunes the subtree if it is not satisfying contraints. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. Attention reader! Writing code in comment? Please use ide.

Subset Sum Problem Dynamic Programming

Load Comments. We use cookies to ensure you have the best browsing experience on our website.Subset sum problem is the problem of finding a subset such that the sum of elements equal a given number.

The backtracking approach generates all permutations in the worst case but in general, performs better than the recursive approach towards subset sum problem.

A subset A of n positive integers and a value sum is given, find whether or not there exists any subset of the given set, the sum of whose elements is equal to the given value of sum. In Backtracking algorithm as we go down along depth of tree we add elements so far, and if the added sum is satisfying explicit constraints, we will continue to generate child nodes further.

Whenever the constraints are not met, we stop further generation of sub-trees of that node, and backtrack to previous node to explore the nodes not yet explored. We need to explore the nodes along the breadth and depth of the tree. Generating nodes along breadth is controlled by loop and nodes along the depth are generated using recursion post order traversal. We will follow our backtracking approach. Share this. Visit our discussion forum to ask any question and join our community View Forum.The Subset-Sum Problem can be solved by using the backtracking approach.

In this implicit tree is a binary tree. The root of the tree is selected in such a way that represents that no decision is yet taken on any input. We assume that the elements of the given set are arranged in increasing order:. The left child of the root node indicated that we have to include 'S 1 ' from the set 'S' and the right child of the root indicates that we have to execute 'S 1 '.

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Each node stores the total of the partial solution elements. If at any stage the sum equals to 'X' then the search is successful and terminates.

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Obtain the subset sum using Backtracking approach. Thus, if our partial solution elements sum is equal to the positive integer 'X' then at that time search will terminate, or it continues if all the possible solution needs to be obtained.

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## Subset-Sum Problem

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Control S. Data Mining. Javatpoint Services JavaTpoint offers too many high quality services. The dead end in the tree appears only when either of the two inequalities exists: The sum of s' is too large i.You have to find whether there exists a non-empty subset of A whose sum is greater than or equal to S.

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You have to print the size of minimal subset whose sum is greater than or equal to S. If there exists no such subset then print -1 instead. Input First line will contain an integer, Nwhich is the size of list A. Second line contains N space separated integers, representing the elements of list A. In third line there is an integer, Twhich represent the number of test cases to follow.

Then follows T lines. Each one of them contains an single integer, S. Output For each test case, print the size of minimal subset whose sum is greater than or equal to S. If there's no such subset then print Note Two subsets are different if there's an element a[i] which exists in one of them and not in other. Sample Case There are many possible subsets of size 2 whose sum is not less than We use cookies to ensure you have the best browsing experience on our website.

Please read our cookie policy for more information about how we use cookies. Practice Certification NEW. Problem Submissions Leaderboard Discussions.Given a set of non-negative integers, and a value sumdetermine if there is a subset of the given set with sum equal to given sum.

Complexity Analysis: The above solution may try all subsets of given set in worst case. Therefore time complexity of the above solution is exponential.

The problem is in-fact NP-Complete There is no known polynomial time solution for this problem. Method 2 : To solve the problem in Pseudo-polynomial time use the Dynamic programming.

So we will create a 2D array of size arr. The state DP[i][j] will be true if there exists a subset of elements from A[0…. The approach for the problem is:. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. Attention reader! Writing code in comment? Please use ide. A recursive solution for subset sum. Returns true if there is a subset. Base Cases. If last element is greater than.

Driver program to test above function. This code is contributed by Nikita Tiwari. WriteLine "Found a subset with given sum". WriteLine "No subset with given sum". A Dynamic Programming solution for subset. Returns true if there is a subset of set[].

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The value of subset[i][j] will be. If sum is 0, then answer is true. If sum is not 0 and set is empty. Fill the subset table in botton up manner.

This code is contributed by. Load Comments. We use cookies to ensure you have the best browsing experience on our website.