Print All Subset Recursion

One String is permutation of other or not? Reverse String; Is. Recursion Generating all subsets All subsets of a set 2 Design a recursive algorithm that will output all. The basic idea is say we have A = [1, 2, 3], and f(n, subset) be the solution then: * we start with an empty array and end of the array: f(3, []) * at every state we have 2. This is the best place to expand your knowledge and get prepared for your next interview. The best subsets regression is a model selection approach that consists of testing all possible combination of the predictor variables, and then selecting the best model according to some statistical criteria. Note that this solution is not unique. In many settings, it is a useful way to describe the natural world. * Uses some String library functions. In the solution below, we generate all combinations of subsets by using above logic. Print array using recursion JAVA Example in Recursion - Data structures and Algorithms by Java Examples. Then it gets a list of all files and folders in this directory using the os. In the first case, there must be a subset of X \{x} that sums to T x; in the second case, there must be a subset of X \{x} that sums to T. If the sum so far is equal to the target, we * have found the desired subset and can immediately return true. // Print all subsets of e with n elements, one subset per line, // assuming all elements of e are distinct, and 0 <= n <= e. CMU 15-112: Fundamentals of Programming and Computer Science Class Notes: Recursion (Continued). Write a recursive program that finds all subsets of numbers in the array, which have a sum N. Print all possible words from phone number digits. After combing through dozens of common recursive problems, I've categorized all recursive problems into one of 6 categories. Approaching the problem. The running time is of order O(2 N N), since there are 2 N subsets and, to check each subset, we need to sum at most N elements. We are also not allowed to use any advanced functions. Returns all subsets of a given set. This dictates the placement of the printing relative to the recursion. Any help? counter(){ list=`ls $1` if [ -z "$(ls $1)" ] then. It also prints the empty subset. Motivation: you have a CPU with W free cycles, and want to choose the set of jobs (each taking w i time) that minimizes the number of. 10/2/2017 5:33:10 PM. Otherwise: Fix some element x of the set. Therefore time complexity of the above solution is exponential. java * Execution: java Combinations n * * Enumerates all subsets of n elements using recursion. Given a set S, the power set (or powerset) of S, written P(S), or 2 S, is the set of all subsets of S. C++ recursive string subset? Hi, I have the following problem: Write a recursive function that returns a vector of strings containing all subsets of a string value passed in (the passed string represents a set of characters just like a vector of char's). It uses both loop and recursive call to solve this problem. Note All linked lists are null-terminated. Recursive method to find all permutations of a String : Recursive Method « Class Definition « Java Tutorial. Submissions: 3218 Show Topic Tags Recursion Hide Topic Tags print sums of all subsets in it. Level up your coding skills and quickly land a job. GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. In this C program, we are going to learn how to sum of all digits using recursion method? Here, a number will be entered through the user and program will calculate sum of all digits. First step (with an array): [code]def subsets(n, min_value=1, stack=None): if stack is None: stack = [] print stack for i in xrange(min_value, n+1): stack. Find all possible permutations of a String is one of the most common question that is asked if you are appearing for any good company. The third argument, maxlevels, gives the requested limit to recursion; this will be 0 if there is no requested limit. Write a Program to Print MATRIX;. display(int n) thanks. This program takes a sentence from user and reverses that sentence using recursion. However, I'm not entirely convinced that using sets is the best way to implement this recipe as this precludes multiples of set elements. Output : 0 5 4 9 3 8 7 12 Thanks to cfh for suggesting above iterative solution in a comment. In the solution below, we generate all combinations of subsets by using above logic. Like Find all subsets of a set [1,2,3n] you can ignore the order in which the subsets are generated. With recursive programs that recurse instead of change state, the number of occasions of state change is small and the program variables maintain self-consistency by setting all of the recursion variables at once. I tried inserting print statements but I'm still not sure. Outline, but do not implement, a recursive solution for finding the smallest value in an array. A better exponential time algorithm uses. of S is the set of all subsets of 16 for recursive. But here I specifically want it do it using the sub-set method which means the first level is divided into 2 groups-(a, bcd) & ("", bcd). isfile method. Print all subsets with given sum. ie: ACEG -->. We can generate all possible subset using binary counter. At the top level of the recursion, we may want to print all anagrams of east, without printing any letters before each anagram. There is a specific language which is recursively enumerable but not recursive Recursive Recursively Enumerable. I need it to work urgently but I am not able to figure out a solution. Guidelines: The problem is not very different from the task with finding all subsets among a given list of strings. Both sets sum to 5, and they partition S. I`ll be thankful if you help me complete/rewrite this script. For example, the power set of {1,2,3,4} is. Over recursive formulations, this one has the advantage of not. Submissions: 3218 Show Topic Tags Recursion Hide Topic Tags print sums of all subsets in it. of S is the set of all subsets of 16 for recursive. Recursion - subsets - C++ and then print out the possible combinations by calling the function recursively. In this moment we have values on all positions and we print the sequence. display(int m, int n), but how can i do it with only a single variable? eg. Input First line will contain an integer, N, which is the size of list A. Here's simple Program to print prime factors using Recursion and Iteration in C Pro. But here I specifically want it do it using the sub-set method which means the first level is divided into 2 groups-(a, bcd) & ("", bcd). In each iteration, we will have one subset. I mostly use Java to code in this post. For example, all possible subsets of a string "FUN" will be F, U, N, FU, UN, FUN. What you've suggested is a recursive permutation algorithm. It uses both loop and recursive call to solve this problem. // First generate all subsets containing n. First program print all subset of a set using for-loop, second program uses bitwise operator to print all subsets and program uses recursion. You can find all subsets of set or power set using recursion. The input is a string and the output should be all the subset s of the characters in the string in alphabetical oder -the input will be in alphabetical order too. Sort list, from negative to positive. One way of solving the problem is to use backtracking. java program to print linked list in reverse. For example: Consider a set 'A' having elements {a, b, c}. CMU 15-112: Fundamentals of Programming and Computer Science Class Notes: Recursion (Continued). java * Execution: java Combinations n * * Enumerates all subsets of n elements using recursion. Many, many phenomena are well explained by recursive models. A much smaller subset is a countable permutation utilizing the Base-N-Odometer model. Print all pair of anagrams in a given array of strings Remove spaces from a string Lexicographic rank of string Print all anagrams together in a sequence of words Count the number of words String(represents an integer) to value Palindromes in a given range Check rearranged string can form a palindrome print all palindromic partitions Minimum. Write a C++ program to print all prime numbers between 1 to 100 using for loop with sample input and output. Please try again later. As would a C or C++ programmer organize and reuse the code using functions or object methods, in XSL, we can organize code using templates. print current subset else {Consider the next element of those remaining Try adding it to the current subset, and use recursion to build subsets from here Try not adding it to current subset, and use recursion to build subsets from here} In this version of the code, the set elements are represented as characters and a string is used to. C program to calculate the power using recursion This program calculates the power of a number using recursion. Dfs Print All to find out where to get the best deal on Dfs Print All. We are also not allowed to use any advanced functions. If new nodes may be created, then report whether or not space was exhausted, using a boolean reference parameter. Is there an algorithm to find all subsets of a set? of your base set the current subset has. First, it's easy to generate all the subsets of a one-element set: they are the empty set and the set containing only the single element. The subset relation defines a partial order on sets. The subset of a string is the character or the group of characters that are present inside the string. Examples: Input : arr[] = {2, 3, 5, 6, 8, 10} sum = 10 Output. Example: Input: 10 -> 20 -> 30 -> 40 -> 50 -> null. So we can solve SS(X,T)by reducing it to two simpler instances: SS(X\{x},. For each positive number, try all subsets of negative numbers that equal the positive number. In the first case, there must be a subset of X \{x} that sums to T x; in the second case, there must be a subset of X \{x} that sums to T. Recursive graphics. * If we have run out of elements to try, we return false. ) Is there any other interview question you'd like me to cover in the future? You can (anonymously) let me know at: www. The following code finds the all permutations of a given string through command prompt using recursion. A recursive routine performs a task in part by calling itself to perform the subtasks. This dictates the placement of the printing relative to the recursion. Here are C++ programs to print all subsets or all combinations of elements in a set. A Print the sum of characters in a String. Print Sum of Even Numbers in Array using Recursion All C Programs To print all the odd number till 'N' Find Subsets of Given String; Find all Words Ended. C++ recursive string subset? Hi, I have the following problem: Write a recursive function that returns a vector of strings containing all subsets of a string value passed in (the passed string represents a set of characters just like a vector of char's). These Instructions explain how to create a new subset in RMCDS. GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. Recursive calls to the format() method should add additional entries for containers to this dictionary. It uses both loop and recursive call to solve this problem. So, you can also try to write a recursive routine that determines all subsets, and map each of these to its sum. Be careful when applying Subsets, Permutations and Combinations. The basic idea is say we have A = [1, 2, 3], and f(n, subset) be the solution then: * we start with an empty array and end of the array: f(3, []) * at every state we have 2. The problem here is how to generate all the subsets of a given set. This feature is not available right now. First step (with an array): [code]def subsets(n, min_value=1, stack=None): if stack is None: stack = [] print stack for i in xrange(min_value, n+1): stack. Two concepts that often come up in the study of combinatorics are permutaions and combinations of a set of discrete elements. These 6 categories, based around the core pattern used to solve the problem, allow us to put a finite bound on the scope of recursive problems that we could need to solve. CMU 15-112: Fundamentals of Programming and Computer Science Class Notes: Recursion (Continued). Output: Found a subset with given sum. // This is done by setting the nth element true // and generating all subsets of the first n-1 elements subset[n-1] = true; recursiveGenSubsets(n-1, subset); // Then generate all subsets not containing n. In the solution below, we generate all combinations of subsets by using above logic. " Subset under $50. Print all pair of anagrams in a given array of strings Remove spaces from a string Lexicographic rank of string Print all anagrams together in a sequence of words Count the number of words String(represents an integer) to value Palindromes in a given range Check rearranged string can form a palindrome print all palindromic partitions Minimum. Therefore, you can represent a subset as an integer where each bit position corresponds to an element of the set, and it is a 1 if that element is contained in the subset, and 0 o. Listing All Subsets The reader invests a good amount of energy talking about how to generate all of the permutations of a string—that is, how given the string PDQ you can programmatically generate: PDQ PQD DPQ DQP QDP QPD The recursive formulation is easily explained in English, but coding it up is a different matter, so. For maximum compatibility, this program uses only the basic instruction set (S/360) and two ASSIST macros (XDECO, XPRNT) to keep the code as short as possible. [Java] Print out all the subsets in a set. Is there an algorithm to find all subsets of a set? of your base set the current subset has. These 6 categories, based around the core pattern used to solve the problem, allow us to put a finite bound on the scope of recursive problems that we could need to solve. Submissions: 3218 Show Topic Tags Recursion Hide Topic Tags print sums of all subsets in it. It uses both loop and recursive call to solve this problem. Any help? counter(){ list=`ls $1` if [ -z "$(ls $1)" ] then. Count and print all Subarrays with product less than K in O(n) String to Integer (AtoI - ASCII to Integer) - Recursive Solution; Generate all the strings of length n from 0 to k-1. name 1428425;; intermediate version 1 million 428 thousand 425 Advanced Recursion: Subsets. ICS 141: Discrete Mathematics I (Fall 2014) 5. I have the following problem: Given a set a of n positive integers, write a backtracking C function that prints out all the subsets of a such that the product of their elements is p. In this moment we have values on all positions and we print the sequence. Given: I an integer bound W, and I a collection of n items, each with a positive, integer weight w i, nd a subset S of items that: maximizes P i2S w i while keeping P i2S w i W. First program print all subset of a set using for-loop, second program uses bitwise operator to print all subsets and program uses recursion. A Print the sum of characters in a String. The algorithm recursively calculates the permutations of larger and larger subsets of the set (e. ICS 141: Discrete Mathematics I (Fall 2014) 5. 3 Recursive Definitions Recursion is the general term for the practice of defining an object in terms of itself or of part of. Recursion is a method in which the solution of a problem depends on the smaller instances of the same problem. Print all the permutations of a string without repetition using Collections in Java Recursive program to generate power set Given a set represented as string, write a recursive code to print all subsets of it. So for the string "ABC" there are 6 permutations - ABC, ACB, BAC, BCA, CAB, CBA. possible subsets. 1/6/2018 Perfect Sum Problem (Print all subsets with given sum) - GeeksforGeeks 1/9 4 Custom Search Perfect Sum Problem (Print all subsets with given sum) Given an array of integers and a sum, the task is to print all subsets of given array with sum equal to given sum. Declaring Variable as required. The problem here is how to generate all the subsets of a given set. Given a set (represented as a string), I want to print all it's subsets, and I want to do it recursively. Let's look at a simple example. At the top level of the recursion, we may want to print all anagrams of east, without printing any letters before each anagram. How it comes to (n * n!) From the above stack trace picture of a program you can see, for printing permutation of string "ABC" i. GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. First step (with an array): [code]def subsets(n, min_value=1, stack=None): if stack is None: stack = [] print stack for i in xrange(min_value, n+1): stack. This section contains Python programming examples on Recursions. , some type of loop. The subset of a string is the character or the group of characters that are present inside the string. combos = combntns(set,subset) returns a matrix whose rows are the various combinations that can be taken of the elements of the vector set of length subset. Change the method to report not just whether any such subset exists, but the count of all such possible subsets. The permutations can also be taken on a smaller length. Therefore time complexity of the above solution is exponential. There's an algorithm out there that can be used to. Implementations in C++ (Microsoft and GNU) and C#/. In the solution below, we generate all combinations of subsets by using above logic. They are all exponential algorithms so they are only applicable for relative small list sizes. h or for C++, only is allowed and no other library. Learn C programming, Data Structures tutorials, exercises, examples, programs, hacks, tips and tricks online. These Instructions explain how to create a new subset in RMCDS. The algorithm recursively calculates the permutations of larger and larger subsets of the set (e. It sounds like you're trying to find all possible subsets of a given set. I`ll be thankful if you help me complete/rewrite this script. for loop) to print a row of * but I must use a recursive function to control the number of rows. The primitive recursive functions are a subset of the total recursive functions, which are a subset of the partial recursive functions. // This is done by setting the nth element true // and generating all subsets of the first n-1 elements subset[n-1] = true; recursiveGenSubsets(n-1, subset); // Then generate all subsets not containing n. If you are a python beginner and want to start learning the python programming, then keep your close attention in this tutorial as I am going to share a recursive solution for subset sum problem. Learn C programming, Data Structures tutorials, exercises, examples, programs, hacks, tips and tricks online. Implementations in C++ (Microsoft and GNU) and C#/. * Uses some String library functions. For example, in the set shown earlier, the subset 7, -3 also sums to 4, so there are two possible subsets for target 4. However, I'm not entirely convinced that using sets is the best way to implement this recipe as this precludes multiples of set elements. The running time is of order O(2 N N), since there are 2 N subsets and, to check each subset, we need to sum at most N elements. If new nodes may be created, then report whether or not space was exhausted, using a boolean reference parameter. This can be done using a recursive approach which I will try and outline below. Write a C Program to print prime factors using Recursion and Iteration. java * Execution: java Combinations n * * Enumerates all subsets of n elements using recursion. Output: Found a subset with given sum. The key is - If xth bit in number is SET i. The subset relation defines a partial order on sets. My understanding of recursion is very weak. It must be solved only with recursion. This article explains how to find all subsets of a given set of items, without using recursion. Over recursive formulations, this one has the advantage of not. • Sample problem: printing the series of integers from n1 to n2, where n1 <= n2. Please help with Recursive function to generate all the subset of a stirng. Find and print all subsets of a given set! (Given as an array. Write a C Program to print prime factors using Recursion and Iteration. * Uses some String library functions. Q&A for Work. If new nodes may be created, then report whether or not space was exhausted, using a boolean reference parameter. Returns all subsets of a given set. For maximum compatibility, this program uses only the basic instruction set (S/360) and two ASSIST macros (XDECO, XPRNT) to keep the code as short as possible. A much smaller subset is a countable permutation utilizing the Base-N-Odometer model. Both sets sum to 5, and they partition S. They can be impelmented by simple recursion, iteration, bit-operation, and some other approaches. Because a Binary Tree is a recursive data structure Printing all values in a Binary Tree We can easily modify the sum algorithm to print the values in a list:. In this C program, we are going to learn how to sum of all digits using recursion method? Here, a number will be entered through the user and program will calculate sum of all digits. The adjective "recursive" originates from the Latin verb "recurrere", which means "to run back". One way of solving the problem is to use backtracking. The best subsets regression is a model selection approach that consists of testing all possible combination of the predictor variables, and then selecting the best model according to some statistical criteria. I've stumbled upon this very interesting question on Stack Overflow, recently. Write a program the generates the power set of a set of numbers. Coderbyte is a web application that helps you practice your programming skills, prepare for coding bootcamps, and prepare for job interviews with our collection of interview questions, videos, and solutions. It also prints the empty subset. Below diagram will show all paths from root to leaf: Algorithm: Steps for print all paths from root to leaf are: If node is null then return 0 put node. The subset-sum problem is to find a subset of a set of integers that sums to a given value. They can be impelmented by simple recursion, iteration, bit-operation, and some other approaches. Return all subsets of an array 5. In this program, all the subsets of the string need to be printed. The total number of possible subset a set can have is 2^n, where n is the number of elements in the set. But in the next level, one recursive call will be to to display all anagrams of ast, prefixing each with the letter e. After combing through dozens of common recursive problems, I've categorized all recursive problems into one of 6 categories. Write a recursive program that finds all subsets of numbers in the array, which have a sum N. Given an array of positive, negative and zero's. C programming, exercises, solution : Write a program in C to print first 50 natural numbers using recursion. However, a recursive program cannot call itself always, or it would never stop. C program to calculate the power using recursion This program calculates the power of a number using recursion. Otherwise, * take the next vector element and try it both in and out, stopping as soon * as we find a successful subset. Suppose we have an array of positive integer elements: 'arr' and a positive number: 'targetSum'. How can I print all subsets of a set using bash script. But in the next level, one recursive call will be to to display all anagrams of ast, prefixing each with the letter e. Recursion Exercises. • There is a subset of X that excludes x and whose sum is T. Recursion is elegant but iteration is efficient. To print only distinct subsets, we initially sort the subset and exclude all adjacent duplicate elements from the subset along with the current element in case 2. For example, in the set shown earlier, the subset {7, -3} also sums to 4, so there are two possible subsets for target 4. A recursive CTE must contain a UNION ALL statement and, to be recursive, have a second query definition which references the CTE itself. This is a backtracking solution in C that finds all of the subsets that sum to the target value. More Recursion Summary • Topics: more recursion • Subset sum: finding if a subset of an array that sum up to a given target • Permute: finding all permutations of a given string • Subset: finding all subsets of a given string Thinking recursively • Finding the recursive structure of the problem is the hard part • Common patterns. // (This can be derived from previous code, assembling all subsets, // but try to do it more directly. Given a set (represented as a string), I want to print all it's subsets, and I want to do it recursively. Two concepts that often come up in the study of combinatorics are permutaions and combinations of a set of discrete elements. What you've suggested is a recursive permutation algorithm. You do not need to print all of the subsets. For example, the power set of {1,2,3,4} is. Recursion and Recursive Backtracking Computer Science E-119 Harvard Extension School Fall 2012 David G. For each negative number, try all subsets of positive numbers that equal the negative number. This program takes a sentence from user and reverses that sentence using recursion. CMU 15-112: Fundamentals of Programming and Computer Science Class Notes: Recursion (Continued). Let's look at a simple example. Otherwise, * take the next vector element and try it both in and out, stopping as soon * as we find a successful subset. Recursion is a method in which the solution of a problem depends on the smaller instances of the same problem. Iteration • When we encounter a problem that requires repetition, we often use iteration - i. For each positive number, try all subsets of negative numbers that equal the positive number. Write a C program to print all the possible permutations of given digits. products sale. How it comes to (n * n!) From the above stack trace picture of a program you can see, for printing permutation of string "ABC" i. A Subset is a collection of cases taken from the master file. Please help with Recursive function to generate all the subset of a stirng. I've stumbled upon this very interesting question on Stack Overflow, recently. RECURSIVE means that when one member from is being drilled down upon, every consolidated member resulting from that expansion will also be recursively drilled down until level 0 (TM1 level 0 ) is reached. Here's simple Program to print prime factors using Recursion and Iteration in C Pro. Over recursive formulations, this one has the advantage of not. * If we have run out of elements to try, we return false. (Note: All passwords are countable utilizing the entire character set. • There is a subset of X that excludes x and whose sum is T. 2: Recursion tree for computing subsets of [a, b, c]. In this assignment you will write a C program that uses recursion to print out all ????-element subsets of the… Get the answers you need, now!. Given a number N, print all the numbers which are a bitwise subset of the binary representation of N. A better exponential time algorithm uses. of S is the set of all subsets of 16 for recursive. array_walk_recursive (PHP 5, PHP 7) array_walk_recursive — Apply a user function recursively to every member of an array. Permutations means possible way of rearranging in the group or set in the particular order. Recursive method to find all permutations of a String : Recursive Method « Class Definition « Java Tutorial. The first subquery of UNION ALL generates the "seed row(s)" of the recursion, and the second subqeury of UNION ALL generates the recursion based on a SELECT that selects from the table being declared. Got it? We will loop from 0 to (2 raised to n) -1, and for each number num, we will check the SET bits in it and take corresponding elements. This is what we want for recursive backtracking problems, because new solutions build on previous solutions. Level up your coding skills and quickly land a job. The above solution may try all subsets of given set in worst case. Hint: First find the smallest value in the array. You can see that the current parameter goes through all eight subsets of [ a , b , c ]. In each iteration, we will have one subset. The permutations can also be taken on a smaller length. java * Execution: java Combinations n * * Enumerates all subsets of n elements using recursion. Given: I an integer bound W, and I a collection of n items, each with a positive, integer weight w i, nd a subset S of items that: maximizes P i2S w i while keeping P i2S w i W. Newer Post Older Post C++ program to print all distinct elements in. A recursive CTE must contain a UNION ALL statement and, to be recursive, have a second query definition which references the CTE itself. Recursion and Recursive Backtracking Computer Science E-119 Harvard Extension School Fall 2012 David G. For n = 2, all the possible subsets are: { 1 2 } { 1 } { 2 } { }. Creating subsets allows you to work with a part of the cases on the system instead of all of them. For example, in the set shown earlier, the subset 7, -3 also sums to 4, so there are two possible subsets for target 4. Today I am here with you with another problem based upon recursion and back tracking. A better exponential time algorithm uses. data in array and increment len by 1. Print reverse of a string using recursion; Count occurence of each vowel. A recursive CTE must contain a UNION ALL statement and, to be recursive, have a second query definition which references the CTE itself. * Uses some String library functions. For example if input number is 234, possible words which can be formed are (Alphabetical order):. Problem statement:- This program is an implementation about to print first N prime number using recursion function. Hi i have to write a program in java to display all the subsets of a set. CMU 15-112: Fundamentals of Programming and Computer Science Class Notes: Recursion (Continued). Print linked list in reverse order in java. Write a Program to Print MATRIX;. The relationship of one set being a subset of another is called inclusion or sometimes containment. // Print all subsets of e with n elements, one subset per line, // assuming all elements of e are distinct, and 0 <= n <= e. Recursion Exercises. Although I am gonna discuss the Java programs here but you can use the same logic and can code in any programming language whether it is C, C#, C++, php or any other language. print number. The following code finds the all permutations of a given string through command prompt using recursion. C programming, exercises, solution : Write a program in C to print first 50 natural numbers using recursion. ) Is there any other interview question you'd like me to cover in the future? You can (anonymously) let me know at: www. Like Find all subsets of a set [1,2,3n] you can ignore the order in which the subsets are generated. Recursion - subsets - C++ and then print out the possible combinations by calling the function recursively. Returns all subsets of a given set. Recursion is elegant but iteration is efficient. The third argument, maxlevels, gives the requested limit to recursion; this will be 0 if there is no requested limit. You can see that the current parameter goes through all eight subsets of [ a , b , c ]. For example if we want to get permutations of ABC over only 2 places. The optimum subset vector autoregression is found by employing the proposed recursive procedures in conjunction with model selection criteria. This question is asked by companies like microsoft, google, facebook, Amazon. For example, all possible subsets of a string "FUN" will be F, U, N, FU. C++ recursive string subset? Hi, I have the following problem: Write a recursive function that returns a vector of strings containing all subsets of a string value passed in (the passed string represents a set of characters just like a vector of char's). The above code is the root template which will be invoked by the XSLT processor. If we run a loop from 0 to 2 n and create a subset having numbers corresponding to 1s in the binary representation of loop variable, then we will create 2 n subsets covering the entire range of the powerset. Also, if you're asked not to print but to return them, then this solution would still be O(n * 2^n) running time, whereas you may be able to achieve O(2^n) with a different approach.