Subarrays, Subsequences, and Subsets in Array Last Updated : 24 Jul, 2025 Comments Improve Suggest changes Like Article Like Report What is a Subarray?A subarray is a contiguous part of array, i.e., Subarray is an array that is inside another array. In general, for an array of size n, there are n*(n+1)/2 non-empty subarrays. For example, Consider the array [1, 2, 3, 4], There are 10 non-empty sub-arrays. The subarrays are: (1), (2), (3), (4), (1,2), (2,3), (3,4), (1,2,3), (2,3,4), and (1,2,3,4) SubarrayWhat is a Subsequence?A subsequence is a sequence that can be derived from another sequence by removing zero or more elements, without changing the order of the remaining elements. More generally, we can say that for a sequence of size n, we can have (2n – 1) non-empty sub-sequences in total. For the same above example, there are 15 sub-sequences. They are: (1), (2), (3), (4), (1,2), (1,3),(1,4), (2,3), (2,4), (3,4), (1,2,3), (1,2,4), (1,3,4), (2,3,4), (1,2,3,4). SubsequencesWhat is a Subset?If a Set has all its elements belonging to other sets, this set will be known as a subset of the other set. A Subset is denoted as “⊆“. If set A is a subset of set B, it is represented as A ⊆ B. For example, Let Set_A = {m, n, o, p, q}, Set_ B = {k, l, m, n, o, p, q, r} Then, A ⊆ B. SubsetTable of Content What is a Subarray?What is a Subsequence?What is a Subset?Easy Problems on SubarrayMedium Problems on SubarrayHard Problems on SubarrayEasy Problems on SubsequenceMedium Problems on SubsequenceHard Problems on SubsequenceEasy Problems on SubsetMedium Problems on SubsetHard Problems on SubsetEasy Problems on Subarray:Split an array into two equal Sum subarraysCheck if subarray with given product exists in an arraySubarray of size k with given sumSort an array where a subarray of a sorted array is in reverse orderCount subarrays with all elements greater than KMaximum length of the sub-array whose first and last elements are sameCheck whether an Array is Subarray of another ArrayFind array such that no subarray has xor zero or YMaximum subsequence sum such that all elements are K distance apartLongest sub-array with maximum GCDCount of subarrays with sum at least KLength of Smallest subarray in range 1 to N with sum greater than a given valueSum of all subarrays of size KSplit array into K disjoint subarrays such that sum of each subarray is odd.Find an array of size N having exactly K subarrays with sum SFind the subarray of size K with minimum XORLength of the longest alternating even odd subarrayCount of subarrays which start and end with the same elementCount of subarrays having exactly K perfect square numbersSplit array into two subarrays such that difference of their maximum is minimumMedium Problems on Subarray:Print all K digit repeating numbers in a very large numberLength of longest subarray whose sum is not divisible by integer KMin difference between maximum and minimum element in all Y size subarraysLongest subarray of non-empty cells after removal of at most a single empty cellFirst subarray with negative sum from the given ArrayLargest subarray with frequency of all elements sameBitwise operations on Subarrays of size KCount subarrays having sum of elements at even and odd positions equalLongest Subarray consisting of unique elements from an ArrayMinimum Decrements on Subarrays required to reduce all Array elements to zeroSplit array into two subarrays such that difference of their sum is minimumMaximize count of non-overlapping subarrays with sum KSmallest subarray which upon repetition gives the original arraySplit array into maximum subarrays such that every distinct element lies in a single subarrayMaximize product of subarray sum with its minimum elementSum of products of all possible SubarraysCheck if all subarrays contains at least one unique elementLength of smallest subarray to be removed such that the remaining array is sortedLength of longest subarray having frequency of every element equal to KLength of the longest increasing subsequence which does not contain a given sequence as SubarrayHard Problems on Subarray:Length of smallest subarray to be removed to make sum of remaining elements divisible by KMaximum length of same indexed subarrays from two given arrays satisfying the given conditionCount ways to split array into two equal sum subarrays by changing sign of any one array elementLongest subarray in which all elements are smaller than KMaximize product of a strictly increasing or decreasing subarraySum of maximum of all subarrays by adding even frequent maximum twiceLongest subarray of an array which is a subsequence in another arrayCount of subarrays having product as a perfect cubeMinimize difference between maximum and minimum array elements by removing a K-length subarrayMaximum sum submatrixMinimum removal of elements from end of an array required to obtain sum KCheck if any subarray of length M repeats at least K times consecutively or notMinimize flips on K-length subarrays required to make all array elements equal to 1Split array into K subarrays such that sum of maximum of all subarrays is maximizedFind minimum subarray sum for each index i in subarray [i, N-1]Longest subarray with GCD greater than 1Longest subsegment of ‘1’s formed by changing at most k ‘0’sLexicographically smallest Permutation of Array by reversing at most one SubarrayFind a subsequence which upon reversing gives the maximum sum subarrayMinimize steps to make Array elements 0 by reducing same A[i] – X from SubarrayEasy Problems on Subsequence:Longest subsequence having equal numbers of 0 and 1Powers of two and subsequencesLongest Subsequence where index of next element is arr[arr[i] + i]Number of subsequences with zero sumLongest sub-sequence with maximum GCDMaximum Bitwise AND value of subsequence of length KLength of the longest subsequence such that xor of adjacent elements is non-decreasingMaximum product of bitonic subsequence of size 3Length of Smallest Subsequence such that sum of elements is greater than equal to KLongest subsequence of even numbers in an ArrayMaximum length Subsequence with alternating sign and maximum SumCount of possible subarrays and subsequences using given length of ArrayMaximum bitwise OR value of subsequence of length KCount of subsequences consisting of the same elementSmallest occurring element in each subsequenceLength of the longest subsequence consisting of distinct elementsMinimize elements to be added to a given array such that it contains another given array as its subsequenceMaximize subsequences having array elements not exceeding length of the subsequenceLength of longest subsequence consisting of distinct adjacent elementsMaximum Sum SubsequenceMedium Problems on Subsequence:Minimum removals required to make a given array BitonicCheck if a non-contiguous subsequence same as the given subarray exists or notMinimize the number of strictly increasing subsequences in an arrayCount of unique subsequences from given number which are power of 2Minimum number of insertions required such that first K natural numbers can be obtained as sum of a subsequence of the arrayLength of longest subsequence such that prefix sum at every element remains greater than zeroCheck if given Array can be divided into subsequences of K increasing consecutive integersLongest Subsequence such that difference between adjacent elements is either A or BCount subsequences of Array having single digit integer sum KShortest Subsequence with sum exactly KPrinting Longest Bitonic SubsequenceSorted subsequence of size 3 in linear time using constant spaceCount of subsequences having maximum distinct elementsConstruct array having X subsequences with maximum difference smaller than dPrint all subsequences of a string using ArrayListLongest Subsequence with at least one common digit in every elementMaximum Sum Subsequence of length kSum of minimum element of all sub-sequences of a sorted arrayFind all combinations of two equal sum subsequencesMinimum cost of choosing 3 increasing elements in an array of size NHard Problems on Subsequence:Number of subsequences with positive productLongest subsequence having difference atmost KFind all subsequences with sum equals to KMaximize product of digit sum of consecutive pairs in a subsequence of length KCount of subsequences of length atmost K containing distinct prime elementsSum of all subsequences of length KMinimize sum of smallest elements from K subsequences of length LUnique subsequences of length K with given sumSmallest subsequence with sum of absolute difference of consecutive elements maximizedMaximize product of same-indexed elements of same size subsequencesLongest Increasing Subsequence having sum value atmost KLongest subsequence of a number having same left and right rotationMaximize length of Non-Decreasing Subsequence by reversing at most one SubarrayMaximum subsequence sum possible by multiplying each element by its indexGenerate all distinct subsequences of array using backtrackingMaximum subsequence sum such that no K elements are consecutivePrint all possible K-length subsequences of first N natural numbers with sum NLongest subsequence having difference between the maximum and minimum element equal to KMaximize difference between sum of even and odd-indexed elements of a subsequenceConvert an array into another by repeatedly removing the last element and placing it at any arbitrary indexEasy Problems on Subset:Find if there is any subset of size K with 0 sum in an array of -1 and +1Sum of sum of all subsets of a set formed by first N natural numbersCount of subsets not containing adjacent elementsSum of the sums of all possible subsetsFind whether an array is subset of another arrayTotal number of Subsets of size at most KCheck if it is possible to split given Array into K odd-sum subsetsPartition a set into two subsets such that difference between max of one and min of other is minimizedSum of all possible expressions of a numeric string possible by inserting addition operatorsCheck if it’s possible to split the Array into strictly increasing subsets of size at least KLargest subset of Array having sum at least 0Medium Problems on Subset:Number of subsets with sum divisible by mFibonacci sum of a subset with all elements <= kNumber of possible Equivalence Relations on a finite setLargest divisible pairs subsetRecursive program to print all subsets with given sumSubset Sum Queries in a Range using BitsetFind all distinct subset (or subsequence) sums of an array | Set-2Sum of (maximum element – minimum element) for all the subsets of an arrayCount no. of ordered subsets having a particular XOR valueSum of subsets of all the subsets of an arrayPerfect Sum ProblemCount of subsets having sum of min and max element less than KSplit array into two equal length subsets such that all repetitions of a number lies in a single subsetNth Subset of the Sequence consisting of powers of K in increasing order of their SumLargest possible Subset from an Array such that no element is K times any other element in the SubsetCheck if an array can be split into subsets of K consecutive elementsHard Problems on Subset:Minimize count of divisions by D to obtain at least K equal array elementsSplit array into K-length subsets to minimize sum of second smallest element of each subsetMedian of all non-empty subset sumsMinimum removals required such that sum of remaining array modulo M is XSum of length of two smallest subsets possible from a given array with sum at least KReduce sum of any subset of an array to 1 by multiplying all its elements by any valueSum of all subsets whose sum is a Perfect Number from a given arrayMinimize sum of incompatibilities of K equal-length subsets made up of unique elementsMaximize sum of subsets from two arrays having no consecutive valuesProduct of the maximums of all subsets of an arrayCount ways to place ‘+’ and ‘-‘ in front of array elements to obtain sum KCount ways to split array into two subsets having difference between their sum equal to KFind the subset of Array with given LCMCount of subsets whose product is multiple of unique primesMinimum count of elements to be inserted in Array to form all values in [1, K] using subset sumMaximum subset sum having difference between its maximum and minimum in range [L, R]Find all unique subsets of a given set using C++ STLSubset sum problem where Array sum is at most NRelated Articles: Data Structure and Algorithms CourseRecent articles on SubarrayRecent articles on SubsequenceRecent articles on Subset Comment More infoAdvertise with us Next Article Analysis of Algorithms H harendrakumar123 Follow Improve Article Tags : DSA Arrays subset subsequence subarray +1 More Practice Tags : Arrayssubset Similar Reads Basics & PrerequisitesLogic Building ProblemsLogic building is about creating clear, step-by-step methods to solve problems using simple rules and principles. 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