Searching Algorithms Last Updated : 15 May, 2025 Comments Improve Suggest changes Like Article Like Report Searching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input array. Linear Search : It is used for an unsorted array. It mainly does one by one comparison of the item to be search with array elements. It takes linear or O(n) Time.Binary Search : It is used for a sorted array. It mainly compares the array's middle element first and if the middle element is same as input, then it returns. Otherwise it searches in either left half or right half based on comparison result (Whether the mid element is smaller or greater). This algorithm is faster than linear search and takes O(Log n) time.One more common search technique is Two Pointers Technique where we begin searching from both ends of the array.Library Implementations of Binary Searchbinary_search, lower_bound and upper_bound in C++Arrays.binarySearch() in Java Arrays.binarySearch() in Java for Search in subarrayCollections.binarySearch() in JavaBisect in PythonList.BinarySearch in C#Easy ProblemsLargest in an ArraySecond Largest in an array Largest three in an arrayMissing NumberFirst Repeating Missing and RepeatingCount 1’s in a sorted binary arrayClosest to 0 Sum PairPair with the given differencek largest(or smallest) ElementsKth smallest in row and column-wise sorted Common elements in 3 sortedCeiling in a sorted Floor in a Sorted Maximum in a Bitonic Elements that appear more than n/k timesMedium ProblemsTriplets with zero sumPartition PointLargest pair sumK’th Smallest in Unsorted ArraySearch an in a sorted and rotatedMin in a sorted and rotated Max in a sorted and rotatedPeak elementMax and min using minimum comparisonsFind a Fixed Point in a given arrayK most frequent words from a fileK closest elements2 Sum – Pair Sum Closest to Target in Sorted ArrayClosest pair from two sorted arraysThree closest from three sorted arraysBinary Search for Rationals Missing Element in APHard ProblemsMedian of two sorted arraysMedian of two sorted of different sizesSearch in an almost sorted arraySearch in a sorted infinite arrayPair sum in a sorted and rotated arrayK’th Smallest/Largest Element in Unsorted ArrayK’th largest element in a streamBest First Search (Informed Search)More Searching AlgorithmsSentinel Linear SearchMeta Binary Search | One-Sided Binary SearchTernary SearchJump SearchInterpolation SearchExponential SearchFibonacci SearchThe Ubiquitous Binary SearchComparisons Between Different Searching AlgorithmsLinear Search vs Binary SearchInterpolation search vs Binary searchWhy is Binary Search preferred over Ternary Search?Is Sentinel Linear Search better than normal Linear Search?Quick Links:‘Practice Problems’ on Searching Top Searching Interview Questions‘Quizzes’ on Searching Learn Data Structure and Algorithms | DSA Tutorial Comment More infoAdvertise with us Next Article Linear Search Algorithm H harendrakumar123 Follow Improve Article Tags : Searching DSA Practice Tags : Searching Similar Reads Searching Algorithms Searching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input 3 min read Most Common Searching AlgorithmsLinear Search AlgorithmGiven an array, arr of n integers, and an integer element x, find whether element x is present in the array. Return the index of the first occurrence of x in the array, or -1 if it doesn't exist.Input: arr[] = [1, 2, 3, 4], x = 3Output: 2Explanation: There is one test case with array as [1, 2, 3 4] 9 min read Binary Search Algorithm - Iterative and Recursive ImplementationBinary Search Algorithm is a searching algorithm used in a sorted array by repeatedly dividing the search interval in half. The idea of binary search is to use the information that the array is sorted and reduce the time complexity to O(log N). Binary Search AlgorithmConditions to apply Binary Searc 15 min read Other Searching AlgorithmsSentinel Linear SearchSentinel Linear Search as the name suggests is a type of Linear Search where the number of comparisons is reduced as compared to a traditional linear search. In a traditional linear search, only N comparisons are made, and in a Sentinel Linear Search, the sentinel value is used to avoid any out-of-b 7 min read Meta Binary Search | One-Sided Binary SearchMeta binary search (also called one-sided binary search by Steven Skiena in The Algorithm Design Manual on page 134) is a modified form of binary search that incrementally constructs the index of the target value in the array. Like normal binary search, meta binary search takes O(log n) time. Meta B 9 min read Ternary SearchComputer systems use different methods to find specific data. There are various search algorithms, each better suited for certain situations. For instance, a binary search divides information into two parts, while a ternary search does the same but into three equal parts. It's worth noting that tern 15+ min read Jump SearchLike Binary Search, Jump Search is a searching algorithm for sorted arrays. The basic idea is to check fewer elements (than linear search) by jumping ahead by fixed steps or skipping some elements in place of searching all elements.For example, suppose we have an array arr[] of size n and a block (t 11 min read Interpolation SearchGiven a sorted array of n uniformly distributed values arr[], write a function to search for a particular element x in the array. Linear Search finds the element in O(n) time, Jump Search takes O(n) time and Binary Search takes O(log n) time. The Interpolation Search is an improvement over Binary Se 15+ min read Exponential SearchThe name of this searching algorithm may be misleading as it works in O(Log n) time. The name comes from the way it searches an element.Given a sorted array, and an element x to be searched, find position of x in the array.Input: arr[] = {10, 20, 40, 45, 55} x = 45Output: Element found at index 3Inp 15+ min read Fibonacci SearchGiven a sorted array arr[] of size n and an integer x. Your task is to check if the integer x is present in the array arr[] or not. Return index of x if it is present in array else return -1. Examples: Input: arr[] = [2, 3, 4, 10, 40], x = 10Output: 3Explanation: 10 is present at index 3.Input: arr[ 11 min read The Ubiquitous Binary Search | Set 1We are aware of the binary search algorithm. Binary search is the easiest algorithm to get right. I present some interesting problems that I collected on binary search. There were some requests on binary search. I request you to honor the code, "I sincerely attempt to solve the problem and ensure th 15+ min read Comparisons between Searching AlgorithmsLinear Search vs Binary SearchPrerequisite: Linear SearchBinary SearchLINEAR SEARCH Assume that item is in an array in random order and we have to find an item. Then the only way to search for a target item is, to begin with, the first position and compare it to the target. If the item is at the same, we will return the position 11 min read Interpolation search vs Binary searchInterpolation search works better than Binary Search for a Sorted and Uniformly Distributed array. Binary Search goes to the middle element to check irrespective of search-key. On the other hand, Interpolation Search may go to different locations according to search-key. If the value of the search-k 7 min read Why is Binary Search preferred over Ternary Search?The following is a simple recursive Binary Search function in C++ taken from here. C++ // CPP program for the above approach #include <bits/stdc++.h> using namespace std; // A recursive binary search function. It returns location of x in // given array arr[l..r] is present, otherwise -1 int b 11 min read Is Sentinel Linear Search better than normal Linear Search?Sentinel Linear search is a type of linear search where the element to be searched is placed in the last position and then all the indices are checked for the presence of the element without checking for the index out of bound case.The number of comparisons is reduced in this search as compared to a 8 min read Library implementations of Searching algorithmsBinary Search functions in C++ STL (binary_search, lower_bound and upper_bound)In C++, STL provide various functions like std::binary_search(), std::lower_bound(), and std::upper_bound() which uses the the binary search algorithm for different purposes. These function will only work on the sorted data.There are the 3 binary search function in C++ STL:Table of Contentbinary_sea 3 min read Arrays.binarySearch() in Java with Examples | Set 1In Java, the Arrays.binarySearch() method searches the specified array of the given data type for the specified value using the binary search algorithm. The array must be sorted by the Arrays.sort() method before making this call. If it is not sorted, the results are undefined. Example:Below is a si 3 min read Arrays.binarySearch() in Java with examples | Set 2 (Search in subarray)Arrays.binarySearch()| Set 1 Covers how to find an element in a sorted array in Java. This set will cover "How to Search a key in an array within a given range including only start index". Syntax : public static int binarySearch(data_type[] arr, int fromIndex, int toIndex, data_type key) Parameters 5 min read Collections.binarySearch() in Java with Examplesjava.util.Collections.binarySearch() method is a java.util.Collections class method that returns the position of an object in a sorted list.// Returns index of key in a sorted list sorted in// ascending orderpublic static int binarySearch(List slist, T key)// Returns index of key in a sorted list so 4 min read Easy problems on Searching algorithmsFind the Missing NumberGiven an array arr[] of size n-1 with distinct integers in the range of [1, n]. This array represents a permutation of the integers from 1 to n with one element missing. Find the missing element in the array.Examples: Input: arr[] = [8, 2, 4, 5, 3, 7, 1]Output: 6Explanation: All the numbers from 1 t 12 min read Find the first repeating element in an array of integersGiven an array of integers arr[], The task is to find the index of first repeating element in it i.e. the element that occurs more than once and whose index of the first occurrence is the smallest. Examples: Input: arr[] = {10, 5, 3, 4, 3, 5, 6}Output: 5 Explanation: 5 is the first element that repe 8 min read Missing and Repeating in an ArrayGiven an unsorted array of size n. Array elements are in the range of 1 to n. One number from set {1, 2, ...n} is missing and one number occurs twice in the array. The task is to find these two numbers.Examples: Input: arr[] = {3, 1, 3}Output: 3, 2Explanation: In the array, 2 is missing and 3 occurs 15+ min read Count 1's in a sorted binary arrayGiven a binary array arr[] of size n, which is sorted in non-increasing order, count the number of 1's in it. Examples: Input: arr[] = [1, 1, 0, 0, 0, 0, 0]Output: 2Explanation: Count of the 1's in the given array is 2.Input: arr[] = [1, 1, 1, 1, 1, 1, 1]Output: 7Input: arr[] = [0, 0, 0, 0, 0, 0, 0] 7 min read Two Sum - Pair Closest to 0Given an integer array arr[], the task is to find the maximum sum of two elements such that sum is closest to zero. Note: In case if we have two of more ways to form sum of two elements closest to zero return the maximum sum.Examples:Input: arr[] = [-8, 5, 2, -6]Output: -1Explanation: The min absolu 15+ min read Pair with the given differenceGiven an unsorted array and an integer x, the task is to find if there exists a pair of elements in the array whose absolute difference is x. Examples: Input: arr[] = [5, 20, 3, 2, 50, 80], x = 78Output: YesExplanation: The pair is {2, 80}.Input: arr[] = [90, 70, 20, 80, 50], x = 45Output: NoExplana 14 min read Kth smallest element in a row-wise and column-wise sorted 2D arrayGiven an n x n matrix, every row and column is sorted in non-decreasing order. Given a number K where K lies in the range [1, n*n], find the Kth smallest element in the given 2D matrix.Example:Input: mat =[[10, 20, 30, 40], [15, 25, 35, 45], [24, 29, 37, 48], [32, 33, 39, 50]]K = 3Output: 20Explanat 15+ min read Find common elements in three sorted arraysGiven three sorted arrays in non-decreasing order, print all common elements in non-decreasing order across these arrays. If there are no such elements return an empty array. In this case, the output will be -1.Note: In case of duplicate common elements, print only once.Examples: Input: arr1[] = [1, 12 min read Ceiling in a sorted arrayGiven a sorted array and a value x, find index of the ceiling of x. The ceiling of x is the smallest element in an array greater than or equal to x. Note: In case of multiple occurrences of ceiling of x, return the index of the first occurrence.Examples : Input: arr[] = [1, 2, 8, 10, 10, 12, 19], x 13 min read Floor in a Sorted ArrayGiven a sorted array and a value x, find the element of the floor of x. The floor of x is the largest element in the array smaller than or equal to x.Examples:Input: arr[] = [1, 2, 8, 10, 10, 12, 19], x = 5Output: 1Explanation: Largest number less than or equal to 5 is 2, whose index is 1Input: arr[ 9 min read Bitonic Point - Maximum in Increasing Decreasing ArrayGiven an array arr[] of integers which is initially strictly increasing and then strictly decreasing, the task is to find the bitonic point, that is the maximum value in the array. Note: Bitonic Point is a point in bitonic sequence before which elements are strictly increasing and after which elemen 10 min read Given Array of size n and a number k, find all elements that appear more than n/k timesGiven an array of size n and an integer k, find all elements in the array that appear more than n/k times. Examples:Input: arr[ ] = [3, 4, 2, 2, 1, 2, 3, 3], k = 4Output: [2, 3]Explanation: Here n/k is 8/4 = 2, therefore 2 appears 3 times in the array that is greater than 2 and 3 appears 3 times in 15+ min read Medium problems on Searching algorithms3 Sum - Find All Triplets with Zero SumGiven an array arr[], the task is to find all possible indices {i, j, k} of triplet {arr[i], arr[j], arr[k]} such that their sum is equal to zero and all indices in a triplet should be distinct (i != j, j != k, k != i). We need to return indices of a triplet in sorted order, i.e., i < j < k.Ex 11 min read Find the element before which all the elements are smaller than it, and after which all are greaterGiven an array, find an element before which all elements are equal or smaller than it, and after which all the elements are equal or greater.Note: Print -1, if no such element exists.Examples:Input: arr[] = [5, 1, 4, 3, 6, 8, 10, 7, 9]Output: 6 Explanation: 6 is present at index 4. All elements on 14 min read Largest pair sum in an arrayGiven an unsorted of distinct integers, find the largest pair sum in it. For example, the largest pair sum is 74. If there are less than 2 elements, then we need to return -1.Input : arr[] = {12, 34, 10, 6, 40}, Output : 74Input : arr[] = {10, 10, 10}, Output : 20Input arr[] = {10}, Output : -1[Naiv 10 min read K’th Smallest Element in Unsorted ArrayGiven an array arr[] of N distinct elements and a number K, where K is smaller than the size of the array. Find the K'th smallest element in the given array. Examples:Input: arr[] = {7, 10, 4, 3, 20, 15}, K = 3 Output: 7Input: arr[] = {7, 10, 4, 3, 20, 15}, K = 4 Output: 10 Table of Content[Naive Ap 15 min read Search in a Sorted and Rotated ArrayGiven a sorted and rotated array arr[] of n distinct elements, the task is to find the index of given key in the array. If the key is not present in the array, return -1. Examples: Input: arr[] = [5, 6, 7, 8, 9, 10, 1, 2, 3], key = 3Output: 8Explanation: 3 is present at index 8 in arr[].Input: arr[] 15+ min read Minimum in a Sorted and Rotated ArrayGiven a sorted array of distinct elements arr[] of size n that is rotated at some unknown point, the task is to find the minimum element in it. Examples: Input: arr[] = [5, 6, 1, 2, 3, 4]Output: 1Explanation: 1 is the minimum element present in the array.Input: arr[] = [3, 1, 2]Output: 1Explanation: 9 min read Find a Fixed Point (Value equal to index) in a given arrayGiven an array of n distinct integers sorted in ascending order, the task is to find the First Fixed Point in the array. Fixed Point in an array is an index i such that arr[i] equals i. Note that integers in the array can be negative. Note: If no Fixed Point is present in the array, print -1.Example 7 min read K Mmost Frequent Words in a FileGiven a book of words and an integer K. Assume you have enough main memory to accommodate all words. Design a dynamic data structure to find the top K most frequent words in a book. The structure should allow new words to be added in main memory.Examples:Input: fileData = "Welcome to the world of Ge 15+ min read Closest K Elements in a Sorted ArrayYou are given a sorted array arr[] containing unique integers, a number k, and a target value x. Your goal is to return exactly k elements from the array that are closest to x, excluding x itself if it is present in the array.An element a is closer to x than b if:|a - x| < |b - x|, or|a - x| == | 15+ min read 2 Sum - Pair Sum Closest to Target using Binary SearchGiven an array arr[] of n integers and an integer target, the task is to find a pair in arr[] such that it’s sum is closest to target.Note: Return the pair in sorted order and if there are multiple such pairs return the pair with maximum absolute difference. If no such pair exists return an empty ar 10 min read Find the closest pair from two sorted arraysGiven two arrays arr1[0...m-1] and arr2[0..n-1], and a number x, the task is to find the pair arr1[i] + arr2[j] such that absolute value of (arr1[i] + arr2[j] - x) is minimum. Example: Input: arr1[] = {1, 4, 5, 7}; arr2[] = {10, 20, 30, 40}; x = 32Output: 1 and 30Input: arr1[] = {1, 4, 5, 7}; arr2[] 15+ min read Find three closest elements from given three sorted arraysGiven three sorted arrays A[], B[] and C[], find 3 elements i, j and k from A, B and C respectively such that max(abs(A[i] - B[j]), abs(B[j] - C[k]), abs(C[k] - A[i])) is minimized. Here abs() indicates absolute value. Example : Input : A[] = {1, 4, 10} B[] = {2, 15, 20} C[] = {10, 12} Output: 10 15 15+ min read Search in an Array of Rational Numbers without floating point arithmeticGiven a sorted array of rational numbers, where each rational number is represented in the form p/q (where p is the numerator and q is the denominator), the task is to find the index of a given rational number x in the array. If the number does not exist in the array, return -1.Examples: Input: arr[ 9 min read Hard problems on Searching algorithmsMedian of two sorted arrays of same sizeGiven 2 sorted arrays a[] and b[], each of size n, the task is to find the median of the array obtained after merging a[] and b[]. Note: Since the size of the merged array will always be even, the median will be the average of the middle two numbers.Input: a[] = [1, 12, 15, 26, 38], b[] = [2, 13, 17 15+ min read Search in an almost sorted arrayGiven a sorted integer array arr[] consisting of distinct elements, where some elements of the array are moved to either of the adjacent positions, i.e. arr[i] may be present at arr[i-1] or arr[i+1].Given an integer target. You have to return the index ( 0-based ) of the target in the array. If targ 7 min read Find position of an element in a sorted array of infinite numbersGiven a sorted array arr[] of infinite numbers. The task is to search for an element k in the array.Examples:Input: arr[] = [3, 5, 7, 9, 10, 90, 100, 130, 140, 160, 170], k = 10Output: 4Explanation: 10 is at index 4 in array.Input: arr[] = [2, 5, 7, 9], k = 3Output: -1Explanation: 3 is not present i 15+ min read Pair Sum in a Sorted and Rotated ArrayGiven an array arr[] of size n, which is sorted and then rotated around an unknown pivot, the task is to check whether there exists a pair of elements in the array whose sum is equal to a given target value.Examples : Input: arr[] = [11, 15, 6, 8, 9, 10], target = 16Output: trueExplanation: There is 10 min read K’th Smallest/Largest Element in Unsorted Array | Worst case Linear TimeGiven an array of distinct integers arr[] and an integer k. The task is to find the k-th smallest element in the array. For better understanding, k refers to the element that would appear in the k-th position if the array were sorted in ascending order. Note: k will always be less than the size of t 15 min read K'th largest element in a streamGiven an input stream of n integers, represented as an array arr[], and an integer k. After each insertion of an element into the stream, you need to determine the kth largest element so far (considering all elements including duplicates). If k elements have not yet been inserted, return -1 for that 15+ min read Best First Search (Informed Search)Best First Search is a heuristic search algorithm that selects the most promising node for expansion based on an evaluation function. It prioritizes nodes in the search space using a heuristic to estimate their potential. By iteratively choosing the most promising node, it aims to efficiently naviga 13 min read Like