Try it on GfG Practice Given three integers x, n, and M, compute (x^n) % M (remainder when x raised to the power n is divided by M). Examples : Input: x = 3, n = 2, M = 4 Output: 1 Explanation: 32 % 4 = 9 % 4 = 1. Input: x = 2, n = 6, M = 10 Output: 4 Explanation: 26 % 10 = 64 % 10 = 4. Table of…

Try it on GfG Practice Given an array arr[] and an integer k, where arr[i] denotes the number of pages of a book and k denotes total number of students. All the books need to be allocated to k students in contiguous manner, with each student getting at least one book. The task is to minimize the…

Given an n x n matrix, where every row and column is sorted in increasing order. Given a key, how to decide whether this key is in the matrix. Input: x = 62, mat[][] = [[3, 30, 38], [20, 52, 54], [35, 60, 69]] Output: false Explanation: 62 is not present in the matrix. Input: x = 30, mat[][] = [[3,…

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…

The following is a simple recursive Binary Search function in C++ taken from here. C++ // CPP program for the above approach #include using namespace std; // A recursive binary search function. It returns location of x in // given array arr[l..r] is present, otherwise -1 int binarySearch(int arr[],…

Interpolation 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…

Prerequisite: Linear SearchBinary Search LINEAR 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…

We 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…

Given 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 = 10 Output: 3 Explanation: 10 is present at index 3. Input:…

Given 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…

The 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 = 45 Output: Element found at index 3…

Like 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…

Try it on GfG Practice Computer 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…

Meta 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…

Sentinel 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…

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…

Try it on GfG Practice Given 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…

Try it on GfG Practice Given 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 = 16 Output:…

Given 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 = 10 Output: 4 Explanation: 10 is at index 4 in array. Input: arr[] = [2, 5, 7, 9], k = 3 Output: -1 Explanation: 3 is not…

Try it on GfG Practice Given 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…

Try it on GfG Practice Given two sorted arrays, a[] and b[], the task is to find the median of these sorted arrays. Assume that the two sorted arrays are merged and then median is selected from the combined array. This is an extension of Median of two sorted arrays of equal size problem. Here we…

Try it on GfG Practice Given 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,…

Try it on GfG Practice Given an array arr[] that represents elements of arithmetic progression in order. One element is missing in the progression, find the missing number. Note: An element will always exist that, upon inserting into a sequence forms Arithmetic progression. If the given sequence…

Given 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:…

Try it on GfG Practice Given 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[] =…

Try it on GfG Practice Given 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 = 32 Output: 1 and 30 Input:…

Given 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…

Given 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…

Try it on GfG Practice Given an array arr[] where no two adjacent elements are same, find the index of a peak element. An element is considered to be a peak element if it is strictly greater than its adjacent elements. If there are multiple peak elements, return the index of any one of them. Note:…

Given a sorted array arr[] (may contain duplicates) of size n that is rotated at some unknown point, the task is to find the maximum element in it. Examples: Input: arr[] = {5, 6, 1, 2, 3, 4} Output: 6 Explanation: 6 is the maximum element present in the array. Input: arr[] = {3, 2, 2, 2} Output: 3…

Try it on GfG Practice Given 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: 1 Explanation: 1 is the minimum element present in the array. Input: arr[] = [3,…

Try it on GfG Practice Given 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…

Try it on GfG Practice Given an array of size N. The task is to find the maximum and the minimum element of the array using the minimum number of comparisons. Examples: Input: arr[] = {3, 5, 4, 1, 9} Output: Minimum element is: 1 Maximum element is: 9 Input: arr[] = {22, 14, 8, 17, 35, 3} Output:…

Try it on GfG Practice Given 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 = 3 Output: 8 Explanation: 3 is present at…

Try it on GfG Practice Given 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 : 74 Input : arr[] = {10, 10, 10}, Output : 20 Input…

Try it on GfG Practice Given 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…

Try it on GfG Practice Given 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 = 4 Output: [2, 3] Explanation: Here n/k is 8/4 = 2, therefore 2 appears 3 times in the array that is greater than 2…

Try it on GfG Practice Given 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…

Try it on GfG Practice Given 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 = 5 Output: 1 Explanation: Largest number less than or equal to 5 is 2,…

Try it on GfG Practice Given 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.…