C++ vector is a dynamic array that stores collection of elements same type in contiguous memory. It has the ability to resize itself automatically when an element is inserted or deleted. Create a Vector Before creating a vector, we must know that a vector is defined as the std::vector class template…

Try it on GfG Practice Given an array arr[] of size n and an integer target, the task is to find all distinct pairs in the array whose sum is equal to target. We can return pairs in any order, but all the returned pairs should be internally sorted, i.e., for any pair [q1, q2] the following should…

Try it on GfG Practice Given an array arr[] and a target value, the task is to find all possible indices (i, j) of pairs (arr[i], arr[j]) whose sum is equal to target and i != j. We can return pairs in any order, but all the returned pairs should be internally sorted, that is for any pair(i, j), i…

Given an array arr[]. Find the maximum value of prefix sum which is also suffix sum for index i in arr[]. Examples : Input : arr[] = {-1, 2, 3, 0, 3, 2, -1} Output : 4 Explanation : Prefix sum of arr[0..3] = Suffix sum of arr[3..6] Input : arr[] = {-3, 5, 3, 1, 2, 6, -4, 2} Output : 7 Explanation :…

Given a pair-sum array construct the original array. A pair-sum array for an array is the array that contains sum of all pairs in ordered form, i.e., pair[0] is sum of arr[0] and arr[1], pair[1] is sum of arr[0] and arr[2] and so on. Note that if the size of input array is n, then the size of pair…

Try it on GfG Practice Given a 1-based indexing array arr[] of non-negative integers and an integer sum. You mainly need to return the left and right indexes(1-based indexing) of that subarray. In case of multiple subarrays, return the subarray indexes which come first on moving from left to right.…

Try it on GfG Practice Given an unsorted array of positive integers, the task is to find the number of triangles that can be formed with three different array elements as three sides of triangles. For a triangle to be possible from 3 values as sides, the sum of the two values (or sides) must always…

Try it on GfG Practice You are given an array arr, and your task is to find the majority element an element that occurs more than half the length of the array (i.e., arr.size() / 2). If such an element exists return it, otherwise return -1, indicating that no majority element is present. Examples :…

Try it on GfG Practice Given an array arr[] of integers and a number x, the task is to find the smallest subarray with a sum strictly greater than x. Examples: Input: x = 51, arr[] = [1, 4, 45, 6, 0, 19] Output: 3 Explanation: Minimum length subarray is [4, 45, 6] Input: x = 100, arr[] = [1, 10, 5,…

Try it on GfG Practice Given an array arr[] of n integers, construct a product array res[] (of the same size) such that res[i] is equal to the product of all the elements of arr[] except arr[i]. Example: Input: arr[] = [10, 3, 5, 6, 2] Output: [180, 600, 360, 300, 900] Explanation: For i=0, res[i] =…

Given a sorted array of n distinct integers where each integer is in the range from 0 to m-1 and m > n. Find the smallest number that is missing from the array. Examples: Input: {0, 1, 2, 6, 9}, n = 5, m = 10 Output: 3 Input: {4, 5, 10, 11}, n = 4, m = 12 Output: 0 Input: {0, 1, 2, 3}, n = 4, m = 5…

Try it on GfG Practice Given an array arr[] having distinct numbers sorted in increasing order and the array has been right rotated (i.e, the last element will be cyclically shifted to the starting position of the array) k number of times, the task is to find the value of k. Examples: Input: arr[] =…

Given two integer arrays of the same length, arr[] and index[], the task is to reorder the elements in arr[] such that after reordering, each element from arr[i] moves to the position index[i]. The new arrangement reflects the values being placed at their target indices, as described by index[]…

Try it on GfG Practice Given an array of elements of length n, ranging from 0 to n - 1. All elements may not be present in the array. If the element is not present then there will be -1 present in the array. Rearrange the array such that arr[i] = i and if i is not present, display -1 at that place.…

Try it on GfG Practice Given an integer array, the task is to find the maximum product of any subarray. Examples: Input: arr[] = {-2, 6, -3, -10, 0, 2} Output: 180 Explanation: The subarray with maximum product is {6, -3, -10} with product = 6 * (-3) * (-10) = 180 Input: arr[] = {-1, -3, -10, 0, 60}…

Try it on GfG Practice Given an array arr[] of size n, the task is to return an equilibrium index (if any) or -1 if no equilibrium index exists. The equilibrium index of an array is an index such that the sum of all elements at lower indexes equals the sum of all elements at higher indexes. Note:…

Given an array and a number k, find the largest sum of contiguous array in the modified array which is formed by repeating the given array k times. Examples : Input : arr[] = {-1, 10, 20}, k = 2 Output : 59 After concatenating array twice, we get {-1, 10, 20, -1, 10, 20} which has maximum subarray…

Try it on GfG Practice Given an array arr[], the task is to find the subarray that has the maximum sum and return its sum. Examples: Input: arr[] = {2, 3, -8, 7, -1, 2, 3} Output: 11 Explanation: The subarray {7, -1, 2, 3} has the largest sum 11. Input: arr[] = {-2, -4} Output: -2 Explanation: The…

Try it on GfG Practice You are given an array of 0s and 1s in random order. Segregate 0s on left side and 1s on right side of the array [Basically you have to sort the array]. Traverse array only once. Input : [0, 1, 0, 1, 0, 0, 1, 1, 1, 0] Output : [0, 0, 0, 0, 0, 1, 1, 1, 1, 1] Input : [0, 1, 0]…

Try it on GfG Practice Given an array of n integers, find the 3 elements such that a[i] < a[j] < a[k] and i < j < k in 0(n) time. If there are multiple such triplets, then print any one of them. Examples: Input: arr[] = {12, 11, 10, 5, 6, 2, 30} Output: 5, 6, 30 Explanation: As 5 < 6 < 30, and they…

Try it on GfG Practice Given an array of integers, every element in the array appears twice except for one element which appears only once. The task is to identify and return the element that occurs only once. Examples: Input: arr[] = [2, 3, 5, 4, 5, 3, 4] Output: 2 Explanation: Since 2 occurs once,…

Try it on GfG Practice Given an array prices[] of size n denoting the cost of stock on each day, the task is to find the maximum total profit if we can buy and sell the stocks any number of times. Note: We can only sell a stock which we have bought earlier and we cannot hold multiple stocks on any…

Try it on GfG Practice Given an integer array arr[], find the sum of all sub-arrays of the given array. Examples: Input: arr[] = [1, 2, 3] Output: 20 Explanation: {1} + {2} + {3} + {2 + 3} + {1 + 2} + {1 + 2 + 3} = 20 Input: arr[] = [1, 2, 3, 4] Output: 50 Naive Approach - O(n^2) Time and O(1) Space…

Try it on GfG Practice Given an array arr[], sort the array according to the following relations: arr[i] >= arr[i - 1], if i is even, ∀ 1 <= i < narr[i] <= arr[i - 1], if i is odd, ∀ 1 <= i < n Find the resultant array.[consider 1-based indexing] Examples: Input: arr[] = [1, 2, 2, 1] Output: [1 2 1…

Try it on GfG Practice Given an integer array arr[], print all distinct elements from this array. The given array may contain duplicates and the output should contain every element only once. Examples: Input: arr[] = {12, 10, 9, 45, 2, 10, 10, 45} Output: {12, 10, 9, 45, 2} Input: arr[] = {1, 2, 3,…

Given an array arr[], the task is to determine the maximum possible value of the expression i*arr[i] after rotating the array any number of times (including zero). Note: In each rotation, every element of the array shifts one position to the right, and the last element moves to the front. Examples :…

There are many situations where we use integer values as index in array to see presence or absence, we can use bit manipulations to optimize space in such problems.Let us consider below problem as an example. Given two numbers say a and b, mark the multiples of 2 and 5 between a and b using less…

Given an array of n numbers, the task is to answer the following queries: kthSmallest(start, end, k) : Find the Kth smallest number in the range from array index 'start' to 'end'. Examples: Input : arr[] = {3, 2, 5, 1, 8, 9| Query 1: start = 2, end = 5, k = 2 Query 2: start = 1, end = 6, k = 4…

Try it on GfG Practice Given an array arr[] of integers of size N and an array of Q queries, query[], where each query is of type [L, R] denoting the range from index L to index R, the task is to find the LCM of all the numbers of the range for all the queries. Examples: Input: arr[] = {5, 7, 5, 2,…

We have an array arr[0 . . . n-1]. We should be able to efficiently find the minimum value from index L (query start) to R (query end) where 0 <= L <= R <= n-1. Consider a situation when there are many range queries. Example: Input: arr[] = {7, 2, 3, 0, 5, 10, 3, 12, 18}; query[] = [0, 4], [4, 7],…

We have an array arr[]. We need to find the sum of all the elements in the range L and R where 0 <= L <= R <= n-1. Consider a situation when there are many range queries. Examples: Input : 3 7 2 5 8 9 query(0, 5) query(3, 5) query(2, 4) Output : 34 22 15 Note : array is 0 based indexed and queries…

Sparse table concept is used for fast queries on a set of static data (elements do not change). It does preprocessing so that the queries can be answered efficiently. Range Minimum Query Using Sparse Table You are given an integer array arr of length n and an integer q denoting the number of…

Square Root Decomposition Technique is one of the most common query optimization techniques used by competitive programmers. This technique helps us to reduce Time Complexity by a factor of sqrt(N) The key concept of this technique is to decompose a given array into small chunks specifically of size…

Try it on GfG Practice Let us consider the following problem to understand MO's Algorithm. We are given an array and a set of query ranges, we are required to find the sum of every query range. Example: Input: arr[] = {1, 1, 2, 1, 3, 4, 5, 2, 8}; query[] = [0, 4], [1, 3] [2, 4] Output: Sum of arr[]…

Try it on GfG Practice Given two arrays L[] and R[] of size N where L[i] and R[i] (0 ? L[i], R[i] < 106)denotes a range of numbers, the task is to find the maximum occurred integer in all the ranges. If more than one such integer exists, print the smallest one. Examples: Input: L[] = {1, 4, 3, 1},…

Try it on GfG Practice In share trading, a buyer buys shares and sells on a future date. Given the stock price of n days, the trader is allowed to make at most k transactions (a transaction is a combination of a buy and a sell), where a new transaction can only start after the previous transaction…

Try it on GfG Practice Given a sorted array of distinct positive integers arr[] and integer k, the task is to find the kth positive number that is missing from arr[]. Examples : Input: arr[] = [2, 3, 4, 7, 11], k = 5 Output: 9 Explanation: Missing are 1, 5, 6, 8, 9, 10, ... and 5th missing number is…

Try it on GfG Practice Given an integer array arr[] of size n. The task is to find the maximum value of the sum of the value of i * arr[i] where i varies from 0 to n-1. The only operation allowed is to rotate the array any number of times. Examples: Input: arr[] = [8, 3, 1, 2] Output: 29…

Try it on GfG Practice Given a number, in the form of an array num[] of size n containing digits from 1 to 9(inclusive). The task is to find the next smallest palindrome strictly larger than the given number. Examples: Input: num[] = [9, 4, 1, 8, 7, 9, 7, 8, 3, 2, 2] Output: [9, 4, 1, 8, 8, 0, 8, 8,…

Try it on GfG Practice Given an array arr[] and an integer k, the task is to find the count of subarrays such that each subarray has exactly k distinct elements. Examples: Input: arr[] = [1, 2, 2, 3], k = 2 Output: 4 Explanation: Subarrays with exactly 2 distinct elements are: [1, 2], [1, 2, 2] and…