In this problem, we are given a data stream that is continuously reading integers. Our task is to create a program that will read elements and calculate the medians for these elements.The Median of an array is the middle element from a sorted sequence(it can be ascending or descending).Calculating medianFor odd count, the median is the middle elementFor even count, the median is average of two middle elementLet’s take an example to understand the problem, Input − 3, 65, 12, 20, 1At each input, Input - 3 : sequence -(3) : median - 3 Input - 65 : sequence -(3, ... Read More

Problem statementGiven that integers are read from a data stream. Find median of elements read so for in an efficient wayAfter reading 1st element of stream - 10 -> median - 10After reading 2nd element of stream - 10, 20 -> median - 15After reading 3rd element of stream - 10, 20, 30 -> median - 20, so on...Algorithm1. Use a max heap on left side to represent elements that are less than effective median,    and a min heap on right side to represent elements that are greater than effective median 2. After processing an incoming element, the number ... Read More

In this problem, we are given an array of n integers and we are adding K elements to the array and then find the median of the resultant array. Given the condition, N+k is odd.Let’s take an example to understand the problem, Input −array = {23, 65, 76, 67} ; k =1Output −67To solve this problem, we will sort the given elements in ascending order and then add k elements at the end of the array i.e. we will take k greater elements.The condition is given that n+k is odd. So, the median can be calculated using the formula, (n+k)/2.ExampleProgram ... Read More

In this problem, we are given two vessels with capacities x and y and a supply of infinite water. Our task is to create a program that will be able to calculate exactly 1 liter in one vessel. Given the condition that x and y are co-primes. Co-primes also is known as relatively prime, mutually prime are numbers two numbers that have 1 as their only common divisor. So, this implies that their gcd(greatest common divisor) is 1.Here, let’s suppose we have two vessels V1 with capacity x and V2 with capacity y. To measure 1 liter using these two ... Read More

In this problem, we are given an array of n integers and some m querries. Our task is to create a program that calculates the integral value(round down) of the mean of the ranges given by the querries.Let’s take an example to understand the problem, Input −array = {5, 7, 8, 9, 10} m = 2; [0, 3], [2, 4]Output −7 9To solve this problem, we have two methods one is direct and the other is using prefix sum.In the direct approach, for each query, we will loop from the start index to the end index of the range. And ... Read More

In this problem, we are given a 2D array of size n*n. Our task is to create a program that will print the mean and median of the matrix in C++.Mean is the average of the date set. In a matrix mean is the average of all elements of the matrix.Mean = (sum of all elements of the matrix)/(number of elements of the matrix)Median is the middlemost element of the sorted data set. For this, we will have to sort the elements of the matrix.Median is calculated as, If n is odd, median = matrix[n/2][n/2]If n is even, median = ... Read More

In this problem, we are given a matrix of size n X n. Our task is to create a program that will calculate the maximum XOR value of a complete row or a complete column.Let’s take an example to understand the problem, Input −N = 3 mat[N][N] = {{4, 9, 1} {2, 8, 3} {10, 12, 11}}Output −13Explanation −Row1: 4^9^1 = 12 Row2: 2^8^3 = 9 Row3: 10^12^11 = 13 Col1: 4^2^10 = 12 Col2: 9^8^12 = 13 Col3: 1^3^11 = 9Here, we have calculated the XOR of all rows and columns and then the maximum of them is printed.To ... Read More

Problem statementGiven a range [L, R], we need to find two integers in this range such that their XOR is maximum among all possible choices of two integersIf the given range is L = 1 and R = 21 then the output will be 31 as − 31 is XOR of 15 and 16 and it is maximum within range.Algorithm1. Calculate the (L^R) value 2. From most significant bit of this value add all 1s to get the final resultExample#include using namespace std; int getMaxXOR(int L, int R){    int LXR = L ^ R;    int msbPos = ... Read More

In this problem, we are given two positive integers n and k. Our task is to find maximum xor between 1 to n using maximum X numbersLet’s take an example to understand the problem, Input − n = 5, k = 2Output − 7Explanation −elements till 5 is 1, 2, 3, 4, 5 Selecting all XOR pairs: 1^2 = 3, 1^3 = 2, 1^4 = 5, 1^5 = 4 2^3 = 4, 2^4 = 6, 2^5 = 7 3^4 = 7, 3^5 = 6 4^5 = 1 The maximum here is 7.To solve this problem, the maximum XOR can be ... Read More

Problem statementGiven a binary tree, write a function to get the maximum width of the given tree. The width of a tree is the maximum of widths of all levels.Consider below tree −      10      / \     7   4    / \   \   9   2   1          / \         2   5 1. Width at level 1: 1 2. Width at level 2: 2 3. Width at level 3: 3 4. Width at level 4: 2 For above tree answer is 3.Algorithm1. Use ... Read More