Suppose we have two integers n and k. We have to find the maximum value of x, such that n! mod (k^x) = 0. So when n = 5, and k = 2, then output will be 3. As n! = 120, now for different values of x, it will be −120 mod 2^0 = 0, 120 mod 2^1 = 0, 120 mod 2^2 = 0, 120 mod 2^3 = 0, 120 mod 2^4 = 8, 120 mod 2^5 = 24, 120 mod 2^6 = 56, 120 mod 2^7 = 120. As the max value of x = 3, the ... Read More

Suppose we have two integers N and K. We have to find a permutation of integers from the range [1 to N] such that the number of indices (1 – base indexing) where gcd(P[i], i) > 1 is exactly K. So if N = 4 and K = 3, then output will be [1, 2, 3, 4], as gcd(1, 1) = 1, gcd(2, 2) = 2, gcd(3, 3) = 3, gcd(4, 4) = 4If we observe it carefully, we can find that gcd(i, i+1) = 1, gcd(1, i) = 1 and gcd(i, i) = i. As the GCD of any ... Read More

Suppose we have two numbers n and fact. We have to find the largest power of n, that divides fact! (factorial of fact). So if fact = 5, and n = 2, then output will be 3. So 5! = 120, and this is divisible by 2^3 = 8.Here we will use the Legendre’s formula. This finds largest power of a prime, that divides fact!. We will find all prime factors of n, then find largest power of it, that divides fact!.So if fact is 146, and n = 15, then prime factors of n are 5 and 3. Sofor ... Read More

As we know some basic features of an object oriented programming language are the Inheritance, Encapsulation, Polymorphism. Any language that supports these features completely are known as object oriented programming languages. Some languages like C++ supports these three but not fully, so they are partially object oriented language. Let us see the reason why C++ is not known as completely object oriented language.In C++, we need the main() function to start executing, but in C++, the main functions are not present inside the class. So we can also write code without using class in C++. Some OOP languages like JAVA, ... Read More

Suppose we have a number of n digits. We have to find the maximum number that can be obtained using all digits of digits of that number. So if the number is say 339625, then maximum number can be 965332.From the problem, we can see that we can easily sort the digits in non-increasing order, then print them. But we can solve this using more efficient way. We can create one array of size 10 to store the frequency of each digit, then print the numbers from 9 to 0 accordingly.Example Live Demo#include #include using namespace std; int maxNumFromNum(int ... Read More

Here we will see when we need to create own assignment operator in C++. If a class do not have any pointers, then we do not need to create assignment operator and copy constructor. C++ compiler creates copy constructor and assignment operator for each class. If the operators are not sufficient, then we have to create our own assignment operator.Example#include using namespace std; class MyClass { //no user defined assignment operator or copy constructor is present    int *ptr;    public:       MyClass (int x = 0) {          ptr = new int(x);       }       void setValue (int x) {          *ptr = x;       }       void print() {          cout

Suppose we have an array of n elements. We have to find the maximum number of elements to select from the array, such that the absolute difference between any two of the chosen elements is less than or equal to 1. So if the array is like [2, 2, 3, 4, 5], then the element will be 3, so the sequence with maximum count is 2, 2, 3.The absolute difference of 0 and 1 means, that the number can be of type x and x + 1. So the idea is to store the frequencies of array elements. So if ... Read More

Here we will see how to use the sort() function of C++ STL to sort an array So if the array is like A = [52, 14, 85, 63, 99, 54, 21], then the output will be [14 21 52 54 63 85 99]. To sort we will use the sort() function, that is present in the header file . The code is like below −Example Live Demo#include #include using namespace std; int main() {    int arr[] = {52, 14, 85, 63, 99, 54, 21};    int n = sizeof(arr) / sizeof(arr[0]);    cout

Suppose we want to make a stack that can store the maximum element in the stack. And we can get it in O(1) time. The constraint is that, it should use O(1) extra space.We can make one user-defined stack, that will store the max value, when one operation is performed, like pop or peek, then the max will be returned. For peek operation, return the maximum of stack top and the max element, for pop operation, when the top element is larger, then print it and update max as 2*max – top_element. otherwise return top_element. For push operation update the ... Read More

In this section we will see how to create and use complex numbers in C++. We can create complex number class in C++, that can hold the real and imaginary part of the complex number as member elements. There will be some member functions that are used to handle this class.In this example we are creating one complex type class, a function to display the complex number into correct format. Two additional methods to add and subtract two complex numbers etc.Example Live Demo#include using namespace std; class complex{    int real, img;    public:       complex(){       ... Read More