In this problem, we are given an integer N and we have to print all proth prime numbers less than or equal to N.Proth Prime NumberA proth prime number is a positive integer whose value can be represented as n = k* 2n + 1. where k is an odd positive integer and n is a positive integer and both satisfy the 2n > k.Examples − 3, 5, 13…..Let’s take an example to understand the topic better −Input: N = 23 Output: 3, 5, 13, 17.For this, we will find all the prime numbers less than N(for this we will ... Read More

In this problem, we are given a binary tree. And we have to print all the paths from the root to the leaf of the tree. Also, add underscore “_” to show the relative positions of the nodes.Let’s take an example to understand the topic better −Input −Output −_ _ 3 _ 9 1 _3 9 _7 3 _ 4 _ _ 2 3 9 4 1 7 6 2 3 _ 4 6To solve this problem, we will use the concept of the vertical order of the elements of the tree.Based on this, we will print the path from ... Read More

In this problem, we are given an integer N and we have to print all safe prime number whose values are less than N.A safe prime number is a prime number which can be represented as [(2*p)- 1] where p is also a prime number.Examples − 5[(2*2) +1] , 7[(2*3)+1].Let’s take a few examples to understand the problem better −Input: N = 12 Output: 5 7 11.To solve this problem, we will find all the prime numbers less than N(for this we will use Sieve of Eratosthenes). And check if the prime number is a safe prime number or not ... Read More

In this problem, we are given an integer N. and we have to print all the semiprime numbers that are less than or equal to N.Before solving this problem, let’s understand what is a semi-prime number.A semi-prime number is a number whose value is the product of two distinct prime numbers.Let’s take an example, 21 = 3*7 is a semiprime number.25 = 5*5 is not a semiprime number.Now, let’s take an example of semiprime numbers less than or equal to n.Input: N = 15 Output: 6 10 14 15To solve this problem, we have to take each number less than ... Read More

In this problem, we are given two integer values, k, and n. And we have to print all the sequences of length k from numbers from 1 to n in sorted order.Let’s take an example to understand the topic −Input:k = 2 ; n = 3 Output: 1 1 1 2 1 3 2 1 2 2 2 3 3 1 3 2 3 3So in this problem, we have to print the sequence as stated above.A simple way to solve this problem is by incrementing integers of the sequence till they get to the max value i.e. n. The ... Read More

In this problem, we are given three variables n, s, and k and we have to print all the possible sequences that start with the number n and length s having the absolute difference between consecutive elements less than k.Let’s take an example to understand the topic better −Input: n = 3, s = 3 , k = 2 Output: 3 3 3 3 3 4 3 3 2 3 4 4 3 4 5 3 4 3 3 2 2 3 2 3 3 2 1In this problem, we need to obtain the absolute difference less k. For this, ... Read More

In this problem, we are given an array and we have to print all the subset of a given size r that can be formed using the element of the array.Let’s take an example to understand the topic better −Input: array = {3, 5, 6} r = 2 Output: 3 5 3 6 5 6In this problem, we will have to find all the combinations of the numbers of the array. And exclude those r bit combinations which are already in the set.Example Live Demo#include using namespace std; void printSubset(int arr[], int n, int r, int index, int data[], int ... Read More

In this problem, we are given an integer n. And we have to print all substrings of a number that can be formed but converting the string are not allowed i.e. we cannot convert an integer into string or array.Let’s take an example to understand the topic better −Input: number =5678 Output: 5, 56, 567, 5678, 6, 67, 678, 7, 78, 8In order to solve this problem, we will need to use mathematical logic. Here, we will print the most significant bit first, then successive bits are printed.AlgorithmStep1: Take a 10’s power number based on the number of digits. Step2: ... Read More

In this problem, we are given an array of N elements. And need to return all the sums of the elements are divisible by an integer M.Input : array = {4, 7, 3} ; M = 3 Output : 5+4+3 ; 5+4-3To solve this problem, we need to know the concept of a power set that can be used to find all the possible sums obtained. From this sum, print all those which are divisible by M.AlgorithmStep 1: Iterate overall combinations of ‘+’ and ‘-’ using power set. Step 2: If the sum combination is divisible by M, print them ... Read More

In this problem, we are given an undirected graph and we have to print all the cycles that are formed in the graph.Undirected Graph is a graph that is connected together. All the edges of the unidirectional graph are bidirectional. It is also known as an undirected network.Cycle in a graph data structure is a graph in which all vertices form a cycle.Let’s see an example to understand the problem better −Graph-Output-Cycle 1: 2 3 4 5 Cycle 2: 6 7 8For this, we will make use of a few properties of the graph. You need to use graph coloring ... Read More