In this problem, we are given a number and we have to print all words that can be formed by pressing those words in an old fashioned mobile keyboard.We are quite familiar with the QWERTY keyboard style that we use today. But before the invention of QWERTY keypad phones were fitted with keypads with 12 buttons and each button contains words and numbers both. Like they word 6 on the keypad will contain words “MNO” which will be typed by clicking one, twice or thrice the keys.The keypad looked like this −12ABC3DEF4GHI5JKL6MNO7PQRS8TUV9WXYZ*0#In these keywords also all words are present and ... Read More

In this problem, we are given a number N, and we have to find all unique prime factors and their powers that divide the number.Let’s take an example to understand the topic −Input: 55 Output: 5 power 1 11 power 1Explanation −55 is divisible by 5 and 11.To solve this problem, an easy approach to solving the problem is to find prime factors of N. And then find power of the prime number that divides the number N and print it.AlgorithmEfficient ApproachStep 1: Find an array s[N+1]. s[i] = prime factor of i dividing N. Step 2: Find all powers ... Read More

In this problem, we are given a number N and we have to print all prime numbers less than or equal to N.Let’s take an example to understand the topic better −Input: 10 Output: 2 3 5 7A prime number is a number that can be divided by only one and the number itself. Example: 2, 3.A simple approach is to iterate from 2 to N and divide the number by it. If the number is not divisible, then it’s a prime number. Print the number. Do this till the number is equal to N. This approach is not that ... Read More

In this problem, we are given a positive integer N, and we have to print all prime quadruplet less than or equal to n.Prime quadruplets are the set of four prime numbers calculated as {p, p+2, p+6, p+8}. Example − 5 7 11 13.Let’s take an example to understand the problem −Input: N = 15 Output: 5 7 11 13.To solve this problem, a simple approach is to generate all quadruplets of prime number p and check if all p, p+2, p+6, p+8 are prime numbers. This solution is easy but is more complex for the compiler.Another efficient approach is ... Read More

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