Ugly numbers are those number whose prime factors are 2, 3 or 5. From 1 to 15, there are 11 ugly numbers 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15. The numbers 7, 11, 13 are not ugly because they are prime. The number 14 is not ugly because in its prime factor the 7 will come.In this program, we will try to find the nth ugly number.Input and OutputInput: Take the term number. Say it is 10 Output: The 10th ugly number is 12AlgorithmgetUglyNumbers(n)Input: The number of terms.Output: Find nth Ugly numbers.Begin    define array named ... Read More

Shortest common super-sequence is a sequence where each element of both of the given sequences is present. In other words, we can say that the given two strings, both are sub-sequence of Shortest Common Super-Sequence.When there are no common characters in two strings, then we can simply concatenate them to get Super-sequence. But when they have some common characters, then firstly we have to find the longest string, then add extra characters of the other string.Input and OutputInput: Two strings. “ABCDEF” and “XYDEF” Output: The length of the shortest common super-sequence. Here the super-sequence is “ABCDEFXY”. So the length is ... Read More

A rod is given of length n. Another table is also provided, which contains different size and price for each size. Determine the maximum price by cutting the rod and selling them in the market.To get the best price by making a cut at different positions and comparing the prices after cutting the rod.Let the f(n) will return the max possible price after cutting a row with length n. We can simply write the function f(n) like this.f(n) := maximum value from price[i]+f(n – i – 1), where i is in range 0 to (n – 1).Input and OutputInput:The price ... Read More

For this problem, a given set can be partitioned in such a way, that sum of each subset is equal.At first, we have to find the sum of the given set. If it is even, then there is a chance to divide it into two sets. Otherwise, it cannot be divided.For even value of the sum, then we will create a table named partTable, now use the following condition to solve the problem.partTable[i, j] is true, when subset of array[0] to array[j-1] has sum equal to i, otherwise it is false.Input and OutputInput: A set of integers. {3, 1, 1, ... Read More

In this algorithm, the input is a string, a partitioning of that string is palindrome partitioning when every substring of the partition is a palindrome.In this algorithm, we have to find the minimum cuts are needed to palindrome partitioning the given string.Input and OutputInput: A string. Say “ababbbabbababa” Output: Minimum cut to partition as palindrome. Here 3 cuts are needed. The palindromes are: a | babbbab | b | ababaAlgorithmminPalPart(str)Input: The given string.Output: Minimum number of palindromic partitioning from the string.Begin    n := length of str    define cut matrix and pal matrix each of order n x n ... Read More

In a group, there is n number of friends. Each person can remain single or be paired with some other friend. Find the total number of ways, in which friends can remain single or can be paired up.If one pair has two friends’ p and q, then (p, q) or (q, p) are same. For a group of n friends, let f(n) be the number of ways how they can be paired up or remain single. Then either the nth person remains single, or paired up. If the nth person is single, then we recur for (n - 1) friends. If ... Read More

For this problem, one main string and another wildcard patterns are given. In this algorithm, it will check whether the wildcard pattern is matching with the main text or not.The wildcard pattern may contain letters or ‘*’ or ‘?’ Symbols. The ‘?’ Is used to match a single character and ‘*’ is used to match the sequence of characters including empty space.When the character is ‘*’: We can ignore the star character and move to check next characters in the pattern.When the next character is ‘?’, then we can ignore only the current character in the text, and check for ... Read More

In this article, we will discuss a classic Dynamic Programming problem that involves constructing an optimal binary search tree for a given set of keys with their search probabilities. Before diving into the problem, let us understand what are Binary Search Trees and Dynamic Programming. Optimal Binary Search Tree Problem In this problem, you are given: A sorted array of keys[] of size n that contains the keys to make the binary search tree. An array freq[] of size n, where freq[i] is how many times keys[i] is searched. ... Read More

A number is given. Our task is to break the number three times by n/2, n/3, and n/4 and find maximum sum we can make by dividing the number into three parts.For an example, 50 can be divided into {25, 16, 12}, now break each of the set {25, 16, 12}, into three divisions again, and so on. After completing the division up to 3 times, we will calculate the sum to find the maximum of them.This program can be solved in a recursive way, but in the recursive approach, we need to find the same results for multiple times, ... Read More

In this problem, a Numeric mobile keypad is given. We can only press top, bottom, right and left buttons of the current button, diagonal keys are not Allowed. We also cannot press the * and # buttons in the keypad.A digit is given, we have to find the number of possible numbers of given digits can be formed, using the keypad, maintaining given rules.Input and OutputInput: Digit count. Say 3 digit numbers. Output: Number of possible 3 digit numbers, that can be formed with the given conditions. Here the answer is 138.AlgorithmgetCount(n)Input: number of digits n.Output: Possible ways to type n ... Read More