ConceptWith respect of given positive integer n, the task is to verify if n is an Achilles number or not. We have to print 'YES' if N is treated as an Achilles number else print 'NO'.Achilles number: With respect of Mathematics, an Achilles number is defined as a number that is powerful (A number N is said to be Powerful Number if it has been noted that for every prime factor p of it, p^2 also divides it) but not a perfect power.In following, the first few Achilles number are displayed72, 108, 200, 288, 392, 432, 500, 648, 675, 800, ... Read More

ConceptWith respect of given number n, the task is to verify whether n is a Trojan Number or not. Trojan Number is defined as a number that is a strong number without a perfect power. We can say that a number n is treated as a strong number if, for every prime divisor or factor p of n, p^2 is also a divisor. We can say in another way, every prime factor appears at least twice. We should remember that all Trojan numbers are strong. But it is not true for vice-versa that means, not all strong numbers are Trojan ... Read More

Suppose we have n different points (Xi, Yi) in 2D coordinate and each point has a weight Wi, we have to check whether a line at 45 degree can be drawn. So that the sum of weights of points on each side will be same.So, if the input is like[[-1, 1, 3], [-2, 1, 1], [1, -1, 4]], then the output will be True/To solve this, we will follow these steps −n := size of vDefine one map weight_at_xmax_x := -2000, min_x := 2000for initialize i := 0, when i < n, update (increase i by 1), do −temp_x := ... Read More

ConceptWith respect of given infinite chessboard with the same rules as that of chess and given N knights coordinates on the infinite chessboard (-10^9 {3, 4}Output NoThe king can be able to make valid moves.MethodHere, the knight’s move is unusual among chess pieces. Its movement is towards a square that is two squares away horizontally and one square vertically, or two squares vertically and one square horizontally. So, the complete move looks like the letter “L” in every shape possible (8 possible moves). As a result of this, apply a hash map of pairs to mark all possible coordinates where ... Read More

ConceptWith respect of a given array arr1[] with size of array N, one another key X and a segment size K, the task is to determine that the key X present in every segment of size K in arr1[].Input arr1[] = { 4, 6, 3, 5, 10, 4, 2, 8, 4, 12, 13, 4} X = 4 K = 3Output YesThere are existence of 4 non-overlapping segments of size K in the array, {4, 6, 3}, {5, 10, 4}, {2, 8, 4} and {12, 13, 4}. 4 is present all segments.Input arr1[] = { 22, 24, 57, 66, 35, 55, 77, 33, 24, ... Read More

ConceptIt should be validated if a given string is numeric.Input − str = "12.5"Output − trueInput − str = "def"Output − falseInput − str = "2e5"Output − trueInput − 10e4.4Output − falseMethodWe have to handle the following cases in the code.We have to ignore the leading and trailing white spaces.We have to ignore the ‘+’, ‘-‘ and’.’ at the start.We have to ensure that the characters in the string belong to {+, -, ., e, [0-9]}We have to ensure that no ‘.’ comes after ‘e’.A digit should follow a dot character ‘.’.We have to ensure that the character ‘e’ should ... Read More

The Depth First Search (DFS) algorithm can be used to check whether a graph is bipartite by coloring the graph using two colors. This section will discuss how DFS traversal can be used to check if a graph is bipartite. First of all, let's understand what a bipartite graph is. What is Bipartite Graph? A bipartite graph is a special type of graph where you can divide the vertices into two sets, such that no two vertices of the same set are connected. This is why it's possible to color a bipartite graph using just two colors. Technically, a ... Read More

ConceptWith respect of a given binary tree, we need to verify whether it has heap property or not, Binary tree need to satisfy the following two conditions for being a heap –Binary tree should be a complete tree (i.e. all levels except last should be full).Binary tree's every node’s value should be greater than or equal to its child node (considering max-heap).ExampleWith respect of following example this tree contains heap property –The following example does not have heap property –MethodIt is required to verify each of the above condition separately, for verifying completeness isComplete(This function checks if the binary tree ... Read More

ConceptWith respect of a Red-Black Tree, the largest height of a node is at most double the minimum height.For a given Binary Search Tree, we need to verify for following property.With respect of every node, length of the longest leaf to node path has not more than double the nodes on shortest path from node to leaf.Examples13    41 \    / \ 15  11 101 \   /    \ 17 61 151Above tree cannot be a Red-Black Tree Above tree can be Red-Black Tree with any color assignmentMax height of 13 is 1Min height of 13 is 3  ... Read More

ConceptWith respect of given a string str containing characters ‘(‘, ‘)’, ‘{‘, ‘}’, ‘[‘ and ‘]’, the task is to find if brackets are balanced or not.Brackets are denoted as balanced if −We close open brackets must be closed by the same type of brackets.Again we close open brackets according to the correct order.Input − str = “(()){}”Output − YesInput − str = “))(([][”Output − NoMethodAssign two variables a and b to keep track of two brackets to be compared.A count should be maintained whose value increments on encountering opening bracket and decrements on encountering a closing bracket.Assign b = ... Read More