Consider we have a binary tree, this binary tree is not a BST. We have to check whether the binary tree contains same element more than one time or not. To solve this, we will use hashing. We will traverse the given tree, for each node, we will check whether the node is present in the table or not, if that is already present, then return false, otherwise true.Example Live Demo#include #include using namespace std; class Node {    public:    int data;    Node *left;    Node *right; }; Node* getNode(int data){    Node *newNode = new Node; ... Read More

Suppose we have a binary string, another integer k. We have to check the string is containing all permutations of binary of k bits. Suppose a string is like “11001”, and if the K = 2, then it must have all permutations of k bit numbers. (00, 01, 10, 11), the given string has all permutation. So this is valid string.by taking the binary string and the value of k, we have to check whether binary sequences are matched or not. The binary sequence is made of size k. So there will be 2k number of different binary permutations. We ... Read More

Suppose we have one 2D array of size N x M. The task is to check if we can select a number from every row, in such a way that the XOR of those elements is non-zero or greater than 0. Suppose one matrix is like this −77710107If we perform XOR, the answer will be non-zero, as the except last elements of two rows are 7 and 10To solve this problem, the solution will be very easy. Initially check if XOR of the elements of the first column of each row is 0 or not. If it is non-zero then ... Read More

Here we will see how to check whether a matrix is invertible or not. If one matrix is M, then the inverted matrix M-1 will be −$$M^-1=\frac{adj(M)}{|M\lvert}$$So if the determinant of M is non-zero, then only we can get the inverse, otherwise, we will not get the inverse of it. So here we have to check the determinant is non-zero or not. Finding a determinant is one recursive process. We have to find submatrix, then find the determinant of it, then use that result for the final calculation. Let us see the code to get a better idea.Example Live Demo#include ... Read More

Suppose we have a circle and another straight line. Our task is to find if the line touches the circle or intersects it, otherwise, it passes through outside. So there are three different cases like below −Here we will solve it by following steps. These are like below −Find perpendicular P between the center and given a lineCompare P with radius r −if P > r, then outsideif P = r, then touchesotherwise insideTo get the perpendicular distance, we have to use this formula (a center point is (h, k))$$\frac{ah+bk+c}{\sqrt{a^2+b^2}}$$Example Live Demo#include #include using namespace std; void isTouchOrIntersect(int a, ... Read More

To check a strongly connected graph using Kosaraju's algorithm, we need to understand the strongly connected graph and Kosaraju's algorithm. For a graph to be strongly connected, it should be a directed graph, and for any pair of vertices u and v in the directed graph, there exists a directed path from u to v and a directed path from v to u. In this article, we have a directed graph with five vertices. Our task is to use Kosaraju's algorithm to check if the given graph is strongly ... Read More

Here we will see how to check whether a tree graph is linear or not. A linear tree graph can be expressed in one line, suppose this is an example of a linear tree graph.But this is not linear −To check a graph is linear or not, we can follow two conditionsIf the number of nodes is 1, then the tree graph is linearIf (n – 2) of its nodes have in-degree 2Example Live Demo#include #include #define N 4 using namespace std; class Graph{    private:    int V;    vector *adj;    public:    Graph(int v){     ... Read More

Here we will see how to check whether a string is sum-string or not. A string is said to be sum-string if the rightmost substring can be written as the sum of two substrings before it, and the same is recursively true for substring before it. Suppose a string like 12243660 is a sum string, like 12 + 24 = 36, and the 36 is present after 12 and 24 in the string, again 24 + 36 = 60, this is also present in the string.A string S can be called sum-string, if it follows this rule −𝑠𝑢𝑏𝑠𝑡𝑟𝑖𝑛𝑔(𝑖, 𝑥)+𝑠𝑢𝑏𝑠𝑡𝑟𝑖𝑛𝑔(𝑥+1, 𝑗)= ... Read More

We have two circles. The center of both of them is at the origin. The radius of these two circles is given. They are r and R, R > r. Another circle is also present. Its radius (r1) and the center point are given, we have to check whether that point is inside the ring formed by the first two circles or not.We can solve this using the Pythagorean theorem. compute the distance from the center of the circle and origin. Then if (distance – r1) >= r and (distance – r1) = R && dis+r1

Here we will see how to check whether a binary tree is sum-tree or not. Now the question is what is the sum-tree. A sum-tree is a binary tree where a node will hold the sum value of its children. The root of the tree will contain an entire sum of all elements below it. This is an example of sum-tree −To check this, we will follow a simple trick, we will find the sum of left and right subtree elements if the sum value is the same as the root, then that is sum-tree. This will be one recursive ... Read More