You are given a weighted tree T.(As a reminder, a tree T is a graph that is connected and contains no cycle.) Each node of the tree T has a weight, denoted by w(v). You want to select a subset of tree nodes, such that weight of the selected nodes is maximized, and if a node is selected, then none of its neighbors are selected.
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You are given a weighted tree T.(As a reminder, a tree T is a graph that is connected and contains no cycle.) Each node of the tree T has a weight, denoted by w(v). You want to select a subset of tree nodes, such that weight of the selected nodes is maximized, and if a node is selected, then none of its neighbors are selected.
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- 36. Let G be a simple graph on n vertices and has k components. Then the number m of edges of G satisfies n-k ≤m if G is a null graph. This statement is A. sometimes true B. always true C. never true D. Neither true nor falseC++ Given a directed graph. The task is to find a shortest path from vertex 0to a target vertex v. You may adapt Breadth First Traversal of thisgraph starting from 0 to achieve this goal.Note: One can move from node u to node v only if there's an edge from u to v and find the BFS traversal of the graph starting from the 0th vertex, from left to right according to the graph. Also, you should only take nodes directly or indirectly connected from Node 0 in consideration. ExampleInput:6 8 20 10 41 20 33 54 55 23 1Output:0 1 2 Use the driver code typed out below. // { Driver Code Starts #include <bits/stdc++.h>using namespace std; // } Driver Code Endsclass Solution { public: // Function to return a path vector consisting of vertex ids from vertex 0 to target vector shortestPath(int V, vector adj[], int target) { // Enter code here! }}; // { Driver Code Starts.int main() { int tc; cin >> tc; while (tc--) { int V, E, target; cin >> V >> E >> target; vector…5. Consider a directed graph G with n nodes. Write a function findUnreachableNode that takes a node and prints all the nodes that are unreachable from the given node. You can use either adjacency list or adjacency matrix to solve this problem. Function Signature: findUnreachableNode (int node) For example: In the following graph, findUnreachableNode (0) will return 4, 6, 7 as they are unreachable from node 0. 1 7 4 Good luck!!!
- 5. (This question goes slightly beyond what was covered in the lectures, but you can solve it by combining algorithms that we have described.) A directed graph is said to be strongly connected if every vertex is reachable from every other vertex; i.e., for every pair of vertices u, v, there is a directed path from u to v and a directed path from v to u. A strong component of a graph is then a maximal subgraph that is strongly connected. That is all vertices in a strong component can reach each other, and any other vertex in the directed graph either cannot reach the strong component or cannot be reached from the component. (Note that we are considering directed graphs, so for a pair of vertices u and v there could be a path from u to v, but no path path from v back to u; in that case, u and v are not in the same strong component, even though they are connected by a path in one direction.) Given a vertex v in a directed graph D, design an algorithm for com- puting the strong connected…This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played altogether, in all the rounds of the tournament? Your answer: Hint: This is much simpler than you think. When you see the answer you will say "of course".Given a directed graph. The task is write a program given the driver codes to find a shortest path from vertex 0 to a target vertex v. You may adapt Breadth First Traversal of this graph starting from 0 to achieve this goal.Note: One can move from node u to node v only if there's an edge from u to v and find the BFS traversal of the graph starting from the 0th vertex, from left to right according to the graph. Also, you should only take nodes directly or indirectly connected from Node 0 in consideration. ExampleInput:6 8 20 10 41 20 33 54 55 23 1Output:0 1 2 Use the driver code typed out below. // { Driver Code Starts #include <bits/stdc++.h>using namespace std; // } Driver Code Endsclass Solution { public: // Function to return a path vector consisting of vertex ids from vertex 0 to target vector shortestPath(int V, vector adj[], int target) { // Enter code here! }}; // { Driver Code Starts.int main() { int tc; cin >> tc; while (tc--) { int V, E, target; cin >> V…
- In the figure below there is a weighted graph, dots represent vertices, links represent edges, and numbers represent edge weights. S 2 1 2 1 2 3 T 1 1 2 4 (a) Find the shortest path from vertex S to vertex T, i.e., the path of minimum weight between S and T. (b) Find the minimum subgraph (set of edges) that connects all vertices in the graph and has the smallest total weight (sum of edge weights). 2. 3.Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Artem is building another robot. He has a network a comprising of n lines and m sections. The cell situated on the I-th line from the top and the j-th segment from the left has a worth ai,j written in it. In the event that two nearby cells contain a similar worth, the robot will break. A lattice is called acceptable if no two adjoining cells contain a similar worth, where two cells are called nearby on the off chance that they share a side. Artem needs to increase the qualities in certain cells by one to make a decent. All the more officially, find a decent network b that fulfills the accompanying condition — For all substantial (i,j), either bi,j=ai,j or bi,j=ai,j+1. For the imperatives of this issue, it tends to be shown that such a framework b consistently exists. In case there are a few such tables, you can output any of them. Kindly note that you don't need to limit…It's Gary's birthday today and he has ordered his favourite square cake consisting of '0's and '1's . But Gary wants the biggest piece of '1's and no '0's . A piece of cake is defined as a part which consist of only '1's, and all '1's share an edge with each other on the cake. Given the size of cake N and the cake, can you find the count of '1's in the biggest piece of '1's for Gary ?Input Format :The first line of input contains an integer, that denotes the value of N. Each of the following N lines contain N space separated integers.Output Format :Print the count of '1's in the biggest piece of '1's, according to the description in the task.Constraints :1 <= N <= 1000Time Limit: 1 secSample Input 1:21 10 1Sample Output 1:3 Solution: /////////////////public class Solution { static int[][] dir = { { 1, 0 }, { -1, 0 }, { 0, 1 }, { 0, -1 } }; public static int dfs(String[] edge, int n) { boolean[][] visited = new boolean[n][n]; int max = 0; for(int…
- Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. each individual has a rating chart portrayed by a variety of integers an of length n. You are currently refreshing the foundation, so you've made a program to pack these diagrams. The program functions as follows. Given an integer boundary k, the program takes the base of each adjoining subarray of length k in a. All the more officially, for a cluster an of length n and an integer k, characterize the k-pressure exhibit of an as a cluster b of length n−k+1, to such an extent that bj=minj≤i≤j+k−1ai For instance, the 3-pressure cluster of [1,3,4,5,2] is [min{1,3,4},min{3,4,5},min{4,5,2}]=[1,3,2]. A stage of length m is an exhibit comprising of m unmistakable integers from 1 to m in subjective request. For instance, [2,3,1,5,4] is a stage, however [1,2,2] isn't a change (2 shows up twice in the exhibit) and [1,3,4] is likewise not a stage (m=3 but rather there is 4 in the…Suppose a candidate solution p, where p is a phenotype consisting of 4 vertices. Suppose that minimum fitness occurs when no pair of vertices in p are connected, and maximum fitness occurs when all pairs of vertices in p are connected. Write a pseudocode on how to calculate the fitness F of p.Single Point based Search: Fair share problem: Given a set of N positive integers S={x1, x2, x3,…, xk,… xN}, decide whether S can be partitioned into two sets S0 and S1 such that the sum of numbers in S0 equals to the sum of numbers in S1. This problem can be formulated as a minimisation problem using the objective function which takes the absolute value of the difference between the sum of elements in S0 and the sum of elements in S1. Assuming that such a partition is possible, then the minimum for a given problem instance would have an objective value of 0. A candidate solution can be represented using a binary array r=[b1, b2, b3,…, bk,… bN], where bk is a binary variable indicating which set the k-th number in S is partitioned into, that is, if bk =0, then the k-th number is partitioned in to S0, otherwise (which means bk =1) the k-th number is partitioned in to S1. For example, given the set with five integers S={4, 1, 2, 2, 1}, the solution [0,1,0,1,1] indicates that S is…