Given an integer N, the task is to construct a tree such that sum of for all ordered pairs (u, v) is maximum where u != v. Print the maximum possible sum.
Input: N = 4 Output: 26 1 / 2 / 3 / 4 For node 1, 1*2 + 1*2 + 1*1 = 5 For node 2, 2*1 + 2*2 + 2*1 = 8 For node 3, 2*1 + 2*2 + 2*1 = 8 For node 4, 1*1 + 1*2 + 1*2 = 5 Total sum = 5 + 8 + 8 + 5 = 26 Input: N = 6 Output: 82
Approach: We know that sum of the degree of all nodes in a tree is (2 * N) – 2 where N is the number of nodes in the tree. As we have to maximize the sum so we have to minimize the number of leaf nodes as the leaf nodes have the minimum degree among all the nodes of the tree and the tree will be of the form:
1 / 2 / ... / N
where only the root and the only leaf node will have a degree of 1 and all the other nodes will have degree 2.
Below is the implementation of the above approach:
- Minimum Operations to make value of all vertices of the tree Zero
- Possible edges of a tree for given diameter, height and vertices
- Make a tree with n vertices , d diameter and at most vertex degree k
- Find the number of distinct pairs of vertices which have a distance of exactly k in a tree
- Sum of pairwise products
- Maximum Sum of Products of Two Arrays
- Number of Simple Graph with N Vertices and M Edges
- Find the cordinates of the fourth vertex of a rectangle with given 3 vertices
- Number of ways a convex polygon of n+2 sides can split into triangles by connecting vertices
- Maximize the value of x + y + z such that ax + by + cz = n
- Maximize the value of the given expression
- Maximize a value for a semicircle of given radius
- Maximize the product of four factors of a Number
- Maximize volume of cuboid with given sum of sides
- Maximize profit when divisibility by two numbers have associated profits
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