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:
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