We are given an array A of size n ( n <= 1000) , where A[i] = number of nodes in the level i of the tree.
Given this information, what is the maximum possible diameter of the tree. Can anyone help?
# | User | Rating |
---|---|---|
1 | tourist | 3843 |
2 | jiangly | 3705 |
3 | Benq | 3628 |
4 | orzdevinwang | 3571 |
5 | Geothermal | 3569 |
5 | cnnfls_csy | 3569 |
7 | jqdai0815 | 3530 |
8 | ecnerwala | 3499 |
9 | gyh20 | 3447 |
10 | Rebelz | 3409 |
# | User | Contrib. |
---|---|---|
1 | maomao90 | 171 |
2 | adamant | 163 |
2 | awoo | 163 |
4 | TheScrasse | 157 |
5 | nor | 153 |
6 | maroonrk | 152 |
6 | -is-this-fft- | 152 |
8 | Petr | 145 |
9 | orz | 144 |
9 | pajenegod | 144 |
We are given an array A of size n ( n <= 1000) , where A[i] = number of nodes in the level i of the tree.
Given this information, what is the maximum possible diameter of the tree. Can anyone help?
Name |
---|
For a brute force solution, try to construct a tree. Then select a random node $$$p$$$. Do the first bfs/dijkstra to get the furthest vertice $$$u$$$ from $$$p$$$. Do the second bfs/dijkstra to get the furthest vertice $$$v$$$ from $$$p$$$. Then $$$u-v$$$ is the furthest pair in tree, hence the diameter of the tree is the distance from $$$u$$$ to $$$v$$$
For your problem, we move from the root of some subtrees to the furthest possible node $$$u$$$ in the left, remove it from the tree and do the same thing with furthest possible node $$$v$$$ in the right. The diameter of the tree is the distance from $$$u$$$ to $$$v$$$
Any solution other than brute force?
The approaching of not attempting to construct such trees are choosing some substree's root and try to lowest leaf $$$u$$$ and erase the path, then do again and get vertice $$$v$$$, then $$$u-v$$$ would be the diameter of that subtree. The maximal over all diameters is diameter of the whole tree (Removing the path from $$$x$$$ to $$$y$$$ means to reduce the number of nodes of $$$a[x], a[x + 1], ..., a[y - 1], a[y]$$$, all by one)
The number of ways of choosing such subtree is $$$O(n)$$$ and finding diameter in $$$O(n)$$$. But there is still a way to improve this from $$$O(n^2)$$$ solution to linear $$$O(n)$$$ that is to using DP