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can someone help me with this problem

You have a tree (N nodes, undirected). each node can be colored as black or white. 2 node can be connected if they are both white and the path between 2 nodes is the set of only black nodes or these 2 nodes can move to each other by 1 edge. the problem is you need to color the tree to have the maximum connected pair of nodes test inp: first line contains T(T<=10) is the number of test cases, next is N (N<=5000) is the number of nodes in the tree, N-1 next lines is an edge connected 2 nodes U and V output: each test case output 1 number is the maximum pair of nodes can be connected inp: 2 8 1 2 2 3 2 4 4 5 5 6 6 7 6 8 2 1 2 out: 7 1

asked 28 Nov, 13:43

blebleble's gravatar image

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edited 28 Nov, 13:57

Please post the link of problem

(28 Nov, 14:08) admin55★

Call dp[i][j]: The answer for the subtree of i, j represents how many new pairs will be created if i is painted white. The recurrence is simple:

  • Paint vertex i white, for each child v get the maximum of dp[v][j] + j. Set dp[i][1] to the sum of these on all children.
  • Paint vertex i black. dp[i][j] = dp[i][j - k] + dp[v][k] + k * (j - k) (j - k white nodes in i's subtree is connected to k white nodes in v's subtree).

The total complexity is O(T * N ^ 2), which is enough to pass the task.


answered 28 Nov, 19:43

ducpro's gravatar image

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thank you so much

(28 Nov, 21:58) blebleble0★
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question asked: 28 Nov, 13:43

question was seen: 138 times

last updated: 29 Nov, 08:52