Class Solution
- java.lang.Object
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- g2401_2500.s2467_most_profitable_path_in_a_tree.Solution
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public class Solution extends Object
2467 - Most Profitable Path in a Tree.Medium
There is an undirected tree with
n
nodes labeled from0
ton - 1
, rooted at node0
. You are given a 2D integer arrayedges
of lengthn - 1
whereedges[i] = [ai, bi]
indicates that there is an edge between nodesai
andbi
in the tree.At every node
i
, there is a gate. You are also given an array of even integersamount
, whereamount[i]
represents:- the price needed to open the gate at node
i
, ifamount[i]
is negative, or, - the cash reward obtained on opening the gate at node
i
, otherwise.
The game goes on as follows:
- Initially, Alice is at node
0
and Bob is at nodebob
. - At every second, Alice and Bob each move to an adjacent node. Alice moves towards some leaf node , while Bob moves towards node
0
. - For every node along their path, Alice and Bob either spend money to open the gate at that node, or accept the reward. Note that:
- If the gate is already open , no price will be required, nor will there be any cash reward.
- If Alice and Bob reach the node simultaneously , they share the price/reward for opening the gate there. In other words, if the price to open the gate is
c
, then both Alice and Bob payc / 2
each. Similarly, if the reward at the gate isc
, both of them receivec / 2
each.
- If Alice reaches a leaf node, she stops moving. Similarly, if Bob reaches node
0
, he stops moving. Note that these events are independent of each other.
Return the maximum net income Alice can have if she travels towards the optimal leaf node.
Example 1:
Input: edges = [[0,1],[1,2],[1,3],[3,4]], bob = 3, amount = [-2,4,2,-4,6]
Output: 6
Explanation:
The above diagram represents the given tree. The game goes as follows:
- Alice is initially on node 0, Bob on node 3. They open the gates of their respective nodes.
Alice’s net income is now -2.
- Both Alice and Bob move to node 1.
Since they reach here simultaneously, they open the gate together and share the reward.
Alice’s net income becomes -2 + (4 / 2) = 0.
- Alice moves on to node 3. Since Bob already opened its gate, Alice’s income remains unchanged.
Bob moves on to node 0, and stops moving.
- Alice moves on to node 4 and opens the gate there. Her net income becomes 0 + 6 = 6.
Now, neither Alice nor Bob can make any further moves, and the game ends.
It is not possible for Alice to get a higher net income.
Example 2:
Input: edges = [[0,1]], bob = 1, amount = [-7280,2350]
Output: -7280
Explanation:
Alice follows the path 0->1 whereas Bob follows the path 1->0.
Thus, Alice opens the gate at node 0 only. Hence, her net income is -7280.
Constraints:
2 <= n <= 105
edges.length == n - 1
edges[i].length == 2
0 <= ai, bi < n
ai != bi
edges
represents a valid tree.1 <= bob < n
amount.length == n
amount[i]
is an even integer in the range[-104, 104]
.
- the price needed to open the gate at node
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Constructor Summary
Constructors Constructor Description Solution()
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description int
mostProfitablePath(int[][] edges, int bob, int[] amount)
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