How hard is LeetCode 2467. Most Profitable Path in a Tree?

LeetCode 2467. Most Profitable Path in a Tree is rated Medium on LeetCode.

What is the time complexity of LeetCode 2467. Most Profitable Path in a Tree?

The Python solution on this page runs in O(n).

What is the space complexity of LeetCode 2467. Most Profitable Path in a Tree?

The Python solution on this page uses O(n) auxiliary space.

What topics does LeetCode 2467. Most Profitable Path in a Tree cover?

LeetCode 2467. Most Profitable Path in a Tree is tagged Tree, Depth-First Search, Breadth-First Search, Graph and Array on LeetCode.

Most Profitable Path in a Tree — LeetCode 2467 Python Solution

MediumTreeDepth-First SearchBreadth-First SearchGraphArray

Problem: #2467
Pattern: Tree Traversal
Reading time: 7 min
Source: leetcode.com

The problem

There is an undirected tree with n nodes labeled from 0 to n - 1, rooted at node 0. You are given a 2D integer array edges of length n - 1 where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree.

Example

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:

Python solution

Python

class Solution:
    def mostProfitablePath(
        self, edges: List[List[int]], bob: int, amount: List[int]
    ) -> int:
        def dfs1(i, fa, t):
            if i == 0:
                ts[i] = min(ts[i], t)
                return True
            for j in g[i]:
                if j != fa and dfs1(j, i, t + 1):
                    ts[j] = min(ts[j], t + 1)
                    return True
            return False

        def dfs2(i, fa, t, v):
            if t == ts[i]:
                v += amount[i] // 2
            elif t < ts[i]:
                v += amount[i]
            nonlocal ans
            if len(g[i]) == 1 and g[i][0] == fa:
                ans = max(ans, v)
                return
            for j in g[i]:
                if j != fa:
                    dfs2(j, i, t + 1, v)

        n = len(edges) + 1
        g = defaultdict(list)
        ts = [n] * n
        for a, b in edges:
            g[a].append(b)
            g[b].append(a)
        dfs1(bob, -1, 0)
        ts[bob] = 0
        ans = -inf
        dfs2(0, -1, 0, 0)
        return ans

Complexity

Measure	Complexity
Time	O(n)
Space	O(n) auxiliary

Pattern: Tree Traversal

Choose the order — preorder, inorder, postorder, level — and the problem solves itself. LeetCode 2467. Most Profitable Path in a Tree is filed here because LeetCode tags it Tree, which is the vocabulary this hub collects.

The tree traversal guide has the Python template for the pattern and the 225 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 2467. Most Profitable Path in a Tree?: LeetCode 2467. Most Profitable Path in a Tree is rated Medium on LeetCode.
What is the time complexity of LeetCode 2467. Most Profitable Path in a Tree?: The Python solution on this page runs in O(n).
What is the space complexity of LeetCode 2467. Most Profitable Path in a Tree?: The Python solution on this page uses O(n) auxiliary space.
What topics does LeetCode 2467. Most Profitable Path in a Tree cover?: LeetCode 2467. Most Profitable Path in a Tree is tagged Tree, Depth-First Search, Breadth-First Search, Graph and Array on LeetCode.