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Problem solution · Python

Maximum Sum of Edge Values in a Graph

Maximum Sum of Edge Values in a Graph: a Python solution using breadth-first search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Breadth-first search
Source
walkccc LeetCode Solutions
Length
56 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Breadth-first search

For Maximum Sum of Edge Values in a Graph, the implementation explores reachable states in layers, which is the standard shape for unweighted shortest paths and minimum-step transitions.

  1. Model each valid configuration as a state and each legal move as an edge.
  2. Seed the queue with the starting state and mark it immediately.
  3. Expand each state once, recording distance or reachability for unseen neighbours.

Code notes

  • 56 lines of Python from the credited upstream file 3547.py.
  • The implementation visibly relies on sequence storage, ordered lookup, work queue.
  • No explicit loop blocks detected.

Complexity

Verify that each state and transition is processed only a bounded number of times; that determines the traversal cost.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeMaximum Sum of Edge Values in a Graph · PythonPython
Use this to learn the idea, then write your own version.
class Solution:  def maxScore(self, n: int, edges: list[list[int]]) -> int:    ans = 0    graph = [[] for _ in range(n)]    cycleSizes = []  # components where all nodes have degree 2    pathSizes = []  # components that are not cycleSizes    seen = set()     for u, v in edges:      graph[u].append(v)      graph[v].append(u)     for i in range(n):      if i in seen:        continue      component = self._getComponent(graph, i, seen)      if all(len(graph[u]) == 2 for u in component):        cycleSizes.append(len(component))      elif len(component) > 1:        pathSizes.append(len(component))     for cycleSize in cycleSizes:      ans += self._calculateScore(n - cycleSize + 1, n, True)      n -= cycleSize     for pathSize in sorted(pathSizes, reverse=True):      ans += self._calculateScore(n - pathSize + 1, n, False)      n -= pathSize     return ans   def _getComponent(      self,      graph: list[list[int]],      start: int,      seen: set[int],  ) -> list[int]:    component = [start]    seen.add(start)    for u in component:      for v in graph[u]:        if v in seen:          continue        component.append(v)        seen.add(v)    return component   def _calculateScore(self, left: int, right: int, isCycle: bool) -> int:    window = collections.deque([right, right])    score = 0    for value in range(right - 1, left - 1, -1):      windowValue = window.popleft()      score += windowValue * value      window.append(value)    return score + window[0] * window[1] * isCycle

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