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Problem solution · Python

Minimize the Total Price of the Trips

Minimize the Total Price of the Trips: a Python solution using depth-first search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Depth-first search
Source
walkccc LeetCode Solutions
Length
44 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

Depth-first search

For Minimize the Total Price of the Trips, the implementation follows one branch at a time, making it suitable for components, trees, backtracking, or dependency exploration.

  1. Define the state carried into one recursive or stack frame.
  2. Mark or choose the current state before exploring children.
  3. Combine child results or undo the choice when the branch finishes.

Code notes

  • 44 lines of Python from the credited upstream file 2646.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected, together with recursive traversal.

Complexity

Count unique states for graph traversal; for backtracking, count the branching factor and maximum depth.

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 codeMinimize the Total Price of the Trips · PythonPython
Use this to learn the idea, then write your own version.
class Solution:  def minimumTotalPrice(self, n: int, edges: list[list[int]], price: list[int],                        trips: list[list[int]]) -> int:    graph = [[] for _ in range(n)]     for u, v in edges:      graph[u].append(v)      graph[v].append(u)     # count[i] := the number of times i is traversed    count = [0] * n     def dfsCount(u: int, prev: int, end: int, path: list[int]) -> None:      path.append(u)      if u == end:        for i in path:          count[i] += 1        return      for v in graph[u]:        if v != prev:          dfsCount(v, u, end,  path)      path.pop()     for start, end in trips:      dfsCount(start, -1, end, [])     @functools.lru_cache(None)    def dfs(u: int, prev: int, parentHalved: bool) -> int:      """      Returns the minimum price sum for the i-th node, where its parent is      halved parent or not halved not.      """      sumWithFullNode = price[u] * count[u] + sum(dfs(v, u, False)                                                  for v in graph[u]                                                  if v != prev)      if parentHalved:  # Can't halve this node if its parent was halved.        return sumWithFullNode      sumWithHalvedNode = (price[u] // 2) * count[u] + sum(dfs(v, u, True)                                                           for v in graph[u]                                                           if v != prev)      return min(sumWithFullNode, sumWithHalvedNode)     return dfs(0, -1, False)

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