Problem solution · Python

The Most Similar Path in a Graph

The Most Similar Path in a Graph: 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
49 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 The Most Similar Path in a Graph, 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

  • 49 lines of Python from the credited upstream file 1548.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.

Full codeThe Most Similar Path in a Graph · PythonPython
Use this to learn the idea, then write your own version.
class Solution:  def mostSimilar(self, n: int, roads: list[list[int]], names: list[str],                  targetPath: list[str]) -> list[int]:    # cost[i][j] := the minimum cost to start from names[i] in path[j]    cost = [[-1] * len(targetPath) for _ in range(len(names))]    # next[i][j] := the best next of names[i] in path[j]    next = [[0] * len(targetPath) for _ in range(len(names))]    graph = [[] for _ in range(n)]     for u, v in roads:      graph[u].append(v)      graph[v].append(u)     minDist = math.inf    start = 0     def dfs(nameIndex: int, pathIndex: int) -> int:      if cost[nameIndex][pathIndex] != -1:        return cost[nameIndex][pathIndex]       editDist = names[nameIndex] != targetPath[pathIndex]      if pathIndex == len(targetPath) - 1:        return editDist       minDist = math.inf       for v in graph[nameIndex]:        dist = dfs(v, pathIndex + 1)        if dist < minDist:          minDist = dist          next[nameIndex][pathIndex] = v       cost[nameIndex][pathIndex] = editDist + minDist      return editDist + minDist     for i in range(n):      dist = dfs(i, 0)      if dist < minDist:        minDist = dist        start = i     ans = []     while len(ans) < len(targetPath):      ans.append(start)      start = next[start][len(ans) - 1]     return ans 

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