Problem solution · Python

Number Of Ways To Reconstruct A Tree

Number Of Ways To Reconstruct A Tree: 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
51 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 Number Of Ways To Reconstruct A Tree, 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

  • 51 lines of Python from the credited upstream file 1719.py.
  • The implementation visibly relies on sequence storage, hash lookup.
  • 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 codeNumber Of Ways To Reconstruct A Tree · PythonPython
Use this to learn the idea, then write your own version.
class Solution:  def checkWays(self, pairs: list[list[int]]) -> int:    MAX = 501    graph = collections.defaultdict(list)    degrees = [0] * MAX    connected = [[False] * MAX for _ in range(MAX)]     for u, v in pairs:      graph[u].append(v)      graph[v].append(u)      degrees[u] += 1      degrees[v] += 1      connected[u][v] = True      connected[v][u] = True     # For each node, sort its children by degrees in descending order.    for _, children in graph.items():      children.sort(key=lambda x: -degrees[x])     # Find the root with a degree that equals to n - 1.    root = next((i for i, d in enumerate(degrees) if d == len(graph) - 1), -1)    if root == -1:      return 0     hasMoreThanOneWay = False     def dfs(u: int, ancestors: list[int], seen: list[bool]) -> bool:      """      Returns True if each node rooted at u is connected to all of its      ancestors.      """      nonlocal hasMoreThanOneWay      seen[u] = True      for ancestor in ancestors:        if not connected[u][ancestor]:          return False      ancestors.append(u)      for v in graph[u]:        if seen[v]:          continue        if degrees[v] == degrees[u]:          hasMoreThanOneWay = True        if not dfs(v, ancestors, seen):          return False      ancestors.pop()      return True     if not dfs(root, [], [False] * MAX):      return 0    return 2 if hasMoreThanOneWay else 1 

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