Program to find length of the longest path in an n-ary tree in Python

Suppose we have an edge list where each items are holding (u, v) represents u is parent of v. We have to find the length of the longest path in the tree. The path length is 1 + number of nodes in that path.

So, if the input is like

then the output will be 5, because the path is [1, 4, 5, 7], there are 4 nodes in total, so path length is 1 + 4 = 5.

To solve this, we will follow these steps −

• g := adjacency list of the graph from given edge list
• d := a new map
• Define a function bfs() . This will take o
• d[o] := 1
• f := o
• q := [o]
• for each x in q, do
  • for each y in g[x], do
    • if y is not in d, then
      • d[y] := d[x] + 1
      • if d[y] > d[f], then
        • f := y
      • insert y in q
• return f
• From the main method, do the following −
• for each o in g, do
  • f := bfs(o)
  • d := a new map
  • return d[bfs(f)]
• return 0

Example

Let us see the following implementation to get better understanding −

def solve(edges):
   g = {}
   for u, v in edges:
      if u not in g:
         g[u] = []
      g[u] += (v,)
      if v not in g:
         g[v] = []
      g[v] += (u,)
   d = {}

   def bfs(o):
      d[o] = 1
      f = o
      q = [o]
      for x in q:
         for y in g[x]:
            if y not in d:
               d[y] = d[x] + 1
               if d[y] > d[f]:
                  f = y
               q += (y,)
      return f

   for o in g:
      f = bfs(o)
      d = {}
      return d[bfs(f)]
   return 0

edges = [(1, 2),(1, 3),(1, 4),(4, 5),(5,7),(1,6),(4,8)]
print(solve(edges))

Input

[(1, 2),(1, 3),(1, 4),(4, 5),(5,7),(1,6),(4,8)]

Output

5