Program to calculate vertex-to-vertex reachablity matrix in Python

Suppose we have a graph as an adjacency list representation, we have to find 2D matrix M where

• M[i, j] = 1 when there is a path between vertices i and j.

• M[i, j] = 0 otherwise.

So, if the input is like

then the output will be

To solve this, we will follow these steps −

• ans:= a 2d matrix of size n x n, where n is the number of vertices, fill with 0s

• for i in range 0 to n, do

  • q:= a queue, and insert i at first

  • while q is not empty, do

    • node:= first element of q, and delete first element from q

    • if ans[i, node] is non-zero, then

      • go for next iteration

    • ans[i, node]:= 1

    • neighbors:= graph[node]

    • for each n in neighbors, do

      • insert n at the end of q

• return ans

Let us see the following implementation to get better understanding −

Example

class Solution:
   def solve(self, graph):
      ans=[[0 for _ in graph] for _ in graph]
      for i in range(len(graph)):
         q=[i]
         while q:
            node=q.pop(0)
            if ans[i][node]: continue
            ans[i][node]=1
            neighbors=graph[node]
            for n in neighbors:
               q.append(n)
      return ans
ob = Solution()
adj_list = [[1,2],[4],[4],[1,2],[3]]
priunt(ob.solve(adj_list))

Input

[[1,2],[4],[4],[1,2],[3]]

Output

[[1, 1, 1, 1, 1],
   [0, 1, 1, 1, 1],
   [0, 1, 1, 1, 1],
   [0, 1, 1, 1, 1],
   [0, 1, 1, 1, 1]
]