Shortest Path Visiting All Nodes — LeetCode 847 Python Solution

The problem

You have an undirected, connected graph of n nodes labeled from 0 to n - 1. You are given an array graph where graph[i] is a list of all the nodes connected with node i by an edge.

Example

Input

graph = [[1,2,3],[0],[0],[0]]

Output

4

Explanation

One possible path is [1,0,2,0,3]

Python solution

class Solution:
    def shortestPathLength(self, graph: List[List[int]]) -> int:
        n = len(graph)
        q = deque()
        vis = set()
        for i in range(n):
            q.append((i, 1 << i))
            vis.add((i, 1 << i))
        ans = 0
        while 1:
            for _ in range(len(q)):
                i, st = q.popleft()
                if st == (1 << n) - 1:
                    return ans
                for j in graph[i]:
                    nst = st | 1 << j
                    if (j, nst) not in vis:
                        vis.add((j, nst))
                        q.append((j, nst))
            ans += 1

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 847. Shortest Path Visiting All Nodes is filed here because LeetCode tags it Bit Manipulation and Bitmask, which is the vocabulary this hub collects.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

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