Leetcode #847: Shortest Path Visiting All Nodes
In this guide, we solve Leetcode #847 Shortest Path Visiting All Nodes in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Bit Manipulation, Breadth-First Search, Graph, Dynamic Programming, Bitmask
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
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
The time complexity is O(n·m) (typical). The space complexity is O(n·m) or optimized.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.