Minimum Cost to Visit Every Node

Problem Statement

Prereq: Bitmask Introduction

Given a directed weighted graph as a 2D list where graph[i][j] is the edge weight from node i to j (0 means no edge), find the minimum cost to visit every node starting from node 0. You don't need to return to the start. Return -1 if impossible.

graph = [
  [0, 100, 100, 1],
  [0,   0, 100, 0],
  [0,   1,   0, 0],
  [0,  20,   1, 0]
]

Answer: 3 (path: 0 → 3 → 2 → 1)