Dijkstra returns wrong distances

A routing service computes single-source shortest paths with the implementation below. Unit tests pass, but on the production graph dist[3] comes back as 4 although a path of cost 2 exists: 0 → 2 → 1 → 3 with weights 5, -4, 1. Edges are given as (u, v, w). The code itself is a textbook Dijkstra. Find the problem.

1import heapq
2 
3def dijkstra(n, edges, src):
4    adj = [[] for _ in range(n)]
5    for u, v, w in edges:
6        adj[u].append((v, w))
7 
8    dist = [float('inf')] * n
9    dist[src] = 0
10    pq = [(0, src)]
11    done = [False] * n
12 
13    while pq:
14        d, u = heapq.heappop(pq)
15        if done[u]:
16            continue
17        done[u] = True
18        for v, w in adj[u]:
19            if d + w < dist[v]:
20                dist[v] = d + w
21                heapq.heappush(pq, (dist[v], v))
22    return dist
23 
24# production input
25edges = [(0, 1, 3), (0, 2, 5), (2, 1, -4), (1, 3, 1)]
26print(dijkstra(4, edges, 0))   # [0, 3, 5, 4]  — expected dist[3] == 2

1. Confirm the code is a correct Dijkstra. Then look at the *input*: what property of the graph is violated?
2. Trace the algorithm on the given edges and show exactly at which step the wrong answer becomes irreversible.
3. Explain why the greedy "settle the closest vertex" step depends on non-negative weights.
4. Propose a fix. There is more than one reasonable answer — discuss the trade-offs.
5. State the complexity of the fixed approach.