type: session

harness: optiq-lab

name: Using python, implement Dijkstra's algorithm on a randomly generated weighted directed graph with 100 nodes and report t

mode: chat

domain: algorithms and complexity


type: message

role: system

content:
You are OptiQ Lab, running on the user's own machine. You have three tools: web_search for looking things up, python for computation and data work, and terminal for shell one-liners.

The python and terminal tools run in a container with no network and ONLY the Python standard library. numpy, pandas, scipy, sklearn and matplotlib are not installed, so use math, statistics, json, csv, re, itertools, collections and random instead.

Every call gets a FRESH sandbox. Nothing persists between calls: files you write, variables you define and imports you make are all gone by the next one. So do the whole job in a single call and print the result. Do not write a file in one call expecting to read it in the next.

If a call fails, read the error and change approach rather than repeating it. Once you have the answer, state it plainly and stop calling tools.


role: user

content: Using python, implement Dijkstra's algorithm on a randomly generated weighted directed graph with 100 nodes and report the shortest‑path distance from node 0 to node 99.


role: assistant

python

code:
import random
import heapq

N = 100
random.seed(42)

# Generate a random weighted directed graph (edge prob ~0.12, weights 1..100)
while True:
    adj = [[] for _ in range(N)]
    for u in range(N):
        for v in range(N):
            if u != v and random.random() < 0.12:
                w = random.randint(1, 100)
                adj[u].append((v, w))

    # Quick reachability check from 0
    seen = {0}
    stack = [0]
    while stack:
        u = stack.pop()
        for v, _ in adj[u]:
            if v not in seen:
                seen.add(v)
                stack.append(v)
    if 99 in seen:
        break

# Dijkstra's algorithm (binary heap)
def dijkstra(start, adj):
    dist = [float('inf')] * N
    prev = [None] * N
    dist[start] = 0
    pq = [(0, start)]
    while pq:
        d, u = heapq.heappop(pq)
        if d > dist[u]:
            continue
        for v, w in adj[u]:
            nd = d + w
            if nd < dist[v]:
                dist[v] = nd
                prev[v] = u
                heapq.heappush(pq, (nd, v))
    return dist, prev

dist, prev = dijkstra(0, adj)

# Reconstruct path
path = []
node = 99
while node is not None:
    path.append(node)
    node = prev[node]
path.reverse()

print(f"Shortest-path distance from node 0 to node 99: {dist[99]}")
print(f"Path (length {len(path)} nodes): {path}")
print(f"Number of edges in graph: {sum(len(adj[u]) for u in range(N))}")


role: tool

content:
sandbox: container  rc=0
--- stdout ---
Shortest-path distance from node 0 to node 99: 42
Path (length 6 nodes): [0, 82, 19, 72, 65, 99]
Number of edges in graph: 1184

--- stderr ---


content:
Done. I implemented Dijkstra's algorithm with a binary heap (priority queue) in Python on a randomly generated weighted directed graph with 100 nodes (edge probability 0.12, weights 1–100, seeded for reproducibility, regenerated until node 99 was reachable from node 0).

**Result: the shortest-path distance from node 0 to node 99 is 42.**

The shortest path found was: 0 → 82 → 19 → 72 → 65 → 99 (5 edges, total weight 42).