How to Fix Dijkstra's Shortest Path Errors

In this tutorial, you'll learn about How to Fix Dijkstra's Shortest Path Errors. We cover key concepts, practical examples, and best practices.

Fix dijkstra's shortest path errors when heap updates don't refresh distances or negative edges cause wrong results.

Quick Fix

Wrong

def dijk(g,s):
    d={v:float('inf') for v in g}; d[s]=0
    pq=[(0,s)]
    while pq:
        cur,=heapq.heappop(pq)
        for nb,w in g[cur]:
            nd=d[cur]+w
            if nd<d[nb]: d[nb]=nd; heapq.heappush(pq,(nd,nb))

Unpacks tuple incorrectly. Missing visited check causes redundant processing.

Right

import heapq
def dijk(g,s):
    d={v:float('inf') for v in g}; d[s]=0; pq=[(0,s)]; vis=set()
    while pq:
        du,u=heapq.heappop(pq)
        if u in vis: continue
        vis.add(u)
        for v,w in g[u]:
            if d[u]+w<d[v]: d[v]=d[u]+w; heapq.heappush(pq,(d[v],v))
    return d

Graph {0:[(1,4),(2,1)],1:[(3,1)],2:[(1,2),(3,5)],3:[]}, from 0 -> {0:0,1:3,2:1,3:4}. O((V+E)logV).

Prevention

Use visited set to skip stale heap entries. Dijkstra doesn't work with negative edges.

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