Dsa Graph Kruskal

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

Fix kruskal's mst errors when cycle detection missing or edges not sorted by weight.

Quick Fix

Wrong

def kruskal(g):
    edges=[]
    for u in g:
        for v,w in g[u]: edges.append((w,u,v))
    edges.sort()
    mst=[]
    for w,u,v in edges:
        mst.append((u,v,w))  # no cycle check!

No cycle detection. May introduce cycles in MST.

Right

class DSU:
    def find(self,x):
        if self.p[x]!=x: self.p[x]=self.find(self.p[x])
        return self.p[x]
    def union(self,x,y):
        self.p[self.find(x)]=self.find(y)
def kruskal(g):
    edges=[]
    for u in g:
        for v,w in g[u]: edges.append((w,u,v))
    edges.sort()
    dsu=DSU(len(g)); mst=[]
    for w,u,v in edges:
        if dsu.find(u)!=dsu.find(v):
            dsu.union(u,v); mst.append((u,v,w))
    return mst

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

Prevention

Sort edges by weight. Use Union-Find to detect cycles. Only add edge if it connects different components.

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