Dsa Graph Union Find

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

Fix union-find / dsu errors when path compression missing or union direction inconsistent.

Quick Fix

Wrong

class DSU:
    def find(self,x):
        if self.p[x]!=x: return self.find(self.p[x])
        return x
    def union(self,x,y):
        self.p[self.find(x)]=self.find(y)

No path compression. O(n) find. Tree height grows unbounded.

Right

class DSU:
    def __init__(self,n):
        self.p=list(range(n)); self.r=[0]*n
    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):
        rx,ry=self.find(x),self.find(y)
        if rx==ry: return False
        if self.r[rx]<self.r[ry]: self.p[rx]=ry
        elif self.r[rx]>self.r[ry]: self.p[ry]=rx
        else: self.p[ry]=rx; self.r[rx]+=1
        return True

union(0,1),union(1,2),find(0)==find(2) -> True. Nearly O(1) amortized.

Prevention

Always use path compression in find. Use union by rank/size for balanced trees.

DodaTech Tools

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