Weighted Quick Union
Weighted Quick Union
Keep track of size of each tree (number of objects).
Balance by linking root of smaller tree to root of larger tree.


Data structure Same as quick-union, but maintain extra array sz[i]
to count number of objects in the tree rooted at i
.
Java Implementation
public class WeightQuickUnionUF
{
private int[] id;
private int[] sz;
// set id of each object to itself (N array accesses)
public QuickUnionUF(int N)
{
id = new int[N];
sz = new int[N];
for (int i = 0; i < N; i++)
id[i] = i;
sz[i] = i;
}
// chase parent pointers until reach root (depth of i array accesses)
private int root(int i)
{
while (i != id[i]) i = id[i];
return i;
}
// check if p and q have same root (depth of p and q array accesses)
public boolean connected(int p, int q)
{
return root(p) == root(q);
}
/*
* change root of p to point to root of q
* (depth of p and q array accesses)
* Link root of smaller tree to root of larger tree.
*/
public void union(int p, int q)
{
int i = root(p);
int j = root(q);
if (i == j) return;
if (sz[i] < sz[j])
{
id[i] = j;
sz[j] += sz[i];
}
else
{
id[j] = i;
sz[i] += sz[j];
}
}
}
Analysis
Find: takes time proportional to depth of
p
andq
.Union: takes constant time, given roots.
Depth of any node
x
is at mostlog(N)
.
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