Evaluate Division: Weighted UF

Map variable names to indices. For equation $a/b = v$:

• Union $a$ and $b$ with weight $v$

To query $a/c$:

• Find roots of both
• If different roots, return $-1$
• If same root, return $\text{weight}[a] / \text{weight}[c]$

def find(x):
    if parent[x] != x:
        originalParent = parent[x]
        parent[x] = find(parent[x])
        weight[x] *= weight[originalParent]
    return parent[x]

def union(a, b, val):
    rootA, rootB = find(a), find(b)
    if rootA == rootB:
        return
    # rootA/rootB = weight[b] * val / weight[a]
    parent[rootA] = rootB
    weight[rootA] = weight[b] * val / weight[a]

The weight calculation during union ensures consistency.