399. Evaluate Division 

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class Solution {
    private static class UnionFind {
        private final int[] parent;
        private final double[] divisionValues; // 至 parent[x] 的除法值

        public UnionFind(int n) {
            this.parent = new int[n];
            this.divisionValues = new double[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
                divisionValues[i] = 1.0;
            }
        }

        public void union(int x, int y, double divisionValue) {
            int xRoot = getRoot(x);
            int yRoot = getRoot(y);
            if (xRoot == yRoot) {
                return;
            }
            
            // before:
            // x -> xRoot
            // y -> yRoot

            // after:
            // x -> xRoot
            // |      |
            // \/     \/
            // y -> yRoot

            parent[xRoot] = yRoot;
            // x -> xRoot -> yRoot / x -> y -> yRoot 这两条路径都能到达 yRoot
            // 因为改变了 xRoot 的指向，所以此处更新 divisionValues[xRoot] 的值，即更新的 xRoot -> yRoot 这条路径的权重
            divisionValues[xRoot] = divisionValue * divisionValues[y] / divisionValues[x];
        }

        public int getRoot(int x) {
            if (x != parent[x]) {
                int p = parent[x];
                int root = getRoot(p);
                divisionValues[x] *= divisionValues[p];
                parent[x] = root; // path compression
            }

            return parent[x];
        }

        public double getDivisionValue(int x, int y) {
            return divisionValues[x] / divisionValues[y];
        }

        public boolean isUnion(int x, int y) {
            return getRoot(x) == getRoot(y); // 注意此处是比较 root 是否相等，而不是比较 parent 的指向
        }
    }

    public double[] calcEquation(List<List<String>> equations, double[] values, List<List<String>> queries) {
        Map<String, Integer> varToIndexMap = new HashMap<>();
        for (List<String> equation : equations) {
            for (String var : equation) {
                if (!varToIndexMap.containsKey(var)) {
                    varToIndexMap.put(var, varToIndexMap.size());
                }
            }
        }

        UnionFind unionFind = new UnionFind(varToIndexMap.size());

        // 构建至并查集
        for (int i = 0; i < equations.size(); i++) {
            List<String> equation = equations.get(i);
            int index1 = varToIndexMap.get(equation.get(0)), index2 = varToIndexMap.get(equation.get(1));
            unionFind.union(index1, index2, values[i]);
        }

        // 计算结果
        double[] results = new double[queries.size()];
        for (int i = 0; i < queries.size(); i++) {
            List<String> query = queries.get(i);
            Integer index1 = varToIndexMap.get(query.get(0)), index2 = varToIndexMap.get(query.get(1));
            if (index1 == null || index2 == null || !unionFind.isUnion(index1, index2)) {
                results[i] = -1.0;
            } else {
                results[i] = unionFind.getDivisionValue(index1, index2);
            }
        }

        return results;
    }
}

References

399. Evaluate Division
剑指 Offer II 111. 计算除法