Given two sentenceswords1, words2(each represented as an array of strings), and a list of similar word pairspairs, determine if two sentences are similar.

For example,words1 = ["great", "acting", "skills"]andwords2 = ["fine", "drama", "talent"]are similar, if the similar word pairs arepairs = [["great", "good"], ["fine", "good"], ["acting","drama"], ["skills","talent"]].

Note that the similarity relationistransitive. For example, if "great" and "good" are similar, and "fine" and "good" are similar, then "great" and "fine"are similar.

Similarity is also symmetric. For example, "great" and "fine" being similar is the same as "fine" and "great" being similar.

Also, a word is always similar with itself. For example, the sentenceswords1 = ["great"], words2 = ["great"], pairs = []are similar, even though there are no specified similar word pairs.

Finally, sentences can only be similar if they have the same number of words. So a sentence likewords1 = ["great"]can never be similar towords2 = ["doubleplus","good"].

Note:

The length of

words1

and

words2

will not exceed

1000

.

The length of

pairs

will not exceed

2000

.

The length of each

pairs[i]

will be

2

.

The length of each

words[i]

and

pairs[i][j]

will be in the range

[1, 20]

.

tag: union find

class Solution {
    public boolean areSentencesSimilarTwo(String[] words1, String[] words2, String[][] pairs) {
        if (words1.length != words2.length) return false;
        Map<String, Integer> index = new HashMap();
        int count = 0;
        DSU dsu = new DSU(2 * pairs.length);
        for (String[] pair: pairs) {
            for (String p: pair) if (!index.containsKey(p)) {
                index.put(p, count++);
            }
            dsu.union(index.get(pair[0]), index.get(pair[1]));
        }

        for (int i = 0; i < words1.length; ++i) {
            String w1 = words1[i], w2 = words2[i];
            if (w1.equals(w2)) continue;
            if (!index.containsKey(w1) || !index.containsKey(w2) ||
                    dsu.find(index.get(w1)) != dsu.find(index.get(w2)))
                return false;
        }
        return true;
    }
}

class DSU {
    int[] parent;
    public DSU(int N) {
        parent = new int[N];
        for (int i = 0; i < N; ++i)
            parent[i] = i;
    }
    public int find(int x) {
        if (parent[x] != x) parent[x] = find(parent[x]);
        return parent[x];
    }
    public void union(int x, int y) {
        parent[find(x)] = find(y);
    }
}