find-critical-and-pseudo-critical-edges-in-minimum-spanning-tree.cpp

// Time:  O(nlogn)
// Space: O(n)

class Solution {
public:
    vector<vector<int>> findCriticalAndPseudoCriticalEdges(int n, vector<vector<int>>& edges) {
        for (int i = 0; i < edges.size(); ++i) {
            edges[i].push_back(i);
        }
        sort(begin(edges), end(edges),
             [](const auto& a, const auto& b) {
                 return a[2] < b[2];
             });
        int mst = MST(n, edges);
        vector<vector<int>> result(2);
        for (int i = 0; i < edges.size(); ++i) {
            if (mst < MST(n, edges, i)) {
                result[0].emplace_back(edges[i][3]);
            } else if (mst == MST(n, edges, -1, i)) {
                result[1].emplace_back(edges[i][3]);
            }
        }
        return result;
    }
    
private:
    int MST(const int n, const vector<vector<int>>& edges,
            int unused = -1, int used = -1) {
        UnionFind union_find(n);
        int weight = 0;
        if (used != -1) {
            const auto& edge = edges[used];
            if (union_find.union_set(edge[0], edge[1])) {
                weight += edge[2];
            }
        }
        for (int i = 0; i < edges.size(); ++i) {
            if (i == unused) {
                continue;
            }
            const auto& edge = edges[i];
            if (union_find.union_set(edge[0], edge[1])) {
                weight += edge[2];
            }
        }
        return union_find.size() == 1 ? weight : numeric_limits<int>::max();
    }

    class UnionFind {
    public:
        UnionFind(const int n) : set_(n), size_(n) {
            iota(set_.begin(), set_.end(), 0);
        }

        int find_set(const int x) {
           if (set_[x] != x) {
               set_[x] = find_set(set_[x]);  // Path compression.
           }
           return set_[x];
        }

        bool union_set(const int x, const int y) {
            int x_root = find_set(x), y_root = find_set(y);
            if (x_root == y_root) {
                return false;
            }
            set_[min(x_root, y_root)] = max(x_root, y_root);
            --size_;
            return true;
        }

        int size() const {
            return size_;
        }

    private:
        vector<int> set_;
        int size_;
    };
};