Segmentation Fault in C++ implementation of Kruskal's Algorithm

Question

I have written this code which implements the Kruskal's algorithm for Minimum Spanning Tree, which yields segmentation fault when I submit it to an online judge. I think I have narrowed the cause of segmentation fault to the part where I sort the edges. Still, I can't find the exact reason why this code fails.

struct DisjointSet{
    private:
        struct Node{
            int size;
            int repr;
            Node(int rep){
                size = 1;
                repr = rep;
            }
        };
        vector<Node> nodes;
    public:
        int makeSet(){
            nodes.push_back(Node(nodes.size()));
            return nodes.size() - 1;
        }
        int findRepresentative(int ind){
            if(nodes[nodes[ind].repr].size == -1){
                nodes[ind].repr = findRepresentative(nodes[ind].repr);
            }
            return nodes[ind].repr;
        }
        void unionSets(int ind1, int ind2){
            int rep1 = findRepresentative(ind1), rep2 = findRepresentative(ind2);
            if(rep1 != rep2){
                if(nodes[rep1].size < nodes[rep2].size){
                    int t = rep1;
                    rep1 = rep2;
                    rep2 = t;
                }
                nodes[rep1].size += nodes[rep2].size;
                nodes[rep2].size = -1;
                nodes[rep2].repr = rep1;
            }
        }
};

bool compare(const pair<pair<int, int>, int> &p1, const pair<pair<int, int>, int> &p2){
    return (p1.second <= p2.second);
}

int spanningTree(int V, int E, vector<vector<int>> &graph) {
    vector<pair<pair<int, int>, int>> edges;
    for(int i = 0;i < V;i ++){
        for(int j = 0;j < V;j ++){
            if(i <= j){
                if(graph[i][j] != INT_MAX){
                    edges.push_back(make_pair(make_pair(i, j), graph[i][j]));
                }
            }
        }
    }
    sort(edges.begin(), edges.end(), compare);
    DisjointSet d;
    for(int i = 0;i < V;i ++){
        d.makeSet();
    }
    int weight = 0;
    for(int i = 0;i < edges.size();i ++){
        int u = edges[i].first.first, v = edges[i].first.second;
        if(d.findRepresentative(u) != d.findRepresentative(v)){
            d.unionSets(u, v);
            weight += edges[i].second;
        }
    }
    return weight;
}

Answer 1

Your compare function:

bool compare(const pair<pair<int, int>, int> &p1, const pair<pair<int, int>, int> &p2){
    return (p1.second <= p2.second);
}

does not provide a strict-weak ordering, since comparing 2 elements e1 and e2 with the same .second will return true for both e1 < e2 and e2 < e1 , which is not allowed. Using this compare function in sort invokes undefined behavior, potentially causing a segfault.

You need to do something like:

bool compare(const pair<pair<int, int>, int> &p1, const pair<pair<int, int>, int> &p2){
    return p1.second < p2.second;
}