modify-graph-edge-weights.cpp

// Time:  O((|E| + |V|) * log|V|) = O(|E| * log|V|) by using binary heap,
//        if we can further to use Fibonacci heap, it would be O(|E| + |V| * log|V|)
// Space: O(|E| + |V|) = O(|E|)

// dijkstra's algorithm
class Solution {
public:
    vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges, int source, int destination, int target) {
        vector<vector<pair<int, int>>> adj(n);
        for (const auto& e : edges) {
            adj[e[0]].emplace_back(e[1], e[2]);
            adj[e[1]].emplace_back(e[0], e[2]);
        }
        const auto& dijkstra = [&](int start, int x) {
            vector<int> best(size(adj), target + 1);
            best[start] = 0;
            priority_queue<pair<int64_t, int>, vector<pair<int64_t, int>>, greater<pair<int64_t, int>>> min_heap;
            min_heap.emplace(0, start);
            while (!empty(min_heap)) {
                const auto [curr, u] = min_heap.top(); min_heap.pop();
                if (curr > best[u]) {
                    continue;
                }
                for (auto [v, w] : adj[u]) {
                    if (w == -1) {
                        w = x;
                    }
                    if (best[v] - curr <= w) {
                        continue;
                    }
                    best[v] = curr + w;
                    min_heap.emplace(curr + w, v);
                }
            }
            return best;
        };

        const auto& left = dijkstra(source, 1);
        if (!(left[destination] <= target)) {
            return {};
        }
        const auto& right = dijkstra(destination, target + 1);
        if (!(right[source] >= target)) {
            return {};
        }
        for (auto& e : edges) {
            if (e[2] == -1) {
                e[2] = max({target - left[e[0]] - right[e[1]], target - left[e[1]] - right[e[0]], 1});
            }
        }
        return edges;
    }
};