number-of-restricted-paths-from-first-to-last-node.cpp

// Time:  O(|E| * log|V|)
// Space: O(|E| + |V|)

class Solution {
public:
    int countRestrictedPaths(int n, vector<vector<int>>& edges) {
        static const int MOD = 1e9 + 7;
        vector<vector<pair<int, int>>> adj(n);
        for (const auto& e : edges) {
            int u = e[0] - 1, v = e[1] - 1, w = e[2];
            adj[u].emplace_back(v, w);
            adj[v].emplace_back(u, w);
        }
        vector<int> dist(n, numeric_limits<int>::max()), dp(n);
        dist[n - 1] = 0;
        dp[n - 1] = 1;
        priority_queue< pair<int, int>, vector< pair<int, int>>, greater< pair<int, int>>> min_heap;
        min_heap.emplace(0, n - 1);
        while (!empty(min_heap)) {
            const auto [w, u] = min_heap.top(); min_heap.pop();
            if (w > dist[u]) {
                continue;
            }
            for (const auto& [v, d] : adj[u]) {
                if (w + d < dist[v]) {
                    dist[v] = w + d;
                    min_heap.emplace(dist[v], v);
                } else if (w > dist[v]) {
                    dp[u] = (dp[u] + dp[v]) % MOD;
                }
            }
            if (u == 0) {  // early return
                break;
            }
        }
        return dp[0];
    }
};