882. Reachable Nodes In Subdivided Graph

Starting with an undirected graph (the "original graph") with nodes from 0 to N-1, subdivisions are made to some of the edges.

The graph is given as follows: edges[k] is a list of integer pairs (i, j, n) such that (i, j) is an edge of the original graph,

and n is the total number of new nodes on that edge. 

Then, the edge (i, j) is deleted from the original graph, n new nodes (x_1, x_2, ..., x_n) are added to the original graph,

and n+1 new edges (i, x_1), (x_1, x_2), (x_2, x_3), ..., (x_{n-1}, x_n), (x_n, j) are added to the original graph.

Now, you start at node 0 from the original graph, and in each move, you travel along one edge. 

Return how many nodes you can reach in at most M moves.

 

Example 1:

Input: edges = [[0,1,10],[0,2,1],[1,2,2]], M = 6, N = 3
Output: 13
Explanation: 
The nodes that are reachable in the final graph after M = 6 moves are indicated below.

Example 2:

Input: edges = [[0,1,4],[1,2,6],[0,2,8],[1,3,1]], M = 10, N = 4
Output: 23

 

Note:

1. 0 <= edges.length <= 10000
2. 0 <= edges[i][0] < edges[i][1] < N
3. There does not exist any i != j for which edges[i][0] == edges[j][0] and edges[i][1] == edges[j][1].
4. The original graph has no parallel edges.
5. 0 <= edges[i][2] <= 10000
6. 0 <= M <= 10^9
7. 1 <= N <= 3000
8. A reachable node is a node that can be travelled to using at most M moves starting from node 0.

 

Approach #1: C++. [graph/heap]

class Solution {
public:
    int reachableNodes(vector<vector<int>>& edges, int M, int N) {
        unordered_map<int, unordered_map<int, int>> g;
        for (const auto& edge : edges) {
            g[edge[0]][edge[1]] = g[edge[1]][edge[0]] = edge[2];
        }
        
        priority_queue<pair<int, int>> q;  // HP : node
        unordered_map<int, int> HP;  // node : HP
        
        q.push({M, 0});
        
        while (!q.empty()) {
            int hp = q.top().first;
            int cur = q.top().second;
            q.pop();
            if (HP.count(cur)) continue;
            HP[cur] = hp;
            for (const auto& pair : g[cur]) {
                int nxt = pair.first;
                int nxt_hp = hp - pair.second - 1;
                if (HP.count(nxt) || nxt_hp < 0) continue;
                q.push({nxt_hp, nxt});
            }
        }
        
        int ans = HP.size();
        for (const auto& e : edges) {
            int uv = HP.count(e[0]) ? HP[e[0]] : 0;
            int vu = HP.count(e[1]) ? HP[e[1]] : 0;
            ans += min(e[2], uv + vu);
        }
        
        return ans;
    }
};

　　

Analysis:

https://zxi.mytechroad.com/blog/graph/leetcode-882-reachable-nodes-in-subdivided-graph/