Today is Sunday, I gonna review the tasks I've done this week, and finish today's leetcode's September LeetCoding Challenge with cpp.

After this week(end with Sunday), I'll not random a problem and solve it, but just write what I want to, and Daily LeetCoding Challenge, there will be no review anymore unless I found something interesting. I'll try something different, LeetCode bored me already.

September LeetCoding Challenge 12

Description

Reachable Nodes In Subdivided Graph

You are given an undirected graph (the "original graph") with n nodes labeled from 0 to n - 1. You decide to subdivide each edge in the graph into a chain of nodes, with the number of new nodes varying between each edge.

The graph is given as a 2D array of edges where edges[i] = [ui, vi, cnti] indicates that there is an edge between nodes ui and vi in the original graph, and cnti is the total number of new nodes that you will subdivide the edge into. Note that cnti == 0 means you will not subdivide the edge.

To subdivide the edge [ui, vi], replace it with (cnti + 1) new edges and cnti new nodes. The new nodes are x1, x2, ..., xcnti, and the new edges are [ui, x1], [x1, x2], [x2, x3], ..., [xcnti+1, xcnti], [xcnti, vi].

In this new graph, you want to know how many nodes are reachable from the node 0, where a node is reachable if the distance is maxMoves or less.

Given the original graph and maxMoves, return the number of nodes that are reachable from node 0 in the new graph.

Example 1:

Input: edges = [[0,1,10],[0,2,1],[1,2,2]], maxMoves = 6, n = 3
Output: 13
Explanation: The edge subdivisions are shown in the image above.
The nodes that are reachable are highlighted in yellow.

Example 2:

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

Example 3:

Input: edges = [[1,2,4],[1,4,5],[1,3,1],[2,3,4],[3,4,5]], maxMoves = 17, n = 5
Output: 1
Explanation: Node 0 is disconnected from the rest of the graph, so only node 0 is reachable.

Constraints:

• 0 <= edges.length <= min(n * (n - 1) / 2, 104)
• edges[i].length == 3
• 0 <= ui < vi < n
• There are no multiple edges in the graph.
• 0 <= cnti <= 104
• 0 <= maxMoves <= 109
• 1 <= n <= 3000

Solution

auto speedup = [](){
  cin.tie(nullptr);
  cout.tie(nullptr);
  ios::sync_with_stdio(false);
  return 0;
}();
const int MAX = INT_MAX / 2;
class Solution {
  using pi = pair<int, int>;
  vector<vector<pi>> neighbors;
  vector<int> distance;
  void init(int n, vector<vector<int>>& edges) {
    neighbors.resize(n);
    distance.resize(n, MAX);

    for(auto &edge : edges) {
      neighbors[edge[0]].push_back({edge[1], edge[2] + 1});
      neighbors[edge[1]].push_back({edge[0], edge[2] + 1});
    }
  }
  void dijkstra() {
    priority_queue<pi, vector<pi>, greater<pi>> pq;
    pq.push({0, 0});

    while(pq.size()) {
      auto [moves, cur] = pq.top();
      pq.pop();
      if(distance[cur] != MAX) continue;
      distance[cur] = moves;
      for(auto [nxt, edge] : neighbors[cur]) {
        if(distance[nxt] != MAX) continue;
        pq.push({edge + moves, nxt});
      }
    }
  }
public:
  int reachableNodes(vector<vector<int>>& edges, int maxMoves, int n) {
    init(n, edges);
    dijkstra();

    int answer = 0;
    for(auto &edge : edges) {
      if(distance[edge[0]] + edge[2] <= maxMoves \
      || distance[edge[1]] + edge[2] <= maxMoves \
      || 2 * maxMoves - distance[edge[0]] - distance[edge[1]] >= edge[2]) {
        answer += edge[2];
      } else {
        if(distance[edge[0]] < maxMoves) {
          answer += maxMoves - distance[edge[0]];
        }
        if(distance[edge[1]] < maxMoves) {
          answer += maxMoves - distance[edge[1]];
        }
      }
    }

    for(int i = 0; i < n; ++i) {
      answer += distance[i] <= maxMoves;
    }
    
    return answer;
  }
};

// Accepted
// 47/47 cases passed (137 ms)
// Your runtime beats 73.76 % of cpp submissions
// Your memory usage beats 91.4 % of cpp submissions (38.8 MB)