Submission #752238

#	Time	Username	Problem	Language	Result	Execution time	Memory
752238		tch1cherin	Olympic Bus (JOI20_ho_t4)	C++17	37 / 100	1085 ms	83408 KiB

ho_t4

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <bits/stdc++.h>
using namespace std;

// Trash code from https://www.geeksforgeeks.org/pairing-heap/
struct HeapNode {
    pair<int, int> key;
    HeapNode *leftChild;
    HeapNode *nextSibling;
 
    HeapNode():
        leftChild(NULL), nextSibling(NULL) {}
 
    // creates a new node
    HeapNode(pair<int, int> key_, HeapNode *leftChild_, HeapNode *nextSibling_):
        key(key_), leftChild(leftChild_), nextSibling(nextSibling_) {}
         
        // Adds a child and sibling to the node
    void addChild(HeapNode *node) {
        if(leftChild == NULL)
            leftChild = node;
        else {
            node->nextSibling = leftChild;
            leftChild = node;
        }
    }
};
 
// Returns true if root of the tree
// is null otherwise returns false
bool Empty(HeapNode *node) {
    return (node == NULL);
}
 
// Function to merge two heaps
HeapNode *Merge(HeapNode *A, HeapNode *B)
{
    // If any of the two-nodes is null
    // the return the not null node
    if(A == NULL) return B;
    if(B == NULL) return A;
     
    // To maintain the min heap condition compare   
    // the nodes and node with minimum value become 
    // parent of the other node
    if(A->key < B->key) {                 
        A->addChild(B);
        return A;        
    }
    else {
        B->addChild(A);
        return B;
    }
 
    return NULL; // Unreachable
}
 
// Returns the root value of the heap
pair<int, int> Top(HeapNode *node) {
    return node->key;
}
 
// Function to insert the new node in the heap
HeapNode *Insert(HeapNode *node, pair<int, int> key) {
    return Merge(node, new HeapNode(key, NULL, NULL));
}
 
// This method is used when we want to delete root node
HeapNode *TwoPassMerge(HeapNode *node) {
    if(node == NULL || node->nextSibling == NULL)
        return node;
    else {
        HeapNode *A, *B, *newNode;
        A = node;
        B = node->nextSibling;
        newNode = node->nextSibling->nextSibling;
 
        A->nextSibling = NULL;
        B->nextSibling = NULL;
 
        return Merge(Merge(A, B), TwoPassMerge(newNode));
    }
 
    return NULL; // Unreachable
}
 
// Function to delete the root node in heap
HeapNode *Delete(HeapNode *node) {
    return TwoPassMerge(node->leftChild);
}
 
struct PairingHeap {
    HeapNode *root;
 
    PairingHeap():
        root(NULL) {}
 
    bool Empty(void) {
        return ::Empty(root);
    }
 
    pair<int, int> Top(void) {
        return ::Top(root);
    }
 
    void Insert(pair<int, int> key) {
        root = ::Insert(root, key);
    }
 
    void Delete(void) {
        root = ::Delete(root);
    }
 
    void Join(PairingHeap other) {
        root = ::Merge(root, other.root);
    }
     
};

struct edge {
  int from, to, weight, cost, id;

  edge() {}

  edge(int _from, int _to, int _weight, int _cost, int _id) : from(_from), to(_to), weight(_weight), cost(_cost), id(_id) {}
};

struct node {
  int distance, parent;

  node() {
    distance = INT_MAX;
    parent = -1;
  }

  node(int _distance, int _parent) : distance(_distance), parent(_parent) {}
};

struct result {
  int edge;
  vector<int> distances; 
};

vector<node> dijkstra(vector<vector<edge>> graph, int start) {
  int n = (int)graph.size();
  vector<node> answer(n);
  PairingHeap q;
  q.Insert({0, start});
  answer[start].distance = 0;
  while (!q.Empty()) {
    auto [d, u] = q.Top();
    q.Delete();
    if (answer[u].distance > d) {
      continue;
    }
    for (auto [from, to, weight, cost, id] : graph[u]) {
      if (answer[from].distance + weight < answer[to].distance) {
        answer[to] = node(answer[from].distance + weight, id);
        q.Insert({answer[to].distance, to});
      }
    }
  }
  return answer;
}

vector<vector<edge>> transpose(vector<vector<edge>> graph) {
  int n = (int)graph.size();
  vector<vector<edge>> new_graph(n);
  for (int u = 0; u < n; u++) {
    for (auto [from, to, weight, cost, id] : graph[u]) {
      new_graph[to].emplace_back(to, from, weight, cost, id);
    }
  }
  return new_graph;
}

vector<vector<int>> find_shortest_paths_without_each_edge(vector<vector<edge>> graph, int start) {
  int n = (int)graph.size();
  int m = 0;
  for (int u = 0; u < n; u++) {
    for (auto [from, to, weight, cost, id] : graph[u]) {
      m = max(m, 1 + id);
    }
  }
  vector<node> result = dijkstra(graph, start);
  vector<int> dist(n);
  for (int i = 0; i < n; i++) {
    dist[i] = result[i].distance;
  }
  vector<vector<int>> answer(m);
  for (auto [distance, parent] : result) {
    if (parent != -1) {
      vector<vector<edge>> new_graph = graph;
      for (int u = 0; u < n; u++) {
        for (int i = 0; i < (int)new_graph[u].size(); i++) {
          auto [from, to, weight, cost, id] = new_graph[u][i];
          if (id == parent) {
            new_graph[u].erase(new_graph[u].begin() + i);
            break;
          }  
        }
      }
      vector<node> new_result = dijkstra(new_graph, start);
      answer[parent] = vector<int>(n);
      for (int i = 0; i < n; i++) {
        answer[parent][i] = new_result[i].distance;  
      }
    }
  }
  answer.push_back(dist);
  return answer;
}

void solve() {
  int n, m;
  cin >> n >> m;
  vector<vector<edge>> graph(n);
  for (int i = 0; i < m; i++) {
    int from, to, weight, cost;
    cin >> from >> to >> weight >> cost;
    from--, to--;
    graph[from].emplace_back(from, to, weight, cost, i);
  }
  vector<vector<edge>> rev_graph = transpose(graph);
  vector<vector<int>> result_a = find_shortest_paths_without_each_edge(graph, 0);
  vector<vector<int>> result_b = find_shortest_paths_without_each_edge(graph, n - 1);
  vector<vector<int>> rev_result_a = find_shortest_paths_without_each_edge(rev_graph, 0);
  vector<vector<int>> rev_result_b = find_shortest_paths_without_each_edge(rev_graph, n - 1);
  auto get = [](vector<vector<int>>& x, int i, int j) {
    if (x[i].empty()) {
      return x.back()[j];
    } else {
      return x[i][j];
    }
  };
  int ans = INT_MAX;
  if (result_a.back()[n - 1] != INT_MAX && result_b.back()[0] != INT_MAX) {
    ans = result_a.back()[n - 1] + result_b.back()[0];
  }
  for (int u = 0; u < n; u++) {
    for (auto [from, to, weight, cost, id] : graph[u]) {
      int AB = INT_MAX, BA = INT_MAX;
      AB = min(AB, get(result_a, id, n - 1));
      if (get(result_a, id, to) != INT_MAX && get(rev_result_b, id, from) != INT_MAX) {
        AB = min(AB, get(result_a, id, to) + get(rev_result_b, id, from) + weight);
      }
      BA = min(BA, get(result_b, id, 0));
      if (get(result_b, id, to) != INT_MAX && get(rev_result_a, id, from) != INT_MAX) {
        BA = min(BA, get(result_b, id, to) + get(rev_result_a, id, from) + weight); 
      }
      if (AB == INT_MAX || BA == INT_MAX) {
        continue;
      }
      ans = min(ans, AB + BA + cost);
    }
  }
  cout << (ans == INT_MAX ? -1 : ans) << "\n";
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  solve();
}

• Subtask 1: 5 / 5
• Subtask 2: 11 / 11
• Subtask 3: 21 / 21
• Subtask 4: 0 / 63