Submission #2271551

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Source Code Expand

/**
 * File    : E2.cpp
 * Author  : Kazune Takahashi
 * Created : 2018-3-28 12:29:59
 * Powered by Visual Studio Code
 */

#include <iostream>
#include <iomanip>   // << fixed << setprecision(xxx)
#include <algorithm> // do { } while ( next_permutation(A, A+xxx) ) ;
#include <vector>
#include <string> // to_string(nnn) // substr(m, n) // stoi(nnn)
#include <complex>
#include <tuple>
#include <queue>
#include <stack>
#include <map> // if (M.find(key) != M.end()) { }
#include <set>
#include <random> // random_device rd; mt19937 mt(rd());
#include <cctype>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstdlib>
using namespace std;

#define DEBUG 0 // change 0 -> 1 if we need debug.

typedef long long ll;

// const int dx[4] = {1, 0, -1, 0};
// const int dy[4] = {0, 1, 0, -1};

// const int C = 1e6+10;
// const ll M = 1000000007;

const int MAX_SIZE = 1000010;
const long long MOD = 1000000007;

const int UFSIZE = 100010;
int union_find[UFSIZE];

int root(int a) {
  if (a == union_find[a]) return a;
  return (union_find[a] = root(union_find[a]));
}

bool issame(int a, int b) {
  return root(a) == root(b);
}

void unite(int a, int b) {
  union_find[root(a)] = root(b);
}

bool isroot(int a) {
  return root(a) == a;
}

void init() {
  for (auto i=0; i<UFSIZE; i++) {
    union_find[i] = i;
  }
}

long long power(long long x, long long n) {
  if (n == 0) {
    return 1;
  } else if (n%2 == 1) {
    return (x * power(x, n-1)) % MOD;
  } else {
    long long half = power(x, n/2);
    return (half * half) % MOD;
  }
}

typedef tuple<ll, int, int> edge;
typedef tuple<ll, int> path;

int N, M;
ll X;
vector<edge> V;
vector<path> T[1010];
vector<edge> W;

path parent[10][1010];
int depth[1010];

vector<ll> S;

void dfs(int v, int p, ll cost, int d)
{
  parent[0][v] = path(cost, p);
  depth[v] = d;
  for (auto x : T[v])
  {
    if (get<1>(x) != p)
    {
      dfs(get<1>(x), v, get<0>(x), d + 1);
    }
  }
}

void init2()
{
  dfs(0, -1, 0, 0);
  for (auto k = 0; k+1 < 10; k++)
  {
    for (auto v = 0; v < N; v++)
    {
      if (get<1>(parent[k][v]) < 0)
      {
        parent[k + 1][v] = path(0, -1);
      }
      else
      {
        ll cost = get<0>(parent[k][v]);
        int u = get<1>(parent[k][v]);
        int new_u = get<1>(parent[k][u]);
        ll new_cost = max(cost, get<0>(parent[k][u]));
        parent[k + 1][v] = path(new_cost, new_u);
#if DEBUG == 1
        cerr << "parent[" << k + 1 << "][" << v << "] = (" << new_cost << ", " << new_u << ")" << endl;
#endif
      }
    }
  }
}

ll lca(int u, int v)
{
  if (depth[u] > depth[v])
    swap(u, v);
  ll ans = 0;
#if DEBUG == 1
  cerr << "depth[" << u << "] = " << depth[u]
       << ", depth[" << v << "] = " << depth[v] << endl;
#endif
  for (auto k = 0; k < 10; k++)
  {
    if ((depth[v] - depth[u]) >> k & 1)
    {
      ans = max(ans, get<0>(parent[k][v]));
      v = get<1>(parent[k][v]);
    }
  }
  if (u == v)
    return ans;
  for (auto k = 9; k >= 0; k--)
  {
    if (get<1>(parent[k][u]) != get<1>(parent[k][v]))
    {
      ans = max(ans, get<0>(parent[k][u]));
      ans = max(ans, get<0>(parent[k][v]));
      u = get<1>(parent[k][u]);
      v = get<1>(parent[k][v]);
    }
  }
  ans = max(ans, get<0>(parent[0][v]));
  ans = max(ans, get<0>(parent[0][u]));
  return ans;
}

ll f(ll n)
{
  ll c;
  if (S[0] > n)
    c = 0;
  else
  {
    ll lb = 0;
    ll ub = S.size();
    while (ub - lb > 1)
    {
      ll t = (ub + lb) / 2;
      if (S[t] > n)
      {
        ub = t;
      }
      else
      {
        lb = t;
      }
    }
    c = ub;
  }
  if (c == 0)
  {
    return power(2, M);
  }
  else
  {
    return power(2, M - c + 1);
  }
}

int main()
{
  init();
  cin >> N >> M;
  cin >> X;
  for (auto i = 0; i < M; i++)
  {
    int u, v;
    ll w;
    cin >> u >> v >> w;
    u--;
    v--;
    V.push_back(edge(w, u, v));
  }
  sort(V.begin(), V.end());
  ll Y = 0;
  int cnt = 0;
  for (auto e : V)
  {
    ll cost = get<0>(e);
    int u = get<1>(e);
    int v = get<2>(e);
    if (!issame(u, v))
    {
      unite(u, v);
      T[u].push_back(path(cost, v));
      T[v].push_back(path(cost, u));
      Y += cost;
      cnt++;
    }
    else
    {
      W.push_back(e);
    }
  }
#if DEBUG == 1
  cerr << "X = " << X << ", Y = " << Y << endl;
#endif
  init2();
  for (auto i = 0; i < cnt; i++)
  {
    S.push_back(Y);
  }
  for (auto e : W)
  {
    ll cost = get<0>(e);
    int u = get<1>(e);
    int v = get<2>(e);
    S.push_back(cost - lca(u, v) + Y);
  }
  sort(S.begin(), S.end());
#if DEBUG == 1
  for (auto x : S)
  {
    cerr << x << " ";
  }
  cerr << endl;
  cerr << "f(" << X - 1 << ") = " << f(X - 1)
       << ", f(" << X << ") = " << f(X) << endl;
#endif
  cout << (f(X - 1) + MOD - f(X)) % MOD << endl;
}

Submission Info

Judge Result