Submission #103258

#	Time	Username	Problem	Language	Result	Execution time	Memory
103258		wxh010910	Ideal city (IOI12_city)	C++17	100 / 100	112 ms	13692 KiB

city

#include <bits/stdc++.h>

using namespace std;

struct point {
  int x, y, id;

  point(int x = 0, int y = 0, int id = 0): x(x), y(y), id(id) {
  }
};

int DistanceSum(int N, int* X, int* Y) {
  vector<point> p(N);
  for (int i = 0; i < N; ++i) {
    p[i] = point(X[i], Y[i], i);
  }
  sort(p.begin(), p.end(), [&](const point &a, const point &b) {
    return a.x < b.x || (a.x == b.x && a.y < b.y);
  });
  vector<int> to_down(N);
  vector<int> down(N, -1);
  for (int i = 0; i < N; ++i) {
    if (i && p[i].x == p[i - 1].x && p[i].y == p[i - 1].y + 1) {
      to_down[p[i].id] = to_down[p[i - 1].id];
      down[p[i].id] = p[i - 1].id;
    } else {
      to_down[p[i].id] = p[i].id;
    }
  }
  sort(p.begin(), p.end(), [&](const point &a, const point &b) {
    return a.y < b.y || (a.y == b.y && a.x < b.x);
  });
  vector<int> to_left(N);
  vector<int> left(N, -1);
  for (int i = 0; i < N; ++i) {
    if (i && p[i].y == p[i - 1].y && p[i].x == p[i - 1].x + 1) {
      to_left[p[i].id] = to_left[p[i - 1].id];
      left[p[i].id] = p[i - 1].id;
    } else {
      to_left[p[i].id] = p[i].id;
    }
  }
  vector<int> sz_down(N);
  for (int i = 0; i < N; ++i) {
    ++sz_down[to_down[i]];
  }
  vector<int> sz_left(N);
  for (int i = 0; i < N; ++i) {
    ++sz_left[to_left[i]];
  }
  long long ans = 0;
  vector<vector<int>> hor(N);
  for (int i = 0; i < N; ++i) {
    if (left[i] != -1 && (to_down[i] == i || to_down[left[i]] == left[i])) {
      hor[to_down[left[i]]].push_back(to_down[i]);
      hor[to_down[i]].push_back(to_down[left[i]]);
    }
  }
  function<void(int, int)> dfs_hor = [&](int x, int pr) {
    for (auto y : hor[x]) {
      if (y != pr) {
        dfs_hor(y, x);
        ans += (long long) sz_down[y] * (N - sz_down[y]);
        sz_down[x] += sz_down[y];
      }
    }
  };
  for (int i = 0; i < N; ++i) {
    if (sz_down[i]) {
      dfs_hor(i, -1);
      break;
    }
  }
  vector<vector<int>> ver(N);
  for (int i = 0; i < N; ++i) {
    if (down[i] != -1 && (to_left[i] == i || to_left[down[i]] == down[i])) {
      ver[to_left[down[i]]].push_back(to_left[i]);
      ver[to_left[i]].push_back(to_left[down[i]]);
    }
  }
  function<void(int, int)> dfs_ver = [&](int x, int pr) {
    for (auto y : ver[x]) {
      if (y != pr) {
        dfs_ver(y, x);
        ans += (long long) sz_left[y] * (N - sz_left[y]);
        sz_left[x] += sz_left[y];
      }
    }
  };
  for (int i = 0; i < N; ++i) {
    if (sz_left[i]) {
      dfs_ver(i, -1);
      break;
    }
  }
  return (int) (ans % (int) 1e9);
}

• Subtask 1: 11 / 11
• Subtask 2: 21 / 21
• Subtask 3: 23 / 23
• Subtask 4: 45 / 45