Submission #1208767

#	Time	Username	Problem	Language	Result	Execution time	Memory
1208767		spacewalker	Rainforest Jumps (APIO21_jumps)	C++20	4 / 100	624 ms	125680 KiB

jumps

#include "jumps.h"

#include <bits/stdc++.h>

using namespace std;

vector<int> next_greater(const vector<int> &v) {
  int n = v.size();
  vector<int> ans(n, -1);
  vector<int> possible_next{n-1};
  for (int i = n-2; i >= 0; --i) {
    while (!possible_next.empty() && v[i] >= v[possible_next.back()]) possible_next.pop_back();
    if (!possible_next.empty()) ans[i] = possible_next.back();
    possible_next.push_back(i);
  }
  return ans;
}

using interval = pair<int, int>;

interval onion(interval a, interval b) {
  return {min(a.first, b.first), max(a.second, b.second)};
}

bool has_overlap(interval a, interval b) {
  return !(a.second < b.first || b.second < a.first);
}

// fn ((a, b), (a, b)) { (a, b) }
// let onion((x, y), (z, w)) = (min(x, z), max(y, w))

struct Jumper {
  vector<vector<int>> tree_ch;
  vector<vector<int>> locations;
  vector<vector<pair<int, int>>> ranges_crossed;
  Jumper() {}
  Jumper(int root, const vector<int> &tree, const vector<pair<int, int>> init_ranges) : tree_ch(tree.size()), locations(20, vector(tree.size(), -1)), 
    ranges_crossed(20, vector(tree.size(), pair<int, int>{tree.size() + 100, -1})) {
    for (int i = 0; i < tree.size(); ++i) if (tree[i] != -1) {
      tree_ch[tree[i]].push_back(i);
      locations[0][i] = tree[i];
    }

    ranges_crossed[0] = init_ranges;
    for (int i = 0; i < tree.size(); ++i) {
      int layer = 0;
        // cerr << "layer " << layer << " " << i << " -> " << locations[layer][i] << " (" << ranges_crossed[layer][i].first << ", " << ranges_crossed[layer][i].second << ")" << endl;
    }
    for (int layer = 1; layer < locations.size(); ++layer) {
      for (int i = 0; i < tree.size(); ++i) if (locations[layer-1][i] != -1) {
        locations[layer][i] = locations[layer-1][locations[layer-1][i]];
        ranges_crossed[layer][i] = onion(ranges_crossed[layer-1][i], ranges_crossed[layer-1][locations[layer-1][i]]);
        // cerr << "layer " << layer << " " << i << " -> " << locations[layer][i] << " (" << ranges_crossed[layer][i].first << ", " << ranges_crossed[layer][i].second << ")" << endl;
      }
    }

  }

  int last_inside(int v, interval i) {
    int cv = v;
    for (int layer = locations.size() - 1; layer >= 0; --layer) {
      if (locations[layer][cv] != -1 && i.first <= locations[layer][cv] && locations[layer][cv] <= i.second) cv = locations[layer][cv];
    }
    return cv;
  }

  // {vertex, # of steps taken, interval visited}
  tuple<int, int, interval> last_before_overlapping(int v, interval i) {
    int cv = v;
    auto crange = ranges_crossed[0][v];
    int dist = 0;
    for (int layer = locations.size() - 1; layer >= 0; --layer) {
      if (locations[layer][cv] != -1 && !has_overlap(onion(crange, ranges_crossed[layer][cv]), i)) {
        crange = onion(crange, ranges_crossed[layer][cv]);
        cv = locations[layer][cv];
        dist += (1 << layer);
      }
    }
    return {cv, dist, crange};
  }

  int parent(int v) {
    return locations[0][v];
  }
};

Jumper fast, slow;

void init(int N, std::vector<int> H) {
  // impl detail so ng and pg are always defined on nodes that matter
  vector<int> ng = next_greater(H);
  reverse(H.begin(), H.end());
  vector<int> pg = next_greater(H); reverse(H.begin(), H.end());
  reverse(pg.begin(), pg.end());
  for (int &v : pg) v = (v == -1 ? -1 : N - 1 - v);
  
  vector<int> fast_tree(N, -1), slow_tree(N, -1);
  for (int i = 0; i < N; ++i) {
    if (ng[i] == -1 && pg[i] == -1) continue;
    else if (ng[i] == -1 || pg[i] == -1) {
      int par = max(ng[i], pg[i]);
      fast_tree[i] = slow_tree[i] = par;
    } else {
      pair<int, int> target1 = {H[ng[i]], ng[i]}, target2 = {H[pg[i]], pg[i]};
      if (target1 > target2) swap(target1, target2);
      fast_tree[i] = target2.second;
      slow_tree[i] = target1.second;
    }
    // cerr << "jump targets: " << fast_tree[i] << " " << slow_tree[i] << endl;
  }
  int max_idx = distance(begin(H), max_element(begin(H), end(H)));
  // get ranges for the slow tree
  vector slow_tree_init_ranges(N, pair{-1, -1});
  for (int i = 0; i < N; ++i) {
    if (slow_tree[i] != -1) slow_tree_init_ranges[i] = {min(i, slow_tree[i]), max(i, slow_tree[i])};
  }
  // cerr << " == processing slow tree " << endl;
  slow = Jumper(max_idx, slow_tree, slow_tree_init_ranges);

  // from traversal info on the slow tree, get ranges for the fast tree
  vector fast_tree_init_ranges(N, pair{-1, -1});
  for (int i = 0; i < N; ++i) {
    if (fast_tree[i] != -1) {
      pair ft_int{fast_tree[i], fast_tree[i]};
      fast_tree_init_ranges[i] = onion(ft_int, get<2>(slow.last_before_overlapping(i, ft_int)));
    }
  }
  // cerr << " == processing fast tree " << endl;
  fast = Jumper(max_idx, fast_tree, fast_tree_init_ranges);
}

int minimum_jumps(int A, int B, int C, int D) {
  int src = slow.last_inside(A, {A, B});

  // cerr << " starting from " << src << endl;
  auto [v1, dist1, _] = fast.last_before_overlapping(src, {C, D});
  // cerr << " phase 1: " << v1 << endl;
  auto [v2, dist2, __] = slow.last_before_overlapping(v1, {C, D});
  // cerr << " phase 2: " << v2 << endl;
  
  int pot_dst = slow.parent(v2);
  if (C <= pot_dst && pot_dst <= D) return dist1 + dist2 + 1;
  else return -1;

}

// 3 2 1 6 4 5 7

• Subtask 1: 4 / 4
• Subtask 2: 0 / 8
• Subtask 3: 0 / 13
• Subtask 4: 0 / 12
• Subtask 5: 0 / 23
• Subtask 6: 0 / 21
• Subtask 7: 0 / 19