Submission #1208738

#TimeUsernameProblemLanguageResultExecution timeMemory
1208738spacewalkerRainforest Jumps (APIO21_jumps)C++20
4 / 100
568 ms129836 KiB
#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; void find_ranges(int v) { auto &reachable_ranges = ranges_crossed[0]; reachable_ranges[v] = {v, v}; for (int ch : tree_ch[v]) { find_ranges(ch); reachable_ranges[v] = onion(reachable_ranges[v], reachable_ranges[ch]); } for (int ch : tree_ch[v]) { reachable_ranges[ch] = onion(reachable_ranges[ch], pair{min(ch, v), max(ch, v)}); } } Jumper() {} Jumper(int root, const vector<int> &tree) : 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]; } find_ranges(root); 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} pair<int, int> 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}; } 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))); // cerr << " == processing fast tree " << endl; fast = Jumper(max_idx, fast_tree); // cerr << " == processing slow tree " << endl; slow = Jumper(max_idx, slow_tree); } 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
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