oj.uz

Submission #258040

# Submission time Handle Problem Language Result Execution time Memory
258040 2020-08-05T08:45:05 Z atoiz Sky Walking (IOI19_walk) C++14
25 / 100
 4000 ms 81416 KB 
#include "walk.h"
#include <iostream>
#include <vector>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <tuple>
#include <cassert>
#include <numeric>

using namespace std;
using ll = long long;

const int MAXY = 1000100100;
const ll INFLL = 1e16;
int N, M, T;
vector<int> X, H, L, R, Y;
vector<int> valY;

int dist(int i, int j) { return abs(X[i] - X[j]); }
// int pos(int y) { return (int) (upper_bound(valY.begin(), valY.end(), y) - valY.begin() - 1); } // first <=

struct SegmentTree {
	vector<ll> lazy, arr;
	vector<int> cnt;
	SegmentTree(): lazy((T + 2) * 4, INFLL), arr((T + 2) * 4, INFLL), cnt((T + 2) * 4, 0) {}

	void push(int rt, int lo, int hi) {
		if (lazy[rt] != INFLL && cnt[rt]) {
			if (lo == hi) arr[lo] = min(arr[lo], lazy[rt]);
			else {
				int lc = rt << 1, rc = rt << 1 | 1, md = (lo + hi) >> 1;
				lazy[lc] = min(lazy[lc], lazy[rt]), lazy[rc] = min(lazy[rc], lazy[rt]);
				push(lc, lo, md), push(rc, md + 1, hi);
			}
		}
		lazy[rt] = INFLL;
	}

	void insert(int y, ll c) {
		int rt = 1, lo = 0, hi = T - 1;
		while (true) {
			push(rt, lo, hi);
			++cnt[rt];
			if (lo == hi) {
				assert(valY[lo] == y);
				arr[lo] = min(arr[lo], c);
				break;
			}
			int md = (lo + hi) >> 1;
			(y <= valY[md]) ? (rt = rt << 1, hi = md) : (rt = rt << 1 | 1, lo = md + 1);
		}
	}

	void remove(int y) {
		int rt = 1, lo = 0, hi = T - 1;
		while (true) {
			push(rt, lo, hi);
			--cnt[rt];
			if (lo == hi) {
				if (cnt[rt] == 0) arr[lo] = INFLL;
				break;
			}
			int md = (lo + hi) >> 1;
			(y <= valY[md]) ? (rt = rt << 1, hi = md) : (rt = rt << 1 | 1, lo = md + 1);
		}
	}

	void minimize(int l, int r, ll c, int rt, int lo, int hi) {
		if (valY[hi] < l || r < valY[lo] || !cnt[rt] || lazy[rt] <= c) return;
		push(rt, lo, hi);
		if (l <= valY[lo] && valY[hi] <= r) return lazy[rt] = min(lazy[rt], c), void(0);
		int lc = rt << 1, rc = rt << 1 | 1, md = (lo + hi) >> 1;
		minimize(l, r, c, lc, lo, md), minimize(l, r, c, rc, md + 1, hi);
	}
	void minimize(int l, int r, ll c) { minimize(l, r, c, 1, 0, T - 1); }

	ll get(int l, int r, bool minY, int rt, int lo, int hi) {
		if (valY[hi] < l || r < valY[lo] || !cnt[rt]) return INFLL;
		push(rt, lo, hi);
		if (lo == hi) return arr[lo];
		int lc = rt << 1, rc = rt << 1 | 1, md = (lo + hi) >> 1;

		ll ans = INFLL;
		if (minY) {
			ans = get(l, r, minY, lc, lo, md);
			if (ans == INFLL) ans = get(l, r, minY, rc, md + 1, hi);
		} else {
			ans = get(l, r, minY, rc, md + 1, hi);
			if (ans == INFLL) ans = get(l, r, minY, lc, lo, md);
		}
		return ans;
	}
	ll get(int l, int r, bool minY) { return get(l, r, minY, 1, 0, T - 1); }
};

vector<vector<pair<int, ll>>> solve(int start) {
	// cout << "solve " << start << endl;
	vector<vector<pair<int, ll>>> ans(M);

	vector<vector<int>> walksAdd(N), walksRem(N);
	vector<int> walkL(M, -1), walkR(M, -1);
	vector<int> walkIDs(M);
	iota(walkIDs.begin(), walkIDs.end(), 0);
	sort(walkIDs.begin(), walkIDs.end(), [&](int i, int j) { return Y[i] < Y[j]; });
	vector<int> lCols, rCols;
	for (int x = 0; x <= start; lCols.push_back(x++)) while (!lCols.empty() && H[lCols.back()] <= H[x]) lCols.pop_back();
	for (int x = N - 1; x >= start; rCols.push_back(x--)) while (!rCols.empty() && H[rCols.back()] <= H[x]) rCols.pop_back();
	for (int w : walkIDs) {
		if (L[w] <= start && start <= R[w] && Y[w] <= H[start]) { 
			walksAdd[walkL[w] = walkR[w] = start].push_back(w);
			walksRem[L[w]].push_back(w), walksRem[R[w]].push_back(w);
			continue; 
		}

		while (!lCols.empty() && H[lCols.back()] < Y[w]) lCols.pop_back();
		while (!rCols.empty() && H[rCols.back()] < Y[w]) rCols.pop_back();
		if (!rCols.empty() && rCols.back() <= L[w]) walksAdd[L[w]].push_back(w), walksRem[R[w]].push_back(w);
		else if (!lCols.empty() && lCols.back() >= R[w]) walksAdd[R[w]].push_back(w), walksRem[L[w]].push_back(w);
		else {
			if (!lCols.empty() && L[w] <= lCols.back()) walksAdd[walkL[w] = lCols.back()].push_back(w), walksRem[L[w]].push_back(w);
			if (!rCols.empty() && R[w] >= rCols.back()) walksAdd[walkR[w] = rCols.back()].push_back(w), walksRem[R[w]].push_back(w);
		}
	}

	// for (int x = 0; x < N; ++x) {
	// 	cout << x << ":\n";
	// 	for (auto w : walksRem[x]) cout << L[w] << ' ' << R[w] << ' ' << Y[w] << endl;
	// }

	vector<vector<SegmentTree>> st(2, vector<SegmentTree>(2, SegmentTree()));
	for (int w : walksAdd[start]) {
		if (L[w] < start) st[0][0].insert(Y[w], 0), st[0][1].insert(Y[w], Y[w]);
		if (R[w] > start) st[1][0].insert(Y[w], 0), st[1][1].insert(Y[w], Y[w]);
		ans[w].emplace_back(start, 0);
	}

	vector<vector<pair<int, ll>>> updates(N);
	int leftBorder = start, rightBorder = start;
	while (leftBorder > 0 || rightBorder < N - 1) {
		ll leftBest = st[0][0].get(0, MAXY, false), rightBest = st[1][0].get(0, MAXY, false);
		bool k = leftBest > rightBest;
		if (leftBorder == 0) k = 1;
		if (rightBorder == N - 1) k = 0;

		int col = (k == 0 ? --leftBorder : ++rightBorder);

		for (int w : walksAdd[col]) {
			ll curCost = min(st[k][0].get(0, Y[w], false), st[k][1].get(Y[w], H[col], true) - Y[w]);
			st[k][0].insert(Y[w], curCost), st[k][1].insert(Y[w], curCost + Y[w]);
			// cout << "pre dist " << col << ' ' << Y[w] << ": " << curCost << endl;
		}

		for (auto upd : updates[col]) {
			int y = upd.first;
			ll c = upd.second;
			st[k][0].minimize(y, MAXY, c), st[k][1].minimize(0, y, c + y);
		}
		for (int w : walksAdd[col]) {
			ll curCost = min(st[k][0].get(Y[w], Y[w], false), st[k][1].get(Y[w], Y[w], false) - Y[w]);
			// cout << "dist " << col << ' ' << Y[w] << ": " << curCost << endl;
			ans[w].emplace_back(col, curCost);

			if (~walkL[w] && ~walkR[w] && walkL[w] <= start && start <= walkR[w]) {
				if (col == walkL[w]) updates[walkR[w]].emplace_back(Y[w], curCost + X[start] - X[col]);
				if (col == walkR[w]) updates[walkL[w]].emplace_back(Y[w], curCost + X[col] - X[start]);
			}
		}

		for (int w : walksRem[col]) st[k][0].remove(Y[w]), st[k][1].remove(Y[w]);
	}

	return ans;
}

ll min_distance(vector<int> x, vector<int> h, vector<int> l, vector<int> r, vector<int> y, int s, int t) {
	N = (int) x.size(), M = (int) y.size();
	X = x, H = h, L = l, R = r, Y = y;
	valY = Y;
	sort(valY.begin(), valY.end()), valY.erase(unique(valY.begin(), valY.end()), valY.end());
	T = (int) valY.size();

	vector<vector<pair<int, ll>>> ansS = solve(s);
	vector<vector<pair<int, ll>>> ansT = solve(t);
	ll ans = INFLL;
	for (int j = 0; j < M; ++j) {
		for (auto p : ansS[j]) for (auto q : ansT[j]) {
			ll cur = 0;
			cur += (ll) Y[j] * 2;
			cur += (ll) dist(p.first, q.first) + dist(p.first, s) + dist(q.first, t);
			cur += (p.second + q.second) * 2;
			// if (cur == 27) cout << L[j] << ' ' << R[j] << ' ' << Y[j] << " - " << p.first << ' ' << q.first << endl;
			ans = min(ans, cur);
		}
	}

	if (ans == INFLL) ans = -1;
	return ans;
}

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 256 KB Output is correct
2 Correct 0 ms 256 KB Output is correct
3 Correct 0 ms 256 KB Output is correct
4 Correct 1 ms 256 KB Output is correct
5 Correct 0 ms 384 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 0 ms 384 KB Output is correct
8 Correct 1 ms 384 KB Output is correct
9 Correct 0 ms 384 KB Output is correct
10 Correct 1 ms 384 KB Output is correct
11 Correct 0 ms 384 KB Output is correct
12 Correct 1 ms 384 KB Output is correct
13 Correct 1 ms 384 KB Output is correct
14 Correct 1 ms 384 KB Output is correct
15 Correct 0 ms 384 KB Output is correct
16 Correct 1 ms 384 KB Output is correct
17 Correct 1 ms 384 KB Output is correct

Subtask #2
0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 256 KB Output is correct
2 Correct 1 ms 256 KB Output is correct
3 Correct 710 ms 70468 KB Output is correct
4 Incorrect 978 ms 80452 KB Output isn't correct
5 Halted 0 ms 0 KB -

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 83 ms 9960 KB Output is correct
2 Correct 734 ms 69396 KB Output is correct
3 Correct 873 ms 70584 KB Output is correct
4 Correct 1006 ms 79052 KB Output is correct
5 Correct 831 ms 77536 KB Output is correct
6 Correct 835 ms 79072 KB Output is correct
7 Correct 417 ms 44780 KB Output is correct
8 Correct 815 ms 81416 KB Output is correct
9 Correct 732 ms 80124 KB Output is correct
10 Correct 486 ms 51524 KB Output is correct
11 Correct 29 ms 5112 KB Output is correct

Subtask #4
0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 83 ms 9960 KB Output is correct
2 Correct 734 ms 69396 KB Output is correct
3 Correct 873 ms 70584 KB Output is correct
4 Correct 1006 ms 79052 KB Output is correct
5 Correct 831 ms 77536 KB Output is correct
6 Correct 835 ms 79072 KB Output is correct
7 Correct 417 ms 44780 KB Output is correct
8 Correct 815 ms 81416 KB Output is correct
9 Correct 732 ms 80124 KB Output is correct
10 Correct 486 ms 51524 KB Output is correct
11 Correct 29 ms 5112 KB Output is correct
12 Correct 844 ms 70396 KB Output is correct
13 Execution timed out 4051 ms 73592 KB Time limit exceeded
14 Halted 0 ms 0 KB -

Subtask #5
0 / 43.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 256 KB Output is correct
2 Correct 0 ms 256 KB Output is correct
3 Correct 0 ms 256 KB Output is correct
4 Correct 1 ms 256 KB Output is correct
5 Correct 0 ms 384 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 0 ms 384 KB Output is correct
8 Correct 1 ms 384 KB Output is correct
9 Correct 0 ms 384 KB Output is correct
10 Correct 1 ms 384 KB Output is correct
11 Correct 0 ms 384 KB Output is correct
12 Correct 1 ms 384 KB Output is correct
13 Correct 1 ms 384 KB Output is correct
14 Correct 1 ms 384 KB Output is correct
15 Correct 0 ms 384 KB Output is correct
16 Correct 1 ms 384 KB Output is correct
17 Correct 1 ms 384 KB Output is correct
18 Correct 0 ms 256 KB Output is correct
19 Correct 1 ms 256 KB Output is correct
20 Correct 710 ms 70468 KB Output is correct
21 Incorrect 978 ms 80452 KB Output isn't correct
22 Halted 0 ms 0 KB -