oj.uz

Submission #258116

# Submission time Handle Problem Language Result Execution time Memory
258116 2020-08-05T11:39:32 Z atoiz Sky Walking (IOI19_walk) C++14
25 / 100
 1214 ms 81348 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;
				lazy[lc] = min(lazy[lc], lazy[rt]), lazy[rc] = min(lazy[rc], lazy[rt]);
			}
		}
		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, bool &found) {
		if (valY[hi] < l || r < valY[lo] || !cnt[rt] || found) return INFLL;
		push(rt, lo, hi);
		if (lo == hi) return found = true, 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, found);
			if (!found) ans = get(l, r, minY, rc, md + 1, hi, found);
		} else {
			ans = get(l, r, minY, rc, md + 1, hi, found);
			if (!found) ans = get(l, r, minY, lc, lo, md, found);
		}
		return ans;
	}
	ll get(int l, int r, bool minY) { bool found = false; return get(l, r, minY, 1, 0, T - 1, found); }
};
 
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;
	vector<vector<int>> mergers(2, vector<int>(1, start));
	while (leftBorder > 0 || rightBorder < N - 1) {
		ll leftBest = st[0][0].get(0, H[leftBorder], false), rightBest = st[1][0].get(0, H[rightBorder], 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]);
			if (curCost == INFLL - Y[w]) curCost = INFLL;
			st[k][0].insert(Y[w], curCost), st[k][1].insert(Y[w], curCost + Y[w]);
			// cout << "pre dist " << col << ' ' << Y[w] << ": " << curCost << endl;
		}
 
		// cout << "S" << endl;
		for (auto upd : updates[col]) {
			// cout << "." << endl;
			int y = upd.first;
			ll c = upd.second;
			// cout << "upd " << y << ' ' << c << endl;
			st[k][0].minimize(y, H[col], c), st[k][1].minimize(0, y, c + y);
		}


		for (; !mergers[k].empty() && H[mergers[k].back()] <= H[col]; mergers[k].pop_back()) {
			int prv = mergers[k].back();
			ll curCost = st[k][1].get(H[prv] + 1, H[col], true);
			st[k][1].minimize(0, H[prv], curCost);
		}
		mergers[k].push_back(col);

		// cout << "T" << endl;
		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]);
			if (curCost == INFLL - Y[w]) curCost = INFLL;
			// 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 1 ms 256 KB Output is correct
2 Correct 1 ms 256 KB Output is correct
3 Correct 1 ms 256 KB Output is correct
4 Correct 1 ms 256 KB Output is correct
5 Correct 1 ms 384 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 1 ms 384 KB Output is correct
8 Correct 1 ms 384 KB Output is correct
9 Correct 1 ms 256 KB Output is correct
10 Correct 1 ms 384 KB Output is correct
11 Correct 1 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 1 ms 384 KB Output is correct
16 Correct 0 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 1 ms 256 KB Output is correct
2 Correct 1 ms 256 KB Output is correct
3 Correct 698 ms 70452 KB Output is correct
4 Incorrect 1016 ms 80328 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 79 ms 9972 KB Output is correct
2 Correct 779 ms 69280 KB Output is correct
3 Correct 835 ms 70468 KB Output is correct
4 Correct 1073 ms 79044 KB Output is correct
5 Correct 1012 ms 77508 KB Output is correct
6 Correct 940 ms 78944 KB Output is correct
7 Correct 403 ms 44944 KB Output is correct
8 Correct 844 ms 81348 KB Output is correct
9 Correct 852 ms 80128 KB Output is correct
10 Correct 493 ms 51556 KB Output is correct
11 Correct 21 ms 5120 KB Output is correct

Subtask #4
0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 79 ms 9972 KB Output is correct
2 Correct 779 ms 69280 KB Output is correct
3 Correct 835 ms 70468 KB Output is correct
4 Correct 1073 ms 79044 KB Output is correct
5 Correct 1012 ms 77508 KB Output is correct
6 Correct 940 ms 78944 KB Output is correct
7 Correct 403 ms 44944 KB Output is correct
8 Correct 844 ms 81348 KB Output is correct
9 Correct 852 ms 80128 KB Output is correct
10 Correct 493 ms 51556 KB Output is correct
11 Correct 21 ms 5120 KB Output is correct
12 Correct 747 ms 70472 KB Output is correct
13 Correct 1214 ms 79048 KB Output is correct
14 Correct 1143 ms 77456 KB Output is correct
15 Correct 555 ms 41936 KB Output is correct
16 Correct 690 ms 42056 KB Output is correct
17 Correct 748 ms 41956 KB Output is correct
18 Correct 547 ms 41800 KB Output is correct
19 Correct 630 ms 41928 KB Output is correct
20 Correct 564 ms 44020 KB Output is correct
21 Correct 143 ms 10496 KB Output is correct
22 Correct 603 ms 59516 KB Output is correct
23 Correct 636 ms 61012 KB Output is correct
24 Correct 655 ms 64892 KB Output is correct
25 Correct 664 ms 67116 KB Output is correct
26 Correct 628 ms 72136 KB Output is correct
27 Correct 1000 ms 78024 KB Output is correct
28 Correct 968 ms 78916 KB Output is correct
29 Correct 1004 ms 78944 KB Output is correct
30 Correct 549 ms 44740 KB Output is correct
31 Correct 928 ms 80256 KB Output is correct
32 Correct 425 ms 37268 KB Output is correct
33 Incorrect 519 ms 38952 KB Output isn't correct
34 Halted 0 ms 0 KB -

Subtask #5
0 / 43.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 256 KB Output is correct
2 Correct 1 ms 256 KB Output is correct
3 Correct 1 ms 256 KB Output is correct
4 Correct 1 ms 256 KB Output is correct
5 Correct 1 ms 384 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 1 ms 384 KB Output is correct
8 Correct 1 ms 384 KB Output is correct
9 Correct 1 ms 256 KB Output is correct
10 Correct 1 ms 384 KB Output is correct
11 Correct 1 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 1 ms 384 KB Output is correct
16 Correct 0 ms 384 KB Output is correct
17 Correct 1 ms 384 KB Output is correct
18 Correct 1 ms 256 KB Output is correct
19 Correct 1 ms 256 KB Output is correct
20 Correct 698 ms 70452 KB Output is correct
21 Incorrect 1016 ms 80328 KB Output isn't correct
22 Halted 0 ms 0 KB -