oj.uz

Submission #258783

# Submission time Handle Problem Language Result Execution time Memory
258783 2020-08-06T14:40:03 Z atoiz Sky Walking (IOI19_walk) C++14
100 / 100
 1517 ms 85472 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); }
 
	int getPos(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 -1;
		push(rt, lo, hi);
		if (lo == hi) return found = true, lo;
		int lc = rt << 1, rc = rt << 1 | 1, md = (lo + hi) >> 1;
 
		int ans = -1;
		if (minY) {
			ans = getPos(l, r, minY, lc, lo, md, found);
			if (!found) ans = getPos(l, r, minY, rc, md + 1, hi, found);
		} else {
			ans = getPos(l, r, minY, rc, md + 1, hi, found);
			if (!found) ans = getPos(l, r, minY, lc, lo, md, found);
		}
		return ans;
	}
	int getPos(int l, int r, bool minY) { bool found = false; return getPos(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]) {
		st[0][0].insert(Y[w], 0), st[0][1].insert(Y[w], Y[w]);
		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) {
		if (leftBorder >= 0) {
			for (auto upd : updates[leftBorder]) {
				// cout << "." << endl;
				int y = upd.first;
				ll c = upd.second;
				// cout << "upd " << y << ' ' << c << endl;
				st[0][0].minimize(y, H[leftBorder], c), st[0][1].minimize(0, y, c + y);
			}
			updates[leftBorder].clear();
		}
		if (rightBorder <= N - 1) {
			for (auto upd : updates[rightBorder]) {
				// cout << "." << endl;
				int y = upd.first;
				ll c = upd.second;
				// cout << "upd " << y << ' ' << c << endl;
				st[1][0].minimize(y, H[rightBorder], c), st[1][1].minimize(0, y, c + y);
			}
			updates[rightBorder].clear();
		}


		ll leftBest = st[0][0].get(0, MAXY, false), rightBest = st[1][0].get(0, MAXY, false);
		bool k = leftBest > rightBest;
		if (leftBorder == -1) k = 1;
		if (rightBorder == N) k = 0;
 
		int col = (k == 0 ? leftBorder-- : rightBorder++);

		// 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]) {
			if ((k == 0) ? (L[w] != col) : (R[w] != col)) continue;
			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;
			st[k][0].remove(Y[w]), st[k][1].remove(Y[w]);
			if (curCost != INFLL) {
				int i = st[k][0].getPos(0, Y[w] - 1, false);
				st[k][0].minimize(Y[w], H[col], curCost);
				if (~i) st[k][0].minimize(valY[i], valY[i], curCost + Y[w] - valY[i]);
			}
		}
 
 		(k == 0 ? --col : ++col);
 		if (col != -1 && col != N) {
			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;
		}
	}
 
	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 0 ms 256 KB Output is correct
3 Correct 1 ms 256 KB Output is correct
4 Correct 1 ms 384 KB Output is correct
5 Correct 0 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 384 KB Output is correct
10 Correct 1 ms 384 KB Output is correct
11 Correct 1 ms 384 KB Output is correct
12 Correct 2 ms 384 KB Output is correct
13 Correct 0 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 1 ms 384 KB Output is correct
17 Correct 1 ms 384 KB Output is correct

Subtask #2
14.0 / 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 1063 ms 72492 KB Output is correct
4 Correct 1177 ms 84296 KB Output is correct
5 Correct 752 ms 65336 KB Output is correct
6 Correct 743 ms 67264 KB Output is correct
7 Correct 646 ms 66060 KB Output is correct
8 Correct 1068 ms 72644 KB Output is correct
9 Correct 980 ms 80880 KB Output is correct
10 Correct 1111 ms 83064 KB Output is correct
11 Correct 1070 ms 76100 KB Output is correct
12 Correct 1107 ms 85288 KB Output is correct
13 Correct 1102 ms 85316 KB Output is correct
14 Correct 887 ms 79996 KB Output is correct
15 Correct 1159 ms 45016 KB Output is correct
16 Correct 552 ms 34884 KB Output is correct
17 Correct 519 ms 32116 KB Output is correct
18 Correct 1004 ms 81128 KB Output is correct
19 Correct 33 ms 4356 KB Output is correct
20 Correct 411 ms 41192 KB Output is correct
21 Correct 318 ms 30900 KB Output is correct
22 Correct 364 ms 35164 KB Output is correct
23 Correct 891 ms 55908 KB Output is correct
24 Correct 617 ms 35300 KB Output is correct
25 Correct 333 ms 31876 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 97 ms 10612 KB Output is correct
2 Correct 1110 ms 71008 KB Output is correct
3 Correct 1168 ms 72640 KB Output is correct
4 Correct 1300 ms 83012 KB Output is correct
5 Correct 1236 ms 81724 KB Output is correct
6 Correct 1326 ms 83080 KB Output is correct
7 Correct 599 ms 47804 KB Output is correct
8 Correct 991 ms 85472 KB Output is correct
9 Correct 1271 ms 84304 KB Output is correct
10 Correct 680 ms 54976 KB Output is correct
11 Correct 23 ms 5888 KB Output is correct

Subtask #4
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 97 ms 10612 KB Output is correct
2 Correct 1110 ms 71008 KB Output is correct
3 Correct 1168 ms 72640 KB Output is correct
4 Correct 1300 ms 83012 KB Output is correct
5 Correct 1236 ms 81724 KB Output is correct
6 Correct 1326 ms 83080 KB Output is correct
7 Correct 599 ms 47804 KB Output is correct
8 Correct 991 ms 85472 KB Output is correct
9 Correct 1271 ms 84304 KB Output is correct
10 Correct 680 ms 54976 KB Output is correct
11 Correct 23 ms 5888 KB Output is correct
12 Correct 1109 ms 72540 KB Output is correct
13 Correct 1159 ms 83040 KB Output is correct
14 Correct 1217 ms 81420 KB Output is correct
15 Correct 818 ms 45640 KB Output is correct
16 Correct 914 ms 45816 KB Output is correct
17 Correct 889 ms 45860 KB Output is correct
18 Correct 837 ms 45664 KB Output is correct
19 Correct 736 ms 45812 KB Output is correct
20 Correct 615 ms 47096 KB Output is correct
21 Correct 86 ms 12532 KB Output is correct
22 Correct 696 ms 63228 KB Output is correct
23 Correct 693 ms 64724 KB Output is correct
24 Correct 687 ms 68604 KB Output is correct
25 Correct 715 ms 70956 KB Output is correct
26 Correct 681 ms 75876 KB Output is correct
27 Correct 1167 ms 82052 KB Output is correct
28 Correct 1104 ms 83052 KB Output is correct
29 Correct 1353 ms 82992 KB Output is correct
30 Correct 602 ms 47852 KB Output is correct
31 Correct 1217 ms 84432 KB Output is correct
32 Correct 573 ms 40776 KB Output is correct
33 Correct 586 ms 42408 KB Output is correct
34 Correct 683 ms 52032 KB Output is correct
35 Correct 681 ms 43840 KB Output is correct
36 Correct 662 ms 38444 KB Output is correct
37 Correct 265 ms 30848 KB Output is correct
38 Correct 303 ms 35176 KB Output is correct
39 Correct 786 ms 55908 KB Output is correct
40 Correct 547 ms 35364 KB Output is correct
41 Correct 310 ms 32032 KB Output is correct

Subtask #5
43.0 / 43.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 256 KB Output is correct
2 Correct 0 ms 256 KB Output is correct
3 Correct 1 ms 256 KB Output is correct
4 Correct 1 ms 384 KB Output is correct
5 Correct 0 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 384 KB Output is correct
10 Correct 1 ms 384 KB Output is correct
11 Correct 1 ms 384 KB Output is correct
12 Correct 2 ms 384 KB Output is correct
13 Correct 0 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 1 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 1063 ms 72492 KB Output is correct
21 Correct 1177 ms 84296 KB Output is correct
22 Correct 752 ms 65336 KB Output is correct
23 Correct 743 ms 67264 KB Output is correct
24 Correct 646 ms 66060 KB Output is correct
25 Correct 1068 ms 72644 KB Output is correct
26 Correct 980 ms 80880 KB Output is correct
27 Correct 1111 ms 83064 KB Output is correct
28 Correct 1070 ms 76100 KB Output is correct
29 Correct 1107 ms 85288 KB Output is correct
30 Correct 1102 ms 85316 KB Output is correct
31 Correct 887 ms 79996 KB Output is correct
32 Correct 1159 ms 45016 KB Output is correct
33 Correct 552 ms 34884 KB Output is correct
34 Correct 519 ms 32116 KB Output is correct
35 Correct 1004 ms 81128 KB Output is correct
36 Correct 33 ms 4356 KB Output is correct
37 Correct 411 ms 41192 KB Output is correct
38 Correct 318 ms 30900 KB Output is correct
39 Correct 364 ms 35164 KB Output is correct
40 Correct 891 ms 55908 KB Output is correct
41 Correct 617 ms 35300 KB Output is correct
42 Correct 333 ms 31876 KB Output is correct
43 Correct 97 ms 10612 KB Output is correct
44 Correct 1110 ms 71008 KB Output is correct
45 Correct 1168 ms 72640 KB Output is correct
46 Correct 1300 ms 83012 KB Output is correct
47 Correct 1236 ms 81724 KB Output is correct
48 Correct 1326 ms 83080 KB Output is correct
49 Correct 599 ms 47804 KB Output is correct
50 Correct 991 ms 85472 KB Output is correct
51 Correct 1271 ms 84304 KB Output is correct
52 Correct 680 ms 54976 KB Output is correct
53 Correct 23 ms 5888 KB Output is correct
54 Correct 1109 ms 72540 KB Output is correct
55 Correct 1159 ms 83040 KB Output is correct
56 Correct 1217 ms 81420 KB Output is correct
57 Correct 818 ms 45640 KB Output is correct
58 Correct 914 ms 45816 KB Output is correct
59 Correct 889 ms 45860 KB Output is correct
60 Correct 837 ms 45664 KB Output is correct
61 Correct 736 ms 45812 KB Output is correct
62 Correct 615 ms 47096 KB Output is correct
63 Correct 86 ms 12532 KB Output is correct
64 Correct 696 ms 63228 KB Output is correct
65 Correct 693 ms 64724 KB Output is correct
66 Correct 687 ms 68604 KB Output is correct
67 Correct 715 ms 70956 KB Output is correct
68 Correct 681 ms 75876 KB Output is correct
69 Correct 1167 ms 82052 KB Output is correct
70 Correct 1104 ms 83052 KB Output is correct
71 Correct 1353 ms 82992 KB Output is correct
72 Correct 602 ms 47852 KB Output is correct
73 Correct 1217 ms 84432 KB Output is correct
74 Correct 573 ms 40776 KB Output is correct
75 Correct 586 ms 42408 KB Output is correct
76 Correct 683 ms 52032 KB Output is correct
77 Correct 681 ms 43840 KB Output is correct
78 Correct 662 ms 38444 KB Output is correct
79 Correct 265 ms 30848 KB Output is correct
80 Correct 303 ms 35176 KB Output is correct
81 Correct 786 ms 55908 KB Output is correct
82 Correct 547 ms 35364 KB Output is correct
83 Correct 310 ms 32032 KB Output is correct
84 Correct 85 ms 8812 KB Output is correct
85 Correct 1085 ms 72776 KB Output is correct
86 Correct 1306 ms 81988 KB Output is correct
87 Correct 103 ms 13940 KB Output is correct
88 Correct 116 ms 13940 KB Output is correct
89 Correct 98 ms 14064 KB Output is correct
90 Correct 25 ms 3764 KB Output is correct
91 Correct 2 ms 512 KB Output is correct
92 Correct 30 ms 3824 KB Output is correct
93 Correct 396 ms 34588 KB Output is correct
94 Correct 91 ms 12452 KB Output is correct
95 Correct 687 ms 65852 KB Output is correct
96 Correct 697 ms 65344 KB Output is correct
97 Correct 763 ms 69612 KB Output is correct
98 Correct 687 ms 70796 KB Output is correct
99 Correct 1517 ms 83952 KB Output is correct
100 Correct 1197 ms 83144 KB Output is correct
101 Correct 1311 ms 83456 KB Output is correct
102 Correct 578 ms 47804 KB Output is correct
103 Correct 617 ms 40596 KB Output is correct
104 Correct 547 ms 42116 KB Output is correct
105 Correct 635 ms 52212 KB Output is correct
106 Correct 674 ms 56516 KB Output is correct
107 Correct 683 ms 56984 KB Output is correct
108 Correct 65 ms 6840 KB Output is correct
109 Correct 976 ms 66328 KB Output is correct
110 Correct 906 ms 81760 KB Output is correct
111 Correct 895 ms 81220 KB Output is correct
112 Correct 627 ms 39676 KB Output is correct
113 Correct 620 ms 38944 KB Output is correct