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#694046#9520. Concave Hullreal_sigma_team#AC ✓166ms14416kbC++233.0kb2024-10-31 17:09:462024-10-31 17:09:53

Judging History

你现在查看的是最新测评结果

  • [2024-10-31 17:09:53]
  • 评测
  • 测评结果:AC
  • 用时:166ms
  • 内存:14416kb
  • [2024-10-31 17:09:46]
  • 提交

answer

#include<bits/stdc++.h>

#define x first
#define y second

using namespace std;

using vec = std::pair<int64_t, int64_t>;

vec operator+(const vec& a, const vec& b) {
	return {a.x + b.x, a.y + b.y};
}

vec operator-(const vec& a, const vec& b) {
	return {a.x - b.x, a.y - b.y};
}

int64_t dot_prod(const vec& a, const vec& b) {
	return 1ll * a.x * b.x + 1ll * a.y * b.y;
}

int64_t cross_prod(const vec& a, const vec& b) {
	return 1ll * a.x * b.y - 1ll * a.y * b.x;
}

vector<vec> convex_hull(vector<vec> points) {
    vec p0 = points[0];
    for (vec p : points) {
        if (p.x < p0.x || (p.x == p0.x && p.y < p0.y)) {
            p0 = p;
        }
    }
    for (vec &x : points) {
        x.x -= p0.x;
        x.y -= p0.y;
    }
    sort(points.begin(), points.end(), [&](const vec& a, const vec& b){
        return cross_prod(a, b) > 0 || (cross_prod(a, b) == 0 && a.x * a.x + a.y * a.y < b.x * b.x + b.y * b.y);
    });
    vector<vec> hull;
    for (vec p : points) {
        while (hull.size() >= 2 && (cross_prod(p - hull.back(), hull[hull.size() - 2] - hull.back()) <= 0)) {
            hull.pop_back();
        }
        hull.push_back(p);
    }
    for (vec &x : hull) {
        x.x += p0.x;
        x.y += p0.y;
    }
    return hull;
}

void solve() {
	int n;
	cin >> n;
	vector<vec> a(n);
	for (int i = 0; i < n; i++) {
		cin >> a[i].x >> a[i].y;
	}
	int64_t ans = 0;
	vector<vec> hull1 = convex_hull(a);
	for (int i = 0; i < hull1.size(); i++) {
		int j = i + 1;
		if (j == hull1.size()) {
			j = 0;
		}
		ans += cross_prod(hull1[i], hull1[j]);
	}
	set<vec> st(a.begin(), a.end());
	for (auto i : hull1) {
		st.erase(i);
	}
	if (st.size() == 0) {
		cout << "-1\n";
		return;
	}
	vector<vec> hull2;
	if (st.size() < 3) {
		hull2 = vector<vec>(st.begin(), st.end());
	} else {
		hull2 = convex_hull(vector<vec>(st.begin(), st.end()));
	}
	// cout << ans << '\n';
	// cout << "hull1\n"; 
	// for (auto i : hull1) {
	// 	cout << i.x << ' ' << i.y << '\n';
	// }
	// cout << "hull2\n"; 
	// for (auto i : hull2) {
	// 	cout << i.x << ' ' << i.y << '\n';
	// }
	int64_t mn = 8e18;
	for (int i = 0; i < hull1.size(); ++i) {
		auto a = hull1[i];
		auto b = hull1[i == hull1.size() - 1 ? 0 : i + 1];
		auto get = [&](vec c) {
			return std::abs(cross_prod(a - b, c - b));
		};
		int pos = 0;
		for (int k = 20; k >= 0; --k) {
			int l = pos - (1 << k), r = pos + (1 << k);
			for (int j = l; j <= r; j += 1 << k) {
				if (j < 0) j = -(-j % hull2.size());
				int id = (j + hull2.size()) % hull2.size();
				// std::cout << i << ' ' << k << ' ' << j << ' ' << id << ' ' << hull2.size() << std::endl;
				if (get(hull2[id]) < get(hull2[pos])) pos = id;
			}
			// std::cout << i << ' ' << k << ' ' << pos << std::endl;
		}
		mn = std::min(mn, get(hull2[pos]));
	}
	std::cout << ans - mn << '\n';
}

int32_t main() {
	cin.tie(nullptr)->sync_with_stdio(false);
	int t = 1;
	cin >> t;
	while (t--) {
		solve();
	}
}

这程序好像有点Bug,我给组数据试试?

詳細信息

Test #1:

score: 100
Accepted
time: 0ms
memory: 3656kb

input:

2
6
-2 0
1 -2
5 2
0 4
1 2
3 1
4
0 0
1 0
0 1
1 1

output:

40
-1

result:

ok 2 lines

Test #2:

score: 0
Accepted
time: 1ms
memory: 3592kb

input:

10
243
-494423502 -591557038
-493438474 -648991734
-493289308 -656152126
-491185085 -661710614
-489063449 -666925265
-464265894 -709944049
-447472922 -737242534
-415977509 -773788538
-394263365 -797285016
-382728841 -807396819
-373481975 -814685302
-368242265 -818267002
-344482838 -833805545
-279398...

output:

2178418010787347715
1826413114144932145
1651687576234220014
1883871859778998985
2119126281997959892
894016174881844630
2271191316922158910
1998643358049669416
1740474221286618711
1168195646932543192

result:

ok 10 lines

Test #3:

score: 0
Accepted
time: 57ms
memory: 3764kb

input:

1000
125
64661186 -13143076
302828013 -185438065
-418713797 -191594241
430218126 -397441626
354327250 -836704374
149668812 -598584998
311305970 66790541
199720625 -592356787
468137 -584752683
258775829 96211747
-358669612 -134890109
-129221188 -998432368
-277309896 -140056561
356901185 420557649
-51...

output:

1986320445246155278
1900093336073022078
1612088392301142476
2012259136539173407
1819942017252118749
1772230185841892196
1164835025329039520
1527446155241140517
1807368432185303666
1236918659444944569
1306839249967484778
1984123720246784099
1868728080720036006
667458140583450322
2127932992585026491
4...

result:

ok 1000 lines

Test #4:

score: 0
Accepted
time: 86ms
memory: 3520kb

input:

10000
9
484630042 51929469
-40468396 -517784096
98214104 -103353239
629244333 -475172587
106398764 153884485
49211709 -44865749
1 10
166321833 -247717657
406208245 668933360
13
548702216 -631976459
37150086 -292461024
707804811 -486185860
239775286 -903166050
10096571 -541890068
686103484 558731937
...

output:

950319193795831919
1661025342421008544
1285164852091455548
1159924751776806668
1206071151805176722
794021230296144371
699991678992587791
1133990718508584290
1486311831172661605
984875884297072200
1327767982175057345
758247019006396699
1355381234262206155
1139262078529131471
1613462877860621700
12392...

result:

ok 10000 lines

Test #5:

score: 0
Accepted
time: 114ms
memory: 4376kb

input:

100
439
471536154 -312612104
155692036 -937312180
-461624056 -357636609
236656684 -911414873
-288656914 -74788431
-465779694 -381475149
-334197401 -903065737
491513067 -447615916
337664889 -852236281
-281689379 -53519178
-159101704 -920779200
-326159514 -95396204
21868593 -994282736
488425383 -41046...

output:

1973162724053130487
2054612790507830954
1726805687754843724
1699420177872986528
2129388571309147631
2198295137903288810
1697185883164440272
1219697450095721478
2027023581922285255
1674691247127206655
1673105966817209954
2179188692918747442
2146544318743443141
2230356305133660648
1676850321902993764
...

result:

ok 100 lines

Test #6:

score: 0
Accepted
time: 96ms
memory: 4212kb

input:

100
1362
-467257672 -466669
-467054869 -478108
-466973270 -481776
-466556983 -499770
-466329414 -508693
-466248017 -511805
-466158865 -513786
-466101273 -515035
-465927700 -518748
-465717624 -522106
-465303448 -528127
-465124548 -530726
-464649746 -536693
-464554872 -537799
-464478196 -538680
-46416...

output:

1666097696993497
1791366071767866
1806187278469532
1683419854733713
1685891971828916
1730190225081651
1787048201197565
1850308098208660
1710694884375502
1826363113637639
1816375352374659
2047431269497691
1549806516003854
1829438662895747
1678707854135065
1687423392883819
2121960009997761
16687219538...

result:

ok 100 lines

Test #7:

score: 0
Accepted
time: 58ms
memory: 8692kb

input:

2
62666
-486101704 -505730259
-486101698 -506082699
-486101689 -506111362
-486101682 -506126031
-486101528 -506293759
-486101259 -506556385
-486101196 -506613483
-486101154 -506648604
-486100935 -506831392
-486100631 -507083675
-486100470 -507199151
-486100233 -507368923
-486100193 -507397039
-48609...

output:

2178736946152219010
1825181940245096152

result:

ok 2 lines

Test #8:

score: 0
Accepted
time: 158ms
memory: 14312kb

input:

2
100000
301945097 76373292
467957663 -286424714
8245445 -597212507
-474204621 -708828667
184159460 105942538
443435905 -429212625
490658771 -382198656
82512047 -612522436
-228221388 -965890088
394789011 -145801151
-106120174 -528202395
428939626 -194437311
497429477 -527407728
365739746 -114818962
...

output:

2502889432701099511
2267250485735988121

result:

ok 2 lines

Test #9:

score: 0
Accepted
time: 166ms
memory: 14416kb

input:

2
100000
221128057 -975244780
-618765360 -785575858
422567455 -906331476
-988680318 -150037424
-929870145 367887908
-757813541 -652471177
291995621 -956419655
-785381507 619012026
468864522 -883270094
-588416522 808557973
859345881 511394814
988105866 153775152
216931298 -976186873
467050734 8842305...

output:

6283183114882825575
6283183188903854361

result:

ok 2 lines

Test #10:

score: 0
Accepted
time: 0ms
memory: 3864kb

input:

7
5
-1000000000 -1000000000
1000000000 -1000000000
1000000000 1000000000
1 0
-1 0
5
1000000000 1000000000
-1000000000 -1000000000
-2 0
-1 0
1 -1
6
1000000000 1000000000
-1000000000 -1000000000
-3 0
-1 0
0 -1
1 -1
4
-1000000000 -1000000000
1000000000 -1000000000
1000000000 1000000000
-1000000000 1000...

output:

4000000000000000000
7000000000
9000000001
-1
6000000002000000000
7999999998000000000
-1

result:

ok 7 lines

Extra Test:

score: 0
Extra Test Passed