QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#746278 | #7906. Almost Convex | mobbb | TL | 531ms | 3940kb | C++20 | 5.8kb | 2024-11-14 14:05:35 | 2024-11-14 14:05:35 |
Judging History
answer
#include <bits/stdc++.h>
#define ll long long
#define db ll
constexpr db EPS = 0;
int sign(db a){ return a < -EPS ? -1 : a > EPS; }
int cmp(db a,db b) {return sign(a - b);}
struct P {
db x,y;
P() {}
P(db _x,db _y) : x(_x),y(_y){}
P operator+(P p) {return {x + p.x,y + p.y};}
P operator-(P p) {return {x - p.x,y - p.y};}
P operator*(db d) {return {x * d,y * d};}
P operator/(db d) {return {x / d,y / d};}
bool operator < (P p) const{
int c = cmp(x,p.x);
if (c) return c == -1;
return cmp(y , p.y) == -1;
}
bool operator == (P o) const{
return cmp(x,o.x) == 0 && cmp(y,o.y) == 0;
}
db dot(P p){return x * p.x + y * p.y;}
// a * b == |a| * |b| * cos<a,b> ,大于0为锐角小于0为钝角等于0为直角
db det(P p){return {x * p.y - y * p.x};}
// a * b == |a| * |b| * sin<a,b> == - (b * a) ,a逆时针转多少度可以转到b
// 大于0 b在a的逆时针方向,等于0共线,小于0 b在a的顺时针方向
void read(){std::cin >> x >> y;}
void print(){std::cout << x << " " << y << "\n";}
db distTo(P p) {return (*this - p).abs();}
db alpha() {return atan2l(y,x);}
db abs() {return sqrtl(abs2());}
db abs2() {return x * x + y * y;}
P rot90() {return P(-y,x);} // 逆时针旋转90度
int quad(){return sign(y) == 1 || (sign(y) == 0 && sign(x) == 1);}
P unit() {return *this / abs();}
P rot(db an){return {x * cosl(an) - y * sinl(an),x * sinl(an) + y * cosl(an)};}
};
#define cross(p1,p2,p3) ((p2.x - p1.x) * (p3.y - p1.y) - (p2.y - p1.y) * (p3.x - p1.x))
#define crossOp(p1,p2,p3) sign(cross(p1,p2,p3)) // 以p1为起点去考虑<p1,p2> <p1,p3>
// 大于0 p3在p2的逆时针方向,小于0在顺时针,等于0共线
// 两个直线是否相交
bool chkLL(P p1,P p2,P q1,P q2){
db a1 = cross(q1,q2,p1),a2 = -cross(q1,q2,p2);
return sign(a1 + a2) != 0;
}
// 求两直线交点
P isLL(P p1,P p2,P q1,P q2){
db a1 = cross(q1,q2,p1),a2 = -cross(q1,q2,p2);
return (p1 * a2 + p2 * a1) / (a1 + a2);
}
// 判断区间 [l1,r1] ,[l2,r2] 是否相交
bool intersect(db l1,db r1,db l2,db r2){
if (l1 > r1) std::swap(l1,r1);if (l2 > r2) std::swap(l2,r2);
return !(cmp(r1,l2) == -1 || cmp(r2,l1) == -1);
}
// 两线段是否相交
bool isSS(P p1,P p2,P q1,P q2){
return intersect(p1.x,p2.x,q1.x,q2.x) && intersect(p1.y,p2.y,q1.y,q2.y) &&
crossOp(p1,p2,q1) * crossOp(p1,p2,q2) <= 0 && crossOp(q1,q2,p1) * crossOp(q1,q2,p2) <= 0;
}
// 两线段是否严格相交
bool isSS_strict(P p1,P p2,P q1,P q2){
return crossOp(p1,p2,q1) * crossOp(p1,p2,q2) < 0 && crossOp(q1,q2,p1) * crossOp(q1,q2,p2) < 0;
}
// m 在不在a和b之间
bool isMiddle(db a,db m,db b){
return sign(a - m) == 0 || sign(b - m) == 0 || (a < m != b < m);
}
// 点m 在不在a和b之间
bool isMiddle(P a,P m,P b){
return isMiddle(a.x,m.x,b.x) && isMiddle(a.y,m.y,b.y);
}
// 点q在线段上
bool onSeg(P p1,P p2, P q){
return crossOp(p1,p2,q) == 0 && isMiddle(p1,q,p2);
}
// 点q严格在线段上
bool onSeg_strict(P p1,P p2,P q){
return crossOp(p1,p2,q) == 0 && sign((q - p1).dot(p1 - p2)) * sign((q - p2).dot(p1 - p2));
}
// 求 q 到 p1p2的投影
P proj(P p1,P p2,P q){
P dir = p2 - p1;
return p1 + dir * (dir.dot(q - p1) / dir.abs2());
}
// 求 q以直线p1p2为轴的反射
P refect(P p1,P p2,P q){
return proj(p1,p2,q) * 2 - q;
}
// 求q到线段p1p2的最短距离
db nearest(P p1,P p2,P q){
if (p1 == p2) return p1.distTo(q);
P h = proj(p1,p2,q);
if (isMiddle(p1,h,p2)){
return q.distTo(h);
}
return std::min(p1.distTo(q),p2.distTo(q));
}
// 求线段p1p2 与线段q1q2的距离
db disSS(P p1,P p2,P q1,P q2){
if(isSS(p1,p2,q2,q2)) return 0;
return std::min({nearest(p1,p2,q1),nearest(p1,p2,q2),nearest(q1,q2,p1),nearest(q1,q2,p2)});
}
// 极角排序
// sort(p.begin(), p.end(), [&](P a, P b){
// int qa = a.quad(),qb = b.quad();
// if (qa != qb) return qa < qb;
// return sign(a.det(b)) > 0;
// })
std::vector<P> convexHull(std::vector<P> ps){ // need unique , <= strict , < strict
int n = ps.size();
if (n <= 1) return ps;
std::sort(ps.begin(), ps.end());
std::vector<P> qs(n * 2);
int k = 0;
for (int i = 0;i < n;qs[k++] = ps[i++]){
while (k > 1 && crossOp(qs[k - 2],qs[k - 1],ps[i]) <= 0){
k--;
}
}
for (int i = n - 2,t = k;i >= 0;qs[k++] = ps[i--]){
while (k > t && crossOp(qs[k - 2],qs[k - 1],ps[i]) <= 0){
k--;
}
}
qs.resize(k - 1);
return qs;
}
db area(std::vector<P> ps){
db ans = 0;
for (int i = 0;i < ps.size();i++){
ans += ps[i].det(ps[(i + 1) % (ps.size())]);
}
ans /= 2;
return ans;
}
bool check(std::vector<P> p){
int n = p.size();
bool ok = true;
double angle = 0;
for (int i = 0; i < n; i++){
P L = p[i] - p[(i - 1 + n) % n];
P R = p[(i + 1) % n] - p[i];
if (L.det(R) <= 0 || L == P(0, 0) || R == P(0, 0)){
ok = false;
}
}
return ok;
}
int main(){
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
int n;
std::cin >> n;
std::vector<P> p(n);
for (int i = 0; i < n; i++){
p[i].read();
}
auto Hull = convexHull(p);
std::map<P, int> cnt;
for (int i = 0; i < Hull.size(); i++){
cnt[Hull[i]] = 1;
}
assert(check(Hull));
std::vector<P> inside;
for (int i = 0; i < n; i++){
if (cnt.find(p[i]) == cnt.end()){
inside.push_back(p[i]);
}
}
auto select = inside;
int m = Hull.size(), k = inside.size();
int ans = 1;
for (int i = 0; i < m; i++){
P p1 = Hull[i], p2 = Hull[(i + 1) % m];
std::vector<P> cur(2 * k);
int begin = 0, end = -1;
for (int j = 0; j < k; j++){
P l = p1 - select[j], r = p2 - select[j];
bool ok = true;
for (int x = 0; x < k; x++){
P tmp = select[x] - select[j];
if (l.det(tmp) > 0 && r.det(tmp) < 0){
ok = false;
break;
}
}
if (ok){
ans++;
}
}
}
std::cout << ans << '\n';
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3612kb
input:
7 1 4 4 0 2 3 3 1 3 5 0 0 2 4
output:
9
result:
ok 1 number(s): "9"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3708kb
input:
5 4 0 0 0 2 1 3 3 3 1
output:
5
result:
ok 1 number(s): "5"
Test #3:
score: 0
Accepted
time: 0ms
memory: 3620kb
input:
3 0 0 3 0 0 3
output:
1
result:
ok 1 number(s): "1"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3640kb
input:
6 0 0 3 0 3 2 0 2 1 1 2 1
output:
7
result:
ok 1 number(s): "7"
Test #5:
score: 0
Accepted
time: 0ms
memory: 3632kb
input:
4 0 0 0 3 3 0 3 3
output:
1
result:
ok 1 number(s): "1"
Test #6:
score: 0
Accepted
time: 19ms
memory: 3880kb
input:
2000 86166 617851 383354 -277127 844986 386868 -577988 453392 -341125 -386775 -543914 -210860 -429613 606701 -343534 893727 841399 339305 446761 -327040 -218558 -907983 787284 361823 950395 287044 -351577 -843823 -198755 138512 -306560 -483261 -487474 -857400 885637 -240518 -297576 603522 -748283 33...
output:
718
result:
ok 1 number(s): "718"
Test #7:
score: 0
Accepted
time: 19ms
memory: 3664kb
input:
2000 571314 -128802 -57762 485216 -713276 485201 -385009 -844644 371507 403789 338703 -272265 -913641 438001 -792118 -481524 709494 213762 -913577 432978 -397111 709021 840950 328210 -843628 452653 -20721 126607 -107804 -338102 930109 -89787 -949115 -76479 -862141 455623 991761 94852 -635475 625573 ...
output:
658
result:
ok 1 number(s): "658"
Test #8:
score: 0
Accepted
time: 11ms
memory: 3688kb
input:
2000 -510540 -289561 -602648 -189950 -403224 944455 -369582 -41334 358122 -598933 -817147 470207 -440180 -735160 -705634 61719 319062 897001 -905089 -755682 -408371 -520115 -423336 548115 -590242 835990 208155 883477 -202087 142035 -71545 411206 570690 -673204 -228451 -903435 -732876 -570271 -246755...
output:
309
result:
ok 1 number(s): "309"
Test #9:
score: 0
Accepted
time: 8ms
memory: 3688kb
input:
2000 -532115 566389 138405 49337 398814 -97324 116833 113216 381728 877609 222402 641022 109920 952381 -113880 395181 13780 -572931 -676608 605202 -74328 -503839 -207767 926500 -663270 -146303 197877 280349 275865 -663892 -630214 3286 973786 304855 -493735 841584 394901 -505975 757960 204724 -373328...
output:
239
result:
ok 1 number(s): "239"
Test #10:
score: 0
Accepted
time: 15ms
memory: 3940kb
input:
2000 512636 509804 -661126 -592269 755566 -721837 -878213 441853 -236050 -89069 -181220 155656 203391 691764 940154 260513 747075 373881 620423 840991 -409624 335472 270937 -710659 -751290 -673585 250341 -193243 -250535 618887 -739996 543936 -547741 -213681 -82920 -364319 -611672 737719 930798 46731...
output:
1025
result:
ok 1 number(s): "1025"
Test #11:
score: 0
Accepted
time: 3ms
memory: 3696kb
input:
2000 943353 817289 237151 899722 682851 -464873 854225 205354 834550 257948 -260874 298196 -224572 -269157 -667301 881130 -45920 -696359 -634337 792620 -408527 -947513 582880 172669 921645 839423 833813 721080 -836662 -287230 -55783 -408594 108996 -122012 365647 -789544 313812 833502 970009 -737736 ...
output:
218
result:
ok 1 number(s): "218"
Test #12:
score: 0
Accepted
time: 1ms
memory: 3608kb
input:
2000 619248 227987 -252490 -553032 148050 -479727 -333707 -591482 -40488 -503144 561909 255624 -402541 -798967 -245811 -610006 -146584 -517935 226433 -92580 -81939 -828480 72540 -845547 502613 220323 66708 -573015 601886 258752 406443 257854 232970 -671600 -37023 -683767 602339 456757 -440096 -71899...
output:
7
result:
ok 1 number(s): "7"
Test #13:
score: 0
Accepted
time: 0ms
memory: 3876kb
input:
2000 -602451 2956 85982 141739 -185932 -208897 -716095 58215 -468047 155612 -791626 -3105 75700 -484098 609608 -304849 689485 -106857 533177 -285261 -659400 -241162 -369302 165482 406663 265940 -353843 -788313 805885 -75440 -571955 -60471 351360 -81373 -510926 -59456 591713 179588 534794 -118 201630...
output:
66
result:
ok 1 number(s): "66"
Test #14:
score: 0
Accepted
time: 2ms
memory: 3868kb
input:
2000 41203 -675424 -158994 366628 -133859 -595680 435466 687630 687811 -35017 314337 133049 -384711 444777 54850 -760922 526166 282618 572292 94793 -324003 621393 -30308 242225 612969 -231837 -56628 -892609 -492077 58749 29597 -349591 198510 219502 380955 -59845 839171 -40068 88185 -820614 -572977 -...
output:
43
result:
ok 1 number(s): "43"
Test #15:
score: 0
Accepted
time: 3ms
memory: 3636kb
input:
2000 -814040 46114 -324077 -522697 388552 -604274 -252898 43028 -757069 141507 413462 -649779 -281915 -316285 -498931 -573214 -408766 670792 -271435 -393170 87187 731739 89312 -853584 -768680 -307261 -185324 234729 -70493 -354866 16452 164338 -650791 -518077 851196 -259322 -85395 -509349 241593 5074...
output:
129
result:
ok 1 number(s): "129"
Test #16:
score: 0
Accepted
time: 12ms
memory: 3688kb
input:
2000 23103 -796677 -148322 67634 -525131 -446626 2672 584671 -712789 -69579 -91150 -429393 -375635 -487235 -680553 -370975 793181 -383683 -234131 -462420 -734705 -171834 322671 -355011 760005 224249 700248 -352775 416862 -125857 -497951 717254 677084 -451876 -220123 616240 525973 -144881 -300828 553...
output:
1466
result:
ok 1 number(s): "1466"
Test #17:
score: 0
Accepted
time: 35ms
memory: 3744kb
input:
2000 -185174 470373 -772343 -70370 -182314 851727 661615 -250979 -581175 527646 332025 141502 -659052 -506788 -378459 -553180 11233 162287 469975 -572356 679074 217029 -137967 727723 581696 140544 452574 -319370 120895 129820 772655 -330960 122860 823902 -786221 147543 -206152 -373647 -212943 4820 6...
output:
2801
result:
ok 1 number(s): "2801"
Test #18:
score: 0
Accepted
time: 155ms
memory: 3728kb
input:
2000 -718158 695879 655921 595312 -509080 -860718 540612 244159 -83221 -865654 -460513 -542465 102321 -775593 328552 799263 -284269 -725108 152140 549502 -108610 465054 -97837 -449762 -772869 -171472 293831 -711723 508617 -157976 170737 323070 544222 385453 -633043 -233165 -620164 -459706 507218 338...
output:
14445
result:
ok 1 number(s): "14445"
Test #19:
score: 0
Accepted
time: 531ms
memory: 3704kb
input:
2000 -587991 -165467 -530325 -5525 -574943 180654 -496535 -748102 -436469 -160646 110285 237070 -822862 -141480 -177189 327799 -424868 331309 -999274 38095 -745710 192605 -234174 -804258 586432 -176239 -626756 499109 -562606 826724 890245 455480 -32262 -298900 550800 516690 -588632 -368654 405331 -3...
output:
64358
result:
ok 1 number(s): "64358"
Test #20:
score: -100
Time Limit Exceeded
input:
2000 441575 -414673 651578 -449237 287355 -489950 606811 -30288 -733692 679481 -652568 89883 -360110 616801 190405 -368787 -352383 935855 118240 73038 -374899 -927065 -22183 -491455 -146229 638417 998825 -48442 -374469 243261 988830 149043 -778607 -291542 -277026 -167975 372912 -405043 535321 425727...