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ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#746719 | #7906. Almost Convex | mobbb | WA | 1ms | 3812kb | C++20 | 6.9kb | 2024-11-14 15:21:47 | 2024-11-14 15:21:50 |
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]);
}
}
inside = convexHull(inside);
int m = Hull.size(), k = inside.size();
// for (int i = 0; i < m; i++){
// Hull[i].print();
// }
int ans = 1;
// std::cout << k << '\n';
if (inside.empty()){
std::cout << ans << '\n';
return 0;
}
// for (auto x : inside){
// x.print();
// }
for (int i = 0; i < m; i++){
P p1 = Hull[i], p2 = Hull[(i + 1) % m];
std::vector<P> s(k);
int l = 0, r = -1, x = 0;
auto check1 = [=](P L, P R, P mid){
return (L.det(mid) > 0 && R.det(mid) < 0);
};
auto check2 = [=](P L, P R, P mid){
return (L.det(mid) < 0 && R.det(mid) <= 0);
};
for (int j = 0; j < k; j++){
x = std::max(x, j + 1);
x %= k;
while (check1(p1 - inside[j], p2 - inside[j], inside[x] - inside[j]) && r - l + 1 < k){
s[++r] = inside[x];
x = (x + 1) % k;
}
if (r - l + 1 == 0){
ans++;
}
while (l <= r && check2(inside[j] - p1, inside[(j + 1) % k] - p1, s[r] - p1)){
l++;
}
}
// std::cerr << ans << '\n';
}
std::cout << ans << '\n';
return 0;
}
详细
Test #1:
score: 100
Accepted
time: 0ms
memory: 3540kb
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: 3604kb
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: 3548kb
input:
3 0 0 3 0 0 3
output:
1
result:
ok 1 number(s): "1"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3812kb
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: 3456kb
input:
4 0 0 0 3 3 0 3 3
output:
1
result:
ok 1 number(s): "1"
Test #6:
score: -100
Wrong Answer
time: 1ms
memory: 3656kb
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:
1687
result:
wrong answer 1st numbers differ - expected: '718', found: '1687'